Estimation of self-sustained activity produced by persistent inward currents using firing rate profiles of multiple motor units in humans

Abstract

Persistent inward calcium and sodium currents (I_P) activated during motoneuron recruitment help synaptic inputs maintain self-sustained firing until derecruitment. Here, we estimate the contribution of the I_P to self-sustained firing in human motoneurons of varying recruitment threshold by measuring the difference in synaptic input needed to maintain minimal firing once the I_P is fully activated compared with the larger synaptic input required to initiate firing before full I_P activation. Synaptic input to ≈20 dorsiflexor motoneurons simultaneously recorded during ramp contractions was estimated from firing profiles of motor units decomposed from high-density surface electromyography (EMG). To avoid errors introduced when using high-threshold units firing in their nonlinear range, we developed methods where the lowest threshold units firing linearly with force were used to construct a composite (control) unit firing rate profile to estimate synaptic input to higher threshold (test) units. The difference in the composite firing rate (synaptic input) at the time of test unit recruitment and derecruitment (ΔF = F_recruit − F_derecruit) was used to measure I_P amplitude that sustained firing. Test units with recruitment thresholds 1–30% of maximum had similar ΔF values, which likely included both slow and fast motor units activated by small and large motoneurons, respectively. This suggests that the portion of the I_P that sustains firing is similar across a wide range of motoneuron sizes.

NEW & NOTEWORTHY A new method of estimating synaptic drive to multiple, simultaneously recorded motor units provides evidence that the portion of the depolarizing drive from persistent inward currents that contributes to self-sustained firing is similar across motoneurons of different sizes.

INTRODUCTION

Low-voltage-activated persistent inward currents (I_P) flowing through Ca_V1.2/1.3_s and Na_V1.2/1.6 ion channels amplify and prolong the firing behavior of motoneurons in response to synaptic inputs, slowly activating over a relatively wide voltage range (≈10 mV) near the firing threshold (Binder et al. 2020; Carlin et al. 2000; Hounsgaard et al. 1988; Johnson et al. 2017; Li et al. 2004). The functional contribution of I_P and the depolarization, or plateau potential, it produces can be observed from the discharge behavior of motoneurons in response to an increasing and decreasing synaptic current produced, for example, by slow triangular force contractions or graded sensory stimulation in both humans (Gorassini et al. 1998, 2002a; Kiehn and Eken 1997) and animals (Bennett et al. 1998b; 2001a; Gorassini et al. 1999; Hounsgaard et al. 1988). The firing rate profiles of pairs of motor units during such contractions have been used to measure the potential contribution of I_P to self-sustained firing in human motoneurons (Gorassini et al. 2002a), although, as we detail below, this approach has limitations, including only allowing for the quantification of the I_P activated during firing, and not subthreshold to firing, inherently leading to an underestimation of the overall I_P in some motoneurons.

To understand these limitations and develop improved methods of I_P estimation, we start by outlining the basis for estimating the contribution of I_P to self-sustained firing from the firing profiles of motoneurons previously developed from animal studies. When a cat motoneuron is activated with synaptic inputs during a slow muscle stretch, the activation of the I_P always begins below the firing threshold of the motoneuron (Fig. 1Aiv, green trace) (Bennett et al. 1998b). In this example, the contribution of the I_P is inferred from the membrane (plateau) potential revealed when spikes are blocked. The activation of the I_P continues over a wide voltage range up to or sometimes after firing is initiated, producing an acceleration of the membrane depolarization just before firing (Fig. 1Aiv, green arrow). This accelerated depolarization can produce a high firing rate at recruitment and sometimes a steep acceleration at the onset of firing (Fig. 1A, ii and iii) (Bennett et al. 2001b; Hounsgaard et al. 1988; Lee et al. 2003; Li et al. 2004). Importantly, after the termination of the synaptic current that triggers the I_P (Fig. 1Av, dashed line), the extra depolarization from the I_P produces continued firing (self-sustained firing; Fig. 1A, ii and iii), a phenomenon that has been used extensively as an estimate of I_P in humans (Gorassini et al. 1998; Kiehn and Eken 1997). However, this self-sustained firing is only produced by the portion of the I_P that is activated after the firing onset (after the red and purple dashed lines in Fig. 1Aiv), making it generally an underestimation of the I_P. In the extreme case when the I_P and plateau potential are fully activated by the synaptic input before the onset of firing (Fig. 1Ai, pink), or when the I_P and firing are fully activated before the stretch-evoked synaptic input (Fig. 1Avii, blue), the I_P cannot further boost or prolong firing, with the firing rate profile proportional to the synaptic input profile (no self-sustained firing). Likewise, when there is a residual I_P activated by a prior activation of the motoneuron, the I_P does not further activate and the firing rate only increases gradually in proportion to the gradual increase in synaptic input with no self-sustained firing (Fig. 1Avi, black). Thus the largest self-sustained firing seems to occur when the I_P and firing onsets are simultaneous, allowing maximal facilitation of firing by the I_P (Fig. 1Aiii, red).

Fig. 1.

Synaptic and intracellular persistent inward calcium and sodium current (I_P) activation and self-sustained firing. A: synaptic activation of cat soleus motoneuron by sinusoidal muscle stretch. Ai–Aiii: firing response of the motoneuron to muscle stretch (synaptic input) when spiking was slightly impeded (−1 nA; Ai), not altered (0 nA; Aii), or aided (+1 nA; Aiii) with steady somatic current injection that does not much alter the distal dendritic I_P, as detailed and modified from Bennett et al. (1998b). Self-sustained firing (pink shading) increased as more of the I_P was activated above the firing threshold (Aiii). Aiv: membrane potential response to stretch during hyperpolarization to estimate the synaptic input (gray trace) and membrane potential at rest to estimate the contribution of the I_P (green trace), which here is a plateau potential because spikes are blocked with QX-314 (different cell from in Ai–Aiii, smoothed). Av: membrane potential response to stretch during hyperpolarization to estimate the synaptic input in the same cell as in Ai–Aiii (black trace) and with trace from iv overlaid (gray). Avi: firing response of motoneuron where I_P is activated before recruitment due to prior activation (warm-up). Avii: firing response of tonically firing motoneuron with tonic I_P activation. Firing response is proportional to synaptic stretch input profile (gray trace). Dashed vertical line in Aiv–Avi marks the end of synaptic stretch input. Bi, top trace: membrane potential (V_m) of low-threshold motoneuron during spiking in response to triangular injected current (black trace). I_P activation is marked by small acceleration in potential just before onset of firing. Bottom trace, firing duration marked by purple box where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). Firing starts after majority of I_P (green trace with depolarizing inward current depicted in downward direction) is activated, producing a small ΔI (length of black arrow). Bii and Biii: likely firing responses of 2 other hypothetical motoneurons (same as in Bi) but with more of the I_P activated during firing (spike threshold lower relative to I_P onset) to produce a larger ΔI. Biv: voltage-clamp command (black trace) and resulting I_P without (green trace) and with (gray trace) sag in I_P, estimated for motoneuron in Bi. [Modified from Li et al. (2004)]. Dashed line indicates turnaround point of current and start of I_P sag. Bv: firing-current response to triangular current injection displaying primary (black), secondary (pink; during I_P activation), and tertiary (green; after I_P activation) firing ranges. [Modified from Li et al. (2004).]

It is also possible to measure self-sustained firing produced by I_P from a symmetrical, triangular current injection into the motoneuron. When the I_P is activated by current injection into the soma of a motoneuron, there are three classically defined linear regions of the firing rate response: first, if the I_P is not initially activated at all, there is sometimes a gradual increase in firing with current (primary range; Fig. 1Bv, black line) (Heckman et al. 2005; Li et al. 2004). However, this primary range is uncommon and now considered an artifact of injecting current into the soma near the sodium channels underlying the spike and far from the dendritic locations where most I_P and synaptic inputs occur (Bennett et al. 1998b; Lee and Heckman 2000). Thus current injection into the soma favors spiking over I_P activation, whereas natural synaptic input does the opposite, activating the nearby I_P first before spikes as detailed above. Second, as the membrane potential (V_m) is depolarized further, the firing rate abruptly increases more steeply as the I_P is being activated (secondary range; Fig. 1Bv, pink line); this is how many motoneurons start firing with current injection, at least briefly in the secondary range (Li et al. 2004). Finally, after the I_P is steadily activated the firing rate increases more slowly due to an increased conductance provided by the I_P and associated calcium activated K⁺ currents (tertiary region; Fig. 1Bv, green line) (Li and Bennett 2007). Some motoneurons start firing directly in the tertiary range (Fig. 1Bi) (Li et al. 2007). Using this terminology for responses to natural synaptic activation of firing detailed above, firing is initiated either in the secondary range (Fig. 1A, ii and iii) or directly in the tertiary range (Fig. 1A, i and vi) because the I_P is always activated subthreshold to firing (Bennett et al. 2001a; Gorassini et al. 1999; Kiehn and Eken 1997; Li et al. 2004), and primary range firing likely never occurs (Bennett et al. 1998b).

The self-sustained firing can be quantified systematically during these slow triangular somatic current injections, as follows: after an increasing current ramp activates an I_P and the cell is firing in its secondary or tertiary range, the current can be decreased with a similar slow, but descending current ramp, to ascertain how much the I_P contributes to sustain firing (Bennett et al. 2001a; Li et al. 2004). Usually, the firing rate continues in the tertiary range until near derecruitment and then sometimes drops steeply as the I_P is terminated and firing stops (Fig. 1Bv, downward pink arrow to denote secondary range at derecruitment). Importantly, this firing on the descending current ramp continues at injected current levels below the current needed to initiate firing (compare blue dots in Fig. 1B, i–iii) and only stops when the injected current is below the onset current by a value of ΔI that reflects the contribution of the I_P to self-sustained firing (height of boxes in Fig. 1B, i–iii). Again, only the portion of the I_P activated after the onset of firing contributes to self-sustained firing (ΔI; tip of the I_P iceberg so to speak). Thus motoneurons having firing thresholds that are closer to the I_P onset voltage yield the largest ΔI values (Fig. 1Biii, red) for a given fixed I_P size. Theoretically, if the I_P is fully activated entirely subthreshold to firing, the motoneuron begins to fire directly on its tertiary range and responds proportionally to the injected current, starting and stopping firing at the same level of injected current to yield no self-sustained firing (ΔI = 0). In this case, the contribution of the I_P to the activation of the motoneuron cannot be reflected in its discharge behavior because the effects on the membrane potential are all subthreshold to firing.

Sometimes the I_P slowly decreases with time (sags) during these slow triangular current ramps, and this can lead to a downward offset in firing rate and less self-sustained firing (Fig. 1Biv, gray line above green noninactivating I_P). This sag could have a number of causes, including calcium and sodium I_P inactivation (Lee and Heckman 1999; Powers and Heckman 2017) or buildup of calcium-activated potassium (SK) currents (Li and Bennett 2007). The downward offset in firing rate can also be mediated by a rate (direction)-dependent effect of the depolarizing drive on spiking (Kuo et al. 2006; Norton et al. 2008). Faster current ramps should avoid this minor nonlinearity (Revill and Fuglevand 2011), a topic we address later in this article.

When the I_P is fully activated (in the tertiary range), motoneurons often respond remarkably linearly to both increasing injected current or synaptic current, with the firing rate profile (Fig. 1A, vi and vii) accurately reflecting the synaptic input profile Fig. 1Av, gray line) (Bennett et al. 1998b; Lee et al. 2003). Using this linearity, we previously developed a method of estimating the synaptic input to a motoneuron pool from the firing (F) of a continuously firing low-threshold motor unit (control unit), assumed to be in its linear tertiary range (Bennett et al. 2001a; Gorassini et al. 1998; 2002a). This estimate of the synaptic input (F) was then used to compute the degree of self-sustained firing of higher threshold motor units (test units), exactly as we have described for current injection (ΔI calculation), but in this case having participants make triangular force contractions, rather than current injection, to produce a triangular synaptic input profile. Here we measure the difference in the synaptic input needed to terminate firing of the test unit (control unit firing, F_T) compared with the synaptic input needed to recruit firing (control unit firing, F_R), ΔF = F_R − F_T, as a measure of the self-sustained firing produced by the I_P, but otherwise all the issues discussed above for ΔI remain the same. This method has been verified by measuring ΔF in low-threshold motor units in awake rats and then measuring ΔI and the F-I slope (S) with direct intracellular recordings from motoneurons in these same rats, yielding ΔF = S × ΔI (Bennett et al. 2001a). The ΔF and ΔI method has also been validated with computer simulations (Elbasiouny et al. 2006; Powers and Heckman 2015; Powers et al. 2008; Revill and Fuglevand 2011). Subsequently, the paired-unit method has been extensively used in humans, but mostly restricted to low-threshold motor units where we know the linearity assumption for the control unit firing holds (reviewed in Binder et al. 2020; D’Amico et al. 2013; Heckmann et al. 2005, 2008; Johnson et al. 2017). Importantly, this motor unit activity to estimate ΔF has mainly been obtained from intramuscular electromyography (EMG), where it is only possible to identify a few low-threshold test motor units during moderately strong contractions [~10% maximum voluntary contraction (MVC) or less]. Thus we know little about I_P activation in higher threshold test units, a topic we address in this article.

With the advent of new high-density surface EMG arrays and advances in motor unit identification algorithms, we now have the ability to noninvasively identify 20 or more motor units per muscle, such as the tibialis anterior (TA), over a wide range of recruitment thresholds, potentially up to 100% MVC (Del Vecchio 2020; Holobar and Farina 2014; Martinez-Valdes et al. 2016; Negro et al. 2016a). This provides the opportunity to estimate self-sustained firing from many more motoneurons and examine how this differs with motoneuron size. However, it also presents a serious computational problem when estimating ΔF, since there are typically over 20 possible control units to choose from that can each be paired with all other higher threshold test motor units to compute ΔF (Hassan et al. 2020). So, for a given test motor unit, which is the best control unit to pair it with, or should all possible pairings be admitted? Firing rate profiles of motor units during triangular force contractions can have varying degrees of linearity, with some motor units exhibiting very symmetrical linear firing rate profiles suggestive of tertiary range firing (as in Fig. 1A, i, vi, and vii), whereas other motor units exhibit an initial sharp increase in firing rates indicative of secondary range firing with I_P activation during recruitment (as in Fig. 1A, ii and iii) (Bennett et al. 2001a; Binder et al. 2020; Gorassini et al. 1999), likely making them poor control units.

In this study, we developed methods to determine how to best represent the synaptic input profile from several control motor units that likely have the best linear input-output firing behavior (i.e., tertiary range firing), an important requisite for the accuracy of ΔF measures in representing self-sustained firing produced by I_P. The firing properties of simultaneously recorded tibialis anterior (TA) motor units that were activated during a triangular 10-s up and 10-s down isometric contraction were characterized. Voluntary contractions were performed at 10%, 20%, and 30% of maximum (MVC) where ≈70% of all motor units are estimated to be recruited at 30% MVC (Feiereisen et al. 1997). This produced contractions with different speeds over the same time period (i.e., 1%, 2%, and 3% MVC per second), allowing us to also examine the effect of contraction speed on I_P. Firing properties of the TA motor units (motoneurons) during various phases of the contraction and estimates of the contribution of the I_P to self-sustained firing (ΔF values) were compared between motor units of different recruitment thresholds, ultimately allowing us to examine our central questions of how the I_P varies in different sized motoneurons and how suprathreshold I_P activation affects firing in motor units of different sizes.

Finally, one noted constraint in using the firing rate of a control motor unit to represent the synaptic drive to a test unit is the extent to which its firing rate varies with synaptic input (i.e., firing rate modulation). In both animals and humans, ΔF values measured in test units can be positively correlated to the amount of firing rate modulation in the control motor unit, raising the issue that the amplitude of the ΔF is constrained by how much the firing rate of the control motor unit can change in response to a changing synaptic input (Powers et al. 2008; Stephenson and Maluf 2011). A possible source of reduced firing rate modulation in a control unit is rate saturation where increases in synaptic current are not as efficiently transduced into a proportional increase in the rate of action potential generation (Fuglevand et al. 2015; Revill and Fuglevand 2011, 2017). Here, we examined if similar issues with rate saturation and rate modulation constrained our measures of ΔF values at the different contraction strengths when using motor units decomposed from high-density surface EMG. Last, we measured the proportion of time a motor unit was firing in its I_P-mediated, self-sustained firing range and how this may change with recruitment threshold of the motor unit.

METHODS

Experiments were approved by the Health Research Ethics Board of the University of Alberta (Protocols 00023530 and 00076790) and conformed to the Declaration of Helsinki. Ten neurologically intact participants (6 women, 4 men) aged 21–58 yr took part in this study. All participants gave written informed consent before participation.

EMG Recordings

Flexible, high-density surface EMG (HDsEMG) electrodes (GR08MM1305; OT Bioelettronica, Inc., Turin, Italy) were used to record from 64 sites on the tibialis anterior (TA) and soleus muscles of the dominant leg. The recording sites were arranged in a 5 × 13 grid with 8-mm interelectrode distance in both the x and y directions. The 5 columns of electrodes were orientated in the x direction from lateral to medial, and the 13 rows of electrodes were orientated in the y direction from proximal to distal. To maximize the signal-to-noise ratio, the skin was rubbed lightly with abrasive paste (NuPrep; Weaver and Company, CO), and any remaining residue was removed with saline (Hermens et al. 2000) to reduce impedance between the electrode and skin (Merletti and Farina 2016). Electrodes were placed over the entire TA and soleus muscle bellies whose boundaries were visualized from a voluntary contraction. The electrodes were secured to the skin using flexible tape (3M Transpore clear plastic tape; London, Canada). All 64 EMG signals were recorded in a monopolar configuration, where the EMG potential recorded from one grid electrode was referenced to a strap electrode placed around the lower leg near the ipsilateral ankle or knee joint. A Quattrocento system (OT Bioelettronica, Inc., Turin, Italy) was used to amplify the HDsEMG signals (150 times) with filtering set to 10-Hz high pass and 900-Hz low pass, sampled at 5,120 Hz, digitally converted (16-bit resolution), and then transferred to a personal computer. The duration of each file was kept below 200 s to be manageable for postprocessing. Only data obtained from the TA muscle are reported here. The TA muscle was chosen because HDsEMG from the TA typically produces a larger number of decomposed motor units for contractions of 10 to 30% MVC (Del Vecchio 2020).

Experimental Task

Participants were seated comfortably with their foot resting on a custom three-dimensionally (3-D) printed holder coupled to a 150-lb S-type load cell (Interface Force Measurement Solutions, AZ) and with the knee and ankle angle at ~120° of extension and plantarflexion, respectively. A visual display of the exerted dorsiflexion torque was presented on a computer screen, and participants were instructed to track a triangular line drawn on a transparency overlaid on the display. The horizontal (y) scale of the computer display was adjusted to modify the strength of the contraction expressed as a percentage of the participant’s maximum voluntary contraction (%MVC), obtained by averaging the maximum torque produced from two maximal contractions. At least 6–10 contractions were measured at 10%, 20%, and 30% of MVC over two to three trials. The six trials with the smoothest and most symmetrical torque profiles were chosen for analysis (see example good trial in Fig. 2). Within a trial, each contraction was separated by at least 20 s to avoid frequency-dependent facilitation of the motor units (Gorassini et al. 2002b; Hornby et al. 2003). Contraction duration was set to 10 s for both the ascending and descending phase of the triangular contraction, producing rates of contraction/relaxation of 1%, 2%, and 3% MVC/s for the 10%, 20%, and 30% MVC contractions, respectively.

Fig. 2.

Parameters measured from the motor unit firing rate profile. A, top trace: torque profile for a 20% maximum voluntary contraction (MVC) showing recruitment threshold of the motor unit. Second trace, corrected firing rate profile (blue dots) of decomposed motor unit (see below for details) and straight line fit to the secondary (pink) and tertiary (green) firing range. Time of peak firing rate is marked by vertical dashed line and denotes start of lower offset (sag) in firing rate during the descending phase of the contraction. Third trace, uncorrected firing rate profile. The 5th-order polynomial line fit to the firing rate profile is marked with a green line where the coefficient of determination (R²) of the fit was measured. Straight-line fit to the data points on the entire ascending and descending portion of the polynomial line is marked with a dashed pink line from which the ascending (Asc) and descending (Dsc) slope values were measured, respectively. Black downward arrows mark the start and end firing rates measured from the polynomial line. Modulation depth (MoD) is the maximum rate minus the minimum rate measured from the polynomial line. Bottom trace, the train of pulse amplitudes (blue lines) from the decomposition algorithm (marking firing times of the decomposed motor unit) with an accuracy (silouette, SIL) value of 0.94. Red circles mark pulses selected by the blind source algorithm, and black circles mark pulses that were not selected, producing abnormally low firing rate values marked by small black arrows in the firing rate profile of the third trace. Dashed blue arrows point to the reestimated pulses (dotted red circles) following recomputation of the pulse train to include the missed pulses. The resulting corrected firing rate profile after the recalculation/reestimation is plotted in the second trace. Data are from participant 4M. B–D: average number of motor units decomposed from high-density surface electromyography (HDsEMG) per contraction (B), accuracy (silhouette) values (C), and coefficient of determination (R²) of the polynomial line fit to frequency profile (D). Values are averages of the mean values from each of the 7 participants at the 10%, 20%, and 30% MVC trials. Error whiskers are +1 SD. Individual data in Supplemental Table S1.

Data Analysis

Single motor unit identification.

Once the data were recorded and stored on a local computer, the files were then converted into a Matlab file format. MATLAB ver. R2018b/R2019a and custom-built functions were used for data processing and analysis. Before the decomposition process, the sEMG data were divided so that only one contraction was included in a single data file to decrease computation time. Further preprocessing included offset removal, bandpass filtering (4th-order, Butterworth, zero lag, digital filter, 10–500 Hz), and power line interference attenuation using a notch filter. We performed visual inspection of all HDsEMG signals to identify bad channels displaying substantial noise or artifacts. If there were more than six bad channels (≈10% of the 64 channels in the grid), the data were not used.

The remainder of the HDsEMG signals were decomposed into motor unit spike trains (referred to as pulse trains) using the validated decomposition method of convoluted blind source separation (Martinez-Valdes et al. 2017; Negro et al. 2016a). The threshold for the value used to assess the reliability of the estimated discharge timings, or the silhouette value (SIL) (Holobar et al. 2014), was set to 0.85 (Negro et al. 2016a). For a given motor unit that was isolated from the other units, the decomposition algorithm estimated the time of firing for that unit (termed pulse, Fig. 2A, bottom trace) and the inverse of the interval between pulses was displayed as instantaneous firing rate (Fig. 2A, third trace). The amplitude of the pulse was interpreted as the confidence (accuracy) of the algorithm to assign the motor unit to that instant of time relative to nearby pulses buried inside the noise within the pulse train. Thus the amplitude of the pulse is in arbitrary units (a.u.) and can be interpreted as an indication of the pulse-to-noise ratio. However, some of the pulse amplitudes were slightly above the noise level (e.g., above 4–6 a.u. in Fig. 2A, bottom trace) but below the level of nearby pulses that were selected by the k-means clustering used in the algorithm (selected pulses marked by red circles, missed pulses marked with black circles). Because these missed pulses produced firing rates that were half of the mean rate (small black arrows in Fig. 2A, third trace) and likely not physiological, we manually and iteratively included them and reestimated the pulse train (dashed blue arrows in Fig. 2A, bottom trace, point to the reestimated pulse marked by the dotted red circles) to correct the frequency profile (Fig. 2A, second trace) (as per Boccia et al. 2019; Del Vecchio 2020; Hassan et al. 2020; Martinez-Valdes et al. 2020). In other cases (not shown), the algorithm incorrectly assigned two or three pulses to what was likely only a single pulse (i.e., a single discharge time), resulting in instantaneous firing rate(s) that were well above the mean rate. Here, the extraneous pulse(s) were also manually removed and the final pulse trains were reestimated. The majority of estimated pulse trains (≈90%) required manual editing, and once the decomposition accuracy was recalculated after the edit, the accuracy (silhouette) value either increased or only decreased slightly by <0.01.

Data from three subjects were excluded from further analysis because the average number of decomposed motor units per contraction was <7. The excluded participants were 8F (woman aged 42 yr: 6.5 ± 1.5 units, range 3–8, median 7 units), 9F (woman aged 26 yr: 5.5 ± 1.2 units, range 3–7, median 5 units), and 10F (woman aged 21 yr: 1.9 ± 1.8 units, range 0–6, median 1 unit). In these participants there were not enough low-threshold control motor units to obtain ΔF measures for the required six contractions.

Parameters measured from the raw firing frequency profile: Number of units, accuracy and threshold.

The number of units isolated per contraction and the accuracy value of the decomposition for each unit (SIL) were measured and averaged across the six trials for each of the 10%, 20%, and 30% MVC contraction levels (Fig. 2, B and C; values for each participant are listed in Supplemental Table S1 (all Supplemental material is available at https://doi.org/10.6084/m9.figshare.12067344). As with all measurements, the mean value for each of the seven participants was averaged across the group and, along with the SD values, presented in the Supplemental Tables and in the figures. To establish the recruitment order of the multiple decomposed motor units in a given contraction, the level of torque when a motor unit was recruited was measured (Fig. 2A, top trace) and expressed as a % of MVC.

Parameters measured from the polynomial line fit to the firing frequency profile.

The firing frequency profiles for the decomposed motor units were estimated by fitting a fifth-order polynomial line to the instantaneous firing frequency values (green line in Fig. 2A, third trace). The coefficient of determination (R²) of the fit line was averaged for all units at each contraction strength in each participant, and this mean was then averaged across all participants (R² polynomial, Fig. 2D). The start, maximum, and end firing rates were measured from the polynomial line for all units in addition to the firing rate of the control motor units during recruitment and derecruitment of the test motor units. To determine the maximum change in firing rate of a control unit during the contraction, the difference between the maximum and minimum firing frequency from the polynomial line, termed the modulation depth (MoD) was measured (Fig. 2A, third trace).

Although the polynomial line provided a relatively accurate measure of the control unit firing rate when the test unit was recruited and derecruited, the peak of the polynomial line was shifted slightly to the left of the peak torque as demonstrated when fitting a straight line to the secondary (pink) and tertiary (green) firing range (Fig. 2A, second trace). Note that the firing rate during the ascending tertiary range increases until peak torque. As the torque began to decrease during the descending phase of the contraction, the firing rate dropped to a lower offset (sag) and continued to decrease at a similar rate (slope) as on the ascending phase (see also Bennett et al. 2001a; Gorassini et al. 1999; Powers and Heckman 2017). This is in contrast to the profile of the fit polynomial line (green; Fig. 2A, third trace), where the peak occurs ≈1.5 s earlier. Upon visual inspection, most firing rate profiles peaked at maximum torque and then began to sag at the onset of the torque decline during the descending phase of the contraction. Thus we used the peak of contraction torque, rather than the peak of the polynomial line, to indicate the transition point from an ascending to a descending synaptic input, which was important for the measurement of self-sustained firing duration described below. Last, to obtain an overall value of the rate of increase or decrease in firing rate of a motor unit, the slope of the straight line fit to the ascending or descending phase of the polynomial line (Asc and Dsc slope, marked by pink dashed line in Fig. 2A, third trace) was measured. For each contraction level, all measures were averaged across the six trials in each participant with the means ± SD presented in Supplemental Table S1 along with the average of these means (total) across the seven participants.

ΔF measurement.

Estimation of the I_P contributing to self-sustained firing was estimated from pairs of motor units as described previously where the lower threshold “control” motor unit of the pair was used as an estimate of synaptic input to a higher threshold “test” motor unit of the pair (Gorassini et al. 2002a). The firing rate of the control motor unit (values taken from the fit polynomial line) when the test motor unit was derecruited was subtracted from the control unit rate when the test motor unit was recruited to obtain a ΔF value. All possible combinations of relatively lower and higher threshold motor unit pairs were used to measure ΔF for a given contraction, and we referred to this as “pairwise ΔF.” As described in more detail in results, we also constructed a composite control motor unit profile where the firing frequency profiles of the lowest threshold motor units were plotted together and a new fifth-order polynomial curve was fit to the combined data. The selection criteria for a composite control motor unit were a recruitment threshold of less than 3% MVC with a secondary range of less than 2 s. Of the total number of decomposed motor units in each contraction (≈20), there were typically three to six of them with recruitment thresholds less than 3% MVC. In these units, the steep secondary range, as identified visually, was around 1.5 s (detailed in results), so the majority of firing occurred in the linear tertiary range. In four of the participants, typically one low-threshold control motor unit in half of the contraction trials had a very shallow tertiary slope and low (<5 Hz) firing rate modulation (0.4 ± 0.8 units per contraction). These units were not used as controls and were removed from the data set. The remaining units that were recruited after the composite control units were then used as test units to measure the “composite ΔF.”

In addition to the ΔF values, the coefficient of determination (R²) of the relationship between the firing rate of the control motor unit and the firing rate of the test motor unit (i.e., rate-rate plots of control and test polynomial lines) was measured to determine if the control and test units were receiving a common synaptic input (Gorassini et al. 2002a). As with all other measures, this was done for the ΔF values using the pairwise and composite control motor unit methods (rate-rate R² values; see Supplemental Table S3). The interval of time between the recruitment of the control and test motor unit was also measured (ΔT recruitment) and plotted against the corresponding ΔF value to determine if this affected ΔF (Hassan et al. 2020; Udina et al. 2010).

Self-sustained firing duration.

To obtain a measure of the proportion of the total time the test unit was firing at synaptic inputs below the level required to recruit the motor unit, we measured an index of the self-sustained firing duration (SSD). That is, if there were no I_P activation, the motor unit would stop firing at the same level of synaptic input that was needed to initially recruit the unit (at dashed gray vertical line in Fig. 1A). Activation of the I_P after recruitment allows the motoneuron to fire for longer below this level of synaptic input to produce self-sustained firing (pink shaded area in Fig. 1A, ii and iii). We calculated the SSD as follows (further detailed in Fig. 10):

$$\frac{\left(timeoffiringduringdescendingphase-timeoffiringduringascendingphase\right)}{\left(timeoffiringduringascendingphase+timeoffiringduringdescendingphase\right)}\times 100\%$$

As described above, we used the peak of the contraction torque to indicate the transition point from an ascending to a descending synaptic input from which we measured the time of motor unit firing during the descending and ascending phase of the contraction.

Fig. 10.

Self-sustained firing duration (SSD). A: examples of test-composite control unit pairs from participant 3M during a 30% maximum voluntary contraction (MVC) trial. Ai: test unit with large self-sustained firing duration (SSD) index. Aii: test unit with small SSD. Vertical gray lines mark the time that the estimated synaptic input reached the level that recruited the test unit during the ascending (a) and descending (a¹) phase of the contraction. The duration of a = time of test unit recruitment to time of peak synaptic input (torque), the latter marked by the dashed vertical line. The duration of a¹ is estimated by the duration of a. Solid black vertical line marks time of derecruitment of test unit. Distance between right gray vertical line and solid black line indicates duration of self-sustained firing of unit, i.e., duration of time unit fires below synaptic input initially needed to recruit unit (see calculation in text; d = duration of time the test unit was active on the descending phase). Self-sustained firing (ΔF) values calculated as in Fig. 3. B: SSD of test units averaged for the 7 participants plotted against recruitment threshold at each contraction intensity (10%, 20%, and 30% MVC). Bin width 2% MVC. Missing values in 20% and 30% MVC data are due to small number of samples for the lowest and highest threshold units [many of the lowest threshold units were used as control units and some high-threshold short ascending activation (SA) units were removed]. Stars indicate SSD values that are different from the SSD value at the 0–2% MVC bin or 2–4% MVC bin (arrowhead). Gray bars represent the equivalent of every 2 s in time for the 10-s ascending contraction for the different contraction strengths. Error whiskers are ±1 SD.

Statistics

Example data are presented for six of the seven participants in the figures. Data are described in the figures and Supplemental Tables as means and SD for both individual participants and the average of the means across the seven participants. Sigma Plot 11.0 software was used for all statistics. Across the group, Mann–Whitney rank-sum tests were used to compare various parameters of the firing frequency profiles such as start vs. end rates, ascending vs. descending slopes, and pairwise ΔF vs. composite ΔF values. A Bonferroni correction to a significance level of P < 0.025 was used to account for the multiple comparisons at the 10%, 20%, and 30% MVC contractions. Pearson’s product moment correlation (r) was used to determine if there was an association between ΔF and control unit modulation depth (CMod). The coefficient of determination (R²) was calculated for the polynomial line fit to the frequency profiles and to the linear line fit to the control rate-test rate plots, as described previously (Gorassini et al. 2002a). A one-way, repeated measures ANOVA was used to determine if ΔF, ascending slopes, and SSD varied with recruitment threshold of the test unit. Appropriate post hoc t tests were used to determine if values for the lowest threshold test units were different from the higher threshold units.

RESULTS

Motor Unit Decomposition from HD-sEMG

For a given isometric contraction, a maximum of 6–40 single motor units were identified from the decomposition of the 64 channels of monopolar HD-sEMG in the 10 participants tested. Data from three participants (all women) were not included because fewer than eight motor units were identified per contraction (details in methods), with too few low-threshold control units to obtain ΔF values for the required six contractions. In the remaining seven participants, an average of ~20 TA motor units were decomposed per contraction at the 10%, 20%, or 30% MVC isometric contractions (Fig. 2B; see Supplemental Table S1 for individual participant values). Accuracy or silhouette values (described in methods) in decomposing the single motor units were 0.95 (95%) on average for all participants (Fig. 2C and Supplemental Table S1), with firing rate profiles well fit by a fifth-order polynomial as reflected in an average coefficient of determination (R²) between 0.73 and 0.76 for all contraction levels (Fig. 2D and Supplemental Table S1).

Firing Rate Profiles of Decomposed Motor Units

When participants produced slowly increasing and then decreasing triangular isometric contractions (10 s up and 10 s down), the decomposed motor units were gradually activated in order of their recruitment threshold (Fig. 3A; motor units displayed in ascending order of recruitment threshold). Once recruited, the firing rate of the motor units typically increased linearly over most of the ascending ramp until peak torque was reached (at gray dashed line). Immediately following the downward turn in torque during the decreasing effort, the firing rate decreased, again linearly with a slope similar to the that of the ascending phase. However, the slope of the straight line fit to the descending phase was shifted slightly downward (marked in unit 1 by lower green line), likely due to sag as detailed in discussion. These similar upward and downward linear slopes indicate that the firing rates increased and decreased without much rate saturation during the 10 s of increasing and decreasing effort (see also Fig. 2A and methods). We thus considered the peak torque to indicate the peak of the synaptic drive. When a fifth-order polynomial line was fit to the firing rate profile of each unit, the peak of this smooth line was slightly before the peak torque, likely because of the smoothing and the sag mentioned above. However, this polynomial line still provided a relatively accurate representation of the rate of increase and decrease of the firing rate profile (see R² values; Fig. 2D) and, importantly, the firing rate at recruitment and derecruitment of the test motor units.

Fig. 3.

Firing profiles of multiple motor units and self-sustained firing (∆F) calculation. A: firing rate profiles of 19 decomposed motor units during a 22% maximum voluntary contraction (MVC) in participant 1F in ascending order of recruitment threshold over 2 columns (same torque trace over each column). Dashed vertical line marks peak discharge rates at turnaround of torque. Pink and green lines mark secondary and tertiary range firing in units 1 and 10, respectively. Lower green line marks sag during descending phase. Short horizontal colored lines mark 0-Hz baseline for each rate profile. B: overlay of polynomial lines from the 19 motor units in A (participant 1F) using the same color coding (left) and similar polynomial lines from participant 5M during a 30% MVC contraction (right). C: paired unit analysis for units 1 (U1; control) and 2 (U2; test) from A with ∆F of 1.1 Hz (left) and for U1 (control) vs. U9 (test) producing ∆F of 3.7 Hz (right). Dashed vertical lines mark recruitment and derecruitment of test units. D: same as in C but for test U17 paired with control U13 (left) and with control U6 (right) producing ∆F values of −0.3 Hz and 5.3 Hz, respectively. E: ∆F values for each test unit in A, using same rainbow color code, plotted against recruitment threshold. Number of control units paired with each test unit increases with recruitment order to produce progressively larger number of ∆F values. Test units in C and D (U2, U9, and U17) are marked in plot.

In many units the firing rate started with a high initial firing rate and a steep increase in rate (secondary range; e.g., pink line in Fig. 3A, unit 10), likely due to the I_P onset; following this, the firing rate then increased more slowly with a more shallow slope (tertiary range; e.g., green line in Fig. 3A, unit 10). When the force was decreased, the firing rate decreased with a similar shallow slope (tertiary range). Because of the larger secondary range at the onset of firing, the slope of a line fit to the entire ascending phase of the firing rate profile was, on average, steeper compared with the descending phase slope (Figs. 4A, i and ii, and Supplemental Table S1), consistent with I_P activation at the onset of recruitment, which accelerates initial firing rates. Likewise, the average rate at the start of the firing profile was higher compared with at the end of firing (derecruitment) (Fig. 4B), consistent with activation of the I_P at recruitment.

Fig. 4.

Ascending (Asc) and descending (Dsc) rate slopes and start, end, and maximum rates. A: group average across all 7 participants for ascending (i) and descending (ii) slope of polynomial line fit through the firing rate profile at all contraction strengths.*P < 0.05 between ascending and descending slope at each contraction level. B: group average of start, end, and maximum (max) rates for each contraction level taken from the fit polynomial line. *P < 0.01 between start and end rates. C, left: slope of the ascending firing rate of a motor unit plotted against its recruitment threshold from all test units for the 6 contractions at the 10%, 20%, and 30% maximum voluntary contraction (MVC) contraction strengths. Red line is the straight-line fit to the data. Right, group average of slope of straight-line fit through the ascending slope vs. recruitment threshold data. D, left: same as in C but for data during the descending phase of the contraction. Average slope values in C and D (right) are all greater than 0 (all P < 0.001) but not different from each other (P > 0.05). Data in C and D (left) are from participant 7F, who on some trials overshot the 20% MVC target by 5%. Error whiskers are +1 SD. Individual participant data in Supplemental Table S1.

A common feature across all contraction levels was that the slope of the ascending firing rate profile increased as the recruitment threshold of the units increased (Fig. 4C), as also illustrated when all polynomial lines from Fig. 3A are plotted together (Fig. 3B). The shallow slopes of the lowest threshold units (e.g., units 1–3 in Fig. 3A) likely represent motoneurons where the majority of the I_P was recruited below the firing threshold, and thus with the majority of firing occurring in the tertiary range (green lines in unit 1). In higher threshold units (units 4–19), there were more pronounced and prolonged steep increases in firing at recruitment, producing a prolonged secondary range, likely resulting from I_P activation at recruitment (e.g., pink line in Fig. 3A, unit 10). The slope shallowed during the tertiary range after full I_P activation (green lines in Fig. 3A, unit 10), but this tertiary range firing was of shorter duration, and so the overall ascending slope was often dominated by the secondary range in these higher threshold units.

Estimation of I_P-Mediated Self-Sustained Firing from Individual Motor Unit Pairs (Pairwise Method)

The firing rate profiles from the multiple decomposed motor units were used to estimate the self-sustained firing produced by I_P (ΔI) from the paired motor unit analysis (ΔF). As described in introduction, the amount of depolarization provided by the I_P to maintain firing of a test motoneuron can be estimated from the difference in synaptic input needed to maintain minimal firing after the I_P is fully activated (measured at firing termination, F_T) compared with the larger synaptic input required to initiate firing prior to full I_P activation (measured at recruitment, F_R). Here, synaptic input to a test unit is estimated by the firing rate profile of a relatively lower threshold control motor unit. Thus the self-sustained firing produced by I_P can be estimated as ΔF = F_R − F_T. As illustrated in Fig. 3C, left, a low-threshold control motor unit (unit 1 from Fig. 3A) was used as an estimate of synaptic input to a relatively higher threshold test motor unit (unit 2). The firing rate of control unit 1 when test unit 2 was derecruited (6.2 Hz) was subtracted from the firing rate of control unit 1 when test unit 2 was recruited (7.3 Hz) to produce a ΔF value of 1.1 Hz for test unit 2. Many permutations of control and test units are possible, and we systematically computed them all. Specifically, all higher threshold units (units 2 −19) were paired with control unit 1 to compute a ΔF value. Following this, unit 2 was used as a control rather than test motor unit, and ΔF values were computed for units 3–19, and so on. All ΔF values for the 171 possible test-control unit pairs [(19 × 18)/2] are plotted in Fig. 3E according to the recruitment threshold of the test unit, with each test unit color coded as in Fig. 3A. Note the number of ΔF values increased by 1 as the recruitment threshold of the test unit increased, because it was paired with an additional control motor unit.

There are two basic ways to consider the pairing of control and test motor units. First, we can examine the ΔF values of different test units when paired with a common control unit. For example, when the lowest threshold unit is used as a control unit (unit 1) and the ΔF is measured in the next lowest threshold test unit (unit 2) and then in a much higher threshold test unit (unit 9 recruited at 11% MVC), ΔF values of 1.1 Hz and 3.7 Hz are produced, respectively (Fig. 3C). On face value, this suggests that the lower threshold unit 2 had a smaller I_P contributing to self-sustained firing. However, as we detail below (see Floor effect and early control unit derecruitment errors), this lower ΔF could be because unit 2 was activated when control unit 1 fired at a very low rate, perhaps underestimating the ΔF value.

The other way to pair units is to compute the ΔF for a single test unit with different control units. For example, pairing test unit 17 with control units 13 and 6 leads to very different ΔF values of −0.3 Hz and 5.2 Hz, respectively (Fig. 3D). More generally, when all possible pairings of different control units with a given test unit are made, there are a large number of possible ΔF values computed, even though a given test motoneuron can only have one I_P value. This is particularly concerning since we find that the ΔF for a given test unit varied by as much as 8 Hz depending on the control unit it was paired with (Fig. 3E) (see also Hassan et al. 2020). This variability is largely due to variations in the firing linearity of the control unit and the timing of its onset relative to the test unit. Thus, in the following, we detail methods to identify and eliminate inappropriate pairings of control and test motor units.

Floor effect and early control unit derecruitment errors.

When a low-threshold test unit (unit 2) was recruited shortly after its even lower threshold control unit started firing (unit 1), the control unit typically fired at a very low rate (Fig. 3C, left). Thus this estimate of synaptic input (unit 1 firing rate) had little room to be reduced at derecruitment of the test unit, since the firing rate of the control unit cannot go much lower (floor effect). This floor effect contributed, in part, to the artificially low ΔF values for the lowest threshold motoneurons (detailed more in Fig. 9). In other cases (such as comparing control unit 14 with test unit 15; Fig. 3A), the control unit stopped firing before the test unit, making the estimate of synaptic input at derecruitment higher than it should be (or unknown) to artificially underestimate the ΔF value.

Fig. 9.

Self-sustained firing (ΔF) and test motor unit recruitment threshold. A: binned averages of ΔF values across the 7 participants plotted against recruitment threshold of the test unit for the 10%, 20%, and 30% maximum voluntary contraction (MVC) data. Bin widths are 2% MVC. Green circles mark ΔF values from composite control unit method, and black circles mark ΔF values from pairwise method. Stars indicate ΔF values that are different from the ΔF value at the 0–2% MVC bin (arrowheads) for the pairwise data (no bins were different in the composite control data). Missing ΔF value for test units having recruitment thresholds between 28% and 30% MVC in the composite 30% MVC data is due to a small number of values for this bin. Test units with short ascending activation (SA) times were removed from data set. B: binned averages for the slope of the ascending firing rate profile of the test motor units. Same format as in A. Gray bars represent the equivalent of every 2 s in time for the 10-s ascending contraction in each of the different contraction strengths. Error whiskers are ±1 SD.

Nonlinear firing of control unit during I_P activation leads to underestimation errors.

As mentioned above, only the lowest threshold units that fire predominantly in the tertiary range following full or nearly full I_P activation likely provide the most accurate and linear representation of the synaptic drive, like unit 1 in Fig. 3C. Higher threshold units that often have nonlinear firing due to a prolonged secondary range that transitions to a tertiary range many seconds after recruitment provide less accurate measures of synaptic input and thus should not be used as control units. For example, when unit 13 with a steep secondary range at the onset of firing was used as a control unit, it produced a very low ΔF value when paired with test unit 17 (Fig. 3D, left). This is because at the time test unit 17 was recruited, the I_P in unit 13 was likely not fully activated and its firing rate underestimated the synaptic drive at this time, relative to the estimate at derecruitment when the I_P was fully activated, ultimately giving a low ΔF value (−0.3 Hz).

To further illustrate this error in underestimating the ΔF, the ΔF values for each of the six contraction trials at 10%, 20%, and 30% MVC were plotted for all motor unit pair combinations measured from the 19 units in Fig. 3A (Fig. 5A). These pairwise ΔF values were plotted against the time difference between when the control unit was recruited and the time when the test unit was recruited (ΔΤ recruitment). In general, this revealed an underestimation and wide variability of the ΔF at short test-control ΔΤ recruitment times between 0 and 2 s (as for test unit 17 vs. control unit 13; Fig. 3D). The ΔF values then leveled off when the test units were recruited at least 2 s after the control unit, because the test units were no longer being recruited while the control units were within their initial, low-frequency secondary range (as for test unit 9 vs. control unit 1; Fig. 3C). This leveling effect occurred for all ramp speeds (1–3% MVC/s) at the three different contraction strengths (Fig. 5A), although the large variability in ΔF values continued past ΔT recruitment times >2 s. The mean ΔF value for the multiple pairwise comparisons was similar across the 10%, 20%, and 30% MVC contractions (all P > 0.59, black bars in Fig. 5D; Supplemental Table S2).

Fig. 5.

Self-sustained firing (ΔF) from pairwise and composite control methods. A: ∆F values obtained from the pairwise method plotted against ∆T recruitment times (time difference between when control unit was recruited and time when test unit was recruited) for 10%, 20%, and 30% maximum voluntary contraction (MVC) trials from participant 1F. Red line indicates best fit from exponential rise to maximum. Number of ∆F values (n) indicated in bottom right of each graph. B: same as in A but for ∆F values measured from composite control method. Best-fit straight line in red. C: ΔF values for pairwise (Pair) and composite control (Comp) methods for 10%, 20%, and 30% MVC trials in A and B, respectively. Mean is represented by the red line (which covers the black median line), the 25th and 75th percentiles by the box bounds, and the 95th and 5th percentiles by whiskers. Open circles represent outliers. D: comparison of mean ∆F values across the 7 participants for the pairwise (black bars) and composite control (red bars) methods and composite control without ∆F values from test units having short ascending activation (SA) times (see Fig. 8 for details on SA units). E: coefficient of variation (CoV) for the different mean ∆F values as in D. Error whiskers are +1 SD. *P < 0.005. Individual participant data in Supplemental Table S2.

Nonlinear firing of control unit during I_P deactivation leads to overestimation errors.

A control motor unit could also have an early, steep deceleration in firing rate when a test unit is derecruited, as often occurred with the high-threshold units (e.g., units 17 and 18 in Fig. 3A). Here, the amount of synaptic input would be underestimated during test unit derecruitment, which would also produce an overly large ΔF value. Because the slope of the descending phase of the firing rate profiles increased with recruitment threshold of the units (Fig. 4D; see also polynomial overlays in Fig. 3B), this produced varying estimates of synaptic input in different control units for a single derecruitment time of a given test unit. Thus the variable times that the I_P was deactivated to produce the different slopes of descending firing rate contributed to the variability in ΔF values for a single test motor unit, especially for the higher threshold test units.

Variation in control unit sensitivity to synaptic input errors.

Higher threshold units had, on average, higher slopes in their firing rate on both the ascending and descending phases of the ramp (Fig. 4, C and D) and could reach higher firing rates compared with the lower threshold units (see polynomial overlays from participants 1F and 5M; Fig. 3B). This made the higher threshold units more sensitive to changes in synaptic input and thus yielded higher ΔF values when these units were used as control units, compared with the low-threshold control units. Thus it is advisable to settle on a single, low-threshold control unit (or collection of low-threshold units) to measure ΔF values in all the other test units as we detail next.

Measurement of ΔF from a Composite Control Motor Unit Profile

To reduce the number of underestimated and overestimated ΔF values (detailed above), we developed a new method where only the lowest threshold control units that fired primarily within their linear tertiary range were used as estimates of synaptic input to the test units. For each contraction, we selected the lowest threshold motor units (<3% MVC, typically 3–6 units) to construct a “composite” control unit profile (Fig. 6). Compared with the higher threshold units, the lowest threshold units had the shortest initial firing rate accelerations (secondary range) and proportionally longer periods of tertiary range firing. We assumed that in these low-threshold units, the I_P was almost fully activated at the time of recruitment so that their firing rate profiles were more linearly related to the synaptic input profile. An example is shown in Fig. 6A where the firing rates of the three lowest threshold units from Fig. 3A (units 1–3) are superimposed to form a composite control motor unit profile. In these units there is a brief, initial acceleration in firing rate (secondary range; pink line in Fig. 6A), and afterward, the firing rate increases less steeply during the tertiary range (green line). To restrict the composite control unit profile to a single linear range, the firing rate values within the secondary range were identified visually and removed. A new polynomial line (red) was then fit to the edited profile (Fig. 6B). Because of the short duration, the secondary range in these low-threshold control units was easy to distinguish visually from the tertiary range. On average, the first 1.1 ± 0.3 s of the firing rate profile was removed for the 10% MVC contractions, 1.5 ± 0.4 s for the 20% MVC contractions, and 1.5 ± 0.3 s for the 30% MVC contractions, with the start of the edited composite control profile occurring before any higher threshold test unit was recruited. Following removal of the secondary range firing, the ascending slope of the remaining composite control profile (i.e., tertiary range) was 0.63 ± 0.26 Hz/s for the 10%, 0.79 ± 0.26 Hz/s for the 20%, and 0.90 ± 0.33 Hz/s for the 30% MVC contractions, being lower than the average overall ascending slope of the higher threshold test motor units that had a proportionally longer duration of secondary range firing (further described in Fig. 9B).

Fig. 6.

Composite control motor unit profile. A: overlay of firing frequency profiles of unit 1 (pink circles), unit 2 (blue-green circles), and unit 3 (light blue circles) from Fig. 3A. Slope of secondary and tertiary range firing is marked by pink and green lines, respectively. B: same plot as in A but with the frequency points in the secondary range removed. A new 5th-order polynomial line was fit to the edited profile (red line). Removing the frequency points in the secondary range made the slope of the ascending frequency profile (0.74) similar to the slope of the descending frequency profile (−0.72). Slope values were measured from a straight-line fit to the polynomial line. C and D: paired unit analysis using test units U17 and U4 from Fig. 3 paired against the composite control unit profile (Comp). E–H: mean ratio of the ascending and descending firing rate slope for the composite control unit profiles (E), mean R² value of the control rate-test rate plots (F), mean number of motor units in the composite control unit profiles (G), and mean number of total unit pairs across the six contractions in the self-sustained firing (ΔF) analysis (H). Values are averages of mean values from each of the 7 participants for the 10%, 20%, and 30% maximum voluntary contraction (MVC) trials. In F and H, data are displayed for the pairwise (black bars), composite control (red), and composite control without SA test units (green). Error whiskers are+1 SD. Individual participant data in Supplementary Tables S2 and S3.

Removing the secondary range made the slope of the polynomial line on the ascending phase of the composite control profile similar to that on the descending phase, with an ascending-to-descending slope ratio near 1 (Fig. 6E and Supplemental Table S2), especially for the 20% and 30% MVC contractions. A matched ascending and descending rate of synaptic input is important when measuring I_P amplitude to avoid any rate-dependent effects on motor unit recruitment or derecruitment (Desmedt and Godaux 1977; Freund 1983; Kuo et al. 2006). On average, around four to five of the lowest threshold motor units were used to construct the composite control unit profiles at each of the different contraction strengths (Fig. 6G and Supplemental Table S3). The downside of this method is that it does not allow us to estimate the ΔF values of the lowest threshold units since they are used in the composite control profile. However, as discussed above, these units have ΔF values that may be affected by floor effects from their even lower threshold control units and predominant subthreshold I_P activation. Thus these units should be viewed with caution.

The composite control profile reduced the variability of the ΔF values. For example, a ΔF value of 3.6 Hz was obtained when test unit 17 from Fig. 3D was paired with the composite control (Comp) profile (Fig. 6C). This was likely a more accurate estimate of I_P-mediated self-sustained firing compared with the ΔF values of −0.3 Hz and 5.2 Hz obtained with control units 13 and 6 having large secondary range firing. When all the ΔF values measured with the composite control method for this participant are compared with the ΔF values from the pairwise method (Fig. 5B), it is apparent that the very low and high ΔF values were eliminated by the composite control method and that ΔF remained fairly constant regardless of when the test unit was activated in relation to the start of the composite control unit profile (ΔT recruitment). The removal of some of the low ΔF values are simply because the short test-control unit intervals could not occur. The decreased spread of ΔF values is clearly illustrated in Fig. 5C for the three contraction levels for this participant when the composite control (Comp) method is used compared with the pairwise (Pair) method. Likewise, the coefficient of variation (CoV; SD/mean) of the ΔF values across all participants was reduced nearly by half when the composite control method was used, as a result of removing the extreme, and likely inaccurate, ΔF values from some of the pairwise comparisons (Fig. 5E; all P < 0.001, compare black and red bars). The CoV was reduced even though the average number of total unit pairs from the six contractions at the 10%, 20%, and 30% MVC trials was ≈14 times less (Fig. 6H and Supplemental Table S2), with around 230 ΔF values per contraction in the pairwise method compared with 16 ΔF values for the composite method. Despite a reduction in variability, the composite control unit method did not change the mean ΔF across the group (Fig. 5D, all P > 0.65), likely because an equal number of low and high ΔF values were removed. The average coefficient of determination (r²) of the control rate vs. test rate plots (rate-rate; see methods) was well above >0.5 for both the pairwise and composite control method (Fig. 6F and Supplemental Table S3).

Constraints of Modulation Depth of Control Motor Units on the ΔF

If the firing rate of a control motor unit does not represent the full excursion of change in synaptic input to the test unit, which may occur with rate saturation or weak synaptic drive, then the ΔF value for a given test unit may be underestimated. As an indication of this, we plotted the maximum firing rate excursion of a control motor unit (i.e., maximum rate − minimum rate = modulation depth, or CMod; see Fig. 2 and methods) against the ΔF of the corresponding test unit to determine if ΔF was constrained by the modulation depth of the control unit. When the pairwise method was used, some of the ΔF values rested on or near the line of unity (Fig. 7Ai, participant 5M), especially for the 10% MVC contractions, where the CMod of the control units was the lowest. Some of the points along the unity line indicate that the ΔF values were likely constrained by the amount of rate modulation of the control motor unit, especially for test units with low ΔF values. The test units with large (and likely overestimated) ΔF values on the line of unity were paired with high-threshold control units having large, nonlinear firing rate modulation. Although data points tended to move away from the unity line at stronger contractions, there was a significant positive slope when a straight line was fit between ΔF and CMod at all contraction strengths for the pairwise data (black bars in Fig. 7E; slope > 0, all P <0.001; Supplemental Table S2).

Fig. 7.

Self-sustained firing (ΔF) and control unit modulation for pairwise and composite control unit methods. Ai: ΔF values of all 6 contractions plotted against control unit modulation (CMod) for the pairwise ΔF method in participant 5M at the 10%, 20%, and 30% maximum voluntary contraction (MVC) trials. Black line marks the line of unity where ΔF = CMod values. Pearson’s product correlation coefficient (r) and the significance of the correlation are indicated at top left of each graph for the ΔF and CMod relationship. Red line denotes straight-line fit to the data. Aii: same as in Ai but for ΔF measured with the composite control unit method. B: maximum firing rate of the composite control unit profile (CMax_comp) measured from the polynomial line at the 10%, 20%, and 30% MVC trials for participant 5M. Median and mean are represented by black and red lines, the 25th and 75th percentiles by the box bounds, and the 95th and 5th percentiles by whiskers. C: same as in B but for the firing rate of the composite control motor unit when the test motor unit was recruited (C_compRT). D: group data for the composite control unit method, including composite control unit modulation depth (CMod; black bars), ΔF values (red bars), maximum rate of the composite control unit profile (CMax; dark green bars), and composite control unit rate when the test unit was recruited (C_RT; light green bars), averaged across the 7 participants for the 10%, 20%, and 30% MVC trials. E: average slope of the straight line fit to the ΔF vs. CMod data (red lines in A) for the pairwise (Pair; black bars) and composite control unit (Comp; red bars) methods across the 7 participants. Error whiskers are +1 SD. *P < 0.025, difference from a slope of 0. Individual participant data for D and E in Supplemental Table S2.

A similar trend was shown for the ΔF values obtained from the composite control unit profiles, where the ΔF values moved further to the right of the unity line for the stronger contractions (Fig. 7Aii) because ΔF remained fairly constant (red bars in Fig. 7D; Supplemental Table S2) while the modulation depth of the composite control profile (black bars) progressively increased as would be expected for increasingly larger synaptic inputs. In addition, the large ΔF values on the line of unity having high-threshold control units were also removed in the composite control method. For this participant, the slope of the straight line fit to the ΔF and CMod data was close to 0 for the 20% and 30% MVC contractions, indicating no relationship between ΔF and CMod. Across the group, the ΔF-CMod slope was not different from 0 at the 20% and 30% MVC contractions (red bars in Fig. 7E, all P > 0.2; Supplemental Table S2), indicating that an insufficient modulation of the composite control profiles were not constraining the ΔF measures at these higher levels of contraction, unlike that for the weaker 10% MVC contraction and for all of the pairwise ΔF values.

The maximum firing rate of the composite control unit profile (CMax_comp) also increased with contraction strength (Fig. 7B for participant 5M and Fig. 7D for group values). For some participants, the increase in maximal firing rate leveled off from 20% to 30% MVC (Supplemental Table S2). This may indicate some rate saturation of the control units at 30% MVC so that some of the ΔF values may have been underestimated. Despite this, the test motor units were recruited at firing rates of the composite control profile (C_RT) that were smaller than the maximum composite control rates, where rate saturation was less likely (Fig. 7C for participant 5M and Fig. 7D for group values; Supplemental Table S2).

ΔF of test units with short ascending activation (SA) time

A single composite control unit profile made it easier to examine the relationship between the recruitment threshold of a test motor unit and its ΔF value because the recruitment time of the composite control profile was anchored to a single value. In general, we found that the ΔF values did not change in motor units of differing sizes based on their recruitment threshold. However, as shown for the 30% MVC contraction trials in participant 6M (Fig. 8B), a population of test motor units that were recruited near the end of the ascending phase of the contraction (at 23% MVC or greater, red circles) had very low ΔF values. It is possible that these higher threshold units had a smaller I_P. However, test motor units that were also recruited near the end of the 20% and 10% MVC contraction trials also had lower ΔF values (red circles in Fig. 8, C and D), even though these units were recruited near 15% and 10% MVC, respectively. Critically, the same group of motor units that had low ΔF values at the top of the 20 and 10% MVC contractions (red circles in Fig. 8B) had higher, near-normal ΔF values when examined during larger ramps (at arrows on the 30% MVC contractions in Fig. 8B). Thus the low ΔF values are an artifact of being at the top of the contraction ramp, likely due to the amount of time the unit is active for during the ascending phase of the contraction, as we detail next.

Fig. 8.

Test units with short ascending activation (SA) times. Ai: test units (gray circles) paired with composite control motor unit profile (colored circles) in participant 6M for a 30% maximum voluntary contraction (MVC). The test unit was recruited at 13% MVC (torque, top trace) and discharged for 3.6 s during the ascending phase of the firing rate profile. Self-sustained firing (ΔF) value from this test unit (5.7 Hz) is plotted in B as one of the gray circles because it was activated for >2 s on the ascending phase of the contraction. Aii and Aiii: same as in Ai but for 2 test units (red circles) that were recruited >20% MVC and with durations of firing during the ascending frequency profile that were <2s, i.e., having short ascending activation (SA) times. ΔF values for these 2 test units are plotted with red circles in B. B: all ΔF and recruitment threshold values from the 6 contractions at 30% MVC in participant 6M. C and D: ΔF values from this same participant as in B plotted against recruitment torque at the 20% MVC (C) and 10% MVC trials (D). ΔF values marked with red circles had test units with SA times and ΔF values less than −1 SD. ΔF measures with test units having SA times removed from the average are shown in Figs. 5 and 6.

The dependence of activation time during the ascending phase of the contraction on the ΔF value is illustrated in Fig. 8A, i–iii, for three different test units from the 30% MVC data in Fig. 8B. It is apparent that the test unit with a large ΔF that was recruited before 20% MVC fired for more than 2 s during the ascending phase of the contraction (Fig. 8Ai). In contrast, the test motor units recruited after 20% MVC that were activated for less than 2 s during the ascending phase had lower ΔF values (Fig. 8A, ii and iii). As shown previously, test motor units that fire less than 2 s during the ascending phase of the contraction will often have low ΔF and ΔI values (Li et al. 2004, 2007; Stephenson and Maluf 2011; Udina et al. 2010). This may result from the I_P not being fully activated before the synaptic input begins to decrease, and so when synaptic input is reduced during the relaxation phase of the contraction, the I_P is inactivated early. In fact, the ΔF values marked with red circles in Fig. 8, B–D, were all activated for less than 2 s on the ascending phase of the contraction and had ΔF values below −1 SD of the mean. There were other test units with short ascending activation times but whose ΔF values were closer to the mean (gray circles above the red circles in Fig. 8, B–D). It is likely that the I_P in these units were sustained for longer periods of time despite a relatively shorter ascending activation time (see also Fig. 1 in Li et al. 2004). Given the potential for motor units with short ascending activation (SA) times to not have full I_P activation, these units should be treated as a separate population. When these test units with short activation times were removed from the data set (≈1–3 per contraction trial with <2 s of activation on the ascending ramp and ΔF less than −1 SD), the CoV of the ΔF values was further reduced for the 20% and 30% MVC contractions (P < 0.003; Fig. 5E), but the average ΔF (Fig. 5D) and r² values for the rate-rate plots (Fig. 6F) remained the same (see Supplemental Table S3 for individual participant values). Thus in all subsequent analysis we removed these test units with short activation times.

ΔF and Motor Unit Recruitment Threshold (Motoneuron Size)

Correcting for inappropriate control and test unit pairings with the composite control method (and more generally abandoning the pairwise method of using all possible unit pairings as outlined above) allowed us to more accurately compare the ΔF values for test motoneurons of varying sizes (recruitment thresholds), especially for the 20% and 30% MVC contractions where the ΔF was not constrained by the control unit modulation depth. In the composite control method (green circles in Fig. 9A), the ΔF was found to be generally invariant across all motor units, with no effect of recruitment threshold on the ΔF values for both the 20% and 30% MVC trials [F(6,8) = 1.3, P = 0.26 and F(6,13) = 1.5, P = 0.13, respectively, one-way repeated measures ANOVA]. However, there was an overall effect of recruitment torque on ΔF values for the 10% MVC trials [F(6,4) = 3.1, P = 0.04], but no ΔF value at a given recruitment threshold was different from the others in post hoc comparisons. In contrast, for the pairwise method (black circles in Fig. 9A), there was an effect of recruitment threshold on ΔF values for all contraction levels and speeds at 10% [F(6,4) = 3.1, P = 0.01], 20% [F(6,9) = 3.1, P < 0.001], and 30% of MVC [F(6,14) = 3.1, P < 0.001], although we now consider this to be an artifact of errors we discussed above arising from this method. Here, ΔF values with test units having the lowest recruitment thresholds (0–2% MVC, arrowheads in Fig. 9A) were significantly smaller than many of the ΔF values having test units with higher recruitment thresholds (stars in Fig. 9A). In summary, the ΔF values measured from the composite control method remained constant for test motor units of increasing recruitment threshold, whereas the pairwise method led to different, though incorrect, conclusions. An invariant ΔF value with increasing recruitment threshold occurred even though the amount of secondary range firing of the test units also increased with recruitment threshold, as reflected in the increasing slope of their ascending firing rate profiles (Fig. 9B). The significance of this is explained in discussion.

Self-Sustained Firing Duration

The ΔF value provides a measure of how much the firing rate modulation of a motoneuron is mediated by self-sustained firing from the I_P (amplitude estimate of self-sustained firing). For example, the entire firing rate modulation of a motor unit, as measured from the composite control profile, was 6.8 Hz, 8.8 Hz, and 10.5 Hz for the 10%, 20%, and 30% MVC contractions, respectively. Given that the average composite ΔF was 4.1 Hz, 4.5 Hz, and 4.6 Hz at these contraction levels, we can estimate that 60%, 51%, and 44% of the firing rate modulation of a motoneuron was contributed to by the I_P for the 10%, 20%, and 30% MVC contractions, respectively (although values for the 10% MVC should be used with caution). In addition to this amplitude estimate of self-sustained firing, we also determined how the I_P influenced the duration of the self-sustained firing, by measuring the proportion of firing time that continued at synaptic inputs below the level required to recruit the motor unit (see methods for calculation). To do this, a self-sustained firing duration (SSD) index was computed by subtracting the period of time the test unit was active during the ascending phase of the contraction (Fig. 10A, a) from the duration of time the test unit was active on the descending phase (Fig. 10A, d) and normalizing it by the total firing time of the test unit (Fig. 10A, a + d) to give SSD = (d − a)/(a + d) × 100%. The SSD for the two example test units in Fig. 10A, i and ii, are 50% and 14%, with ΔF values of 5.2 Hz and 2.8 Hz, respectively.

On average across the group, the SSD for all test units was ≈20% for each of the three different contraction levels/speeds (Supplemental Table S3). The SSD increased for test units recruited near the end of the ascending phase of the contraction (Fig. 10B). There was an effect of recruitment threshold on the SSD values for the 10% [one-way repeated measures ANOVA: F(6,4) = 28.5, P < 0.001], 20% [F(6,7) = 5.8, P < 0.001], and 30% [F(6,12) = 7.2, P < 0.001] MVC contraction levels. Post hoc, SSD values with test units having the lowest recruitment thresholds (0–2% or 2–4% MVC; arrowheads in Fig. 10B) were significantly smaller than many of the ΔF values having test units with higher recruitment thresholds (stars in Fig. 10B). The highest threshold test units had the largest SSD values whereby 30–40% of their firing occurred when the synaptic input was estimated to be below the recruitment level. These units had the shortest duration of activation during the ascending phase of the contraction (2–3 s) and thus only had to continue to discharge for another 4–6 s during the descending phase of the contraction to reach SDD values of ≈30%.

DISCUSSION

Our results demonstrate that motoneurons recruited over a wide range of force thresholds exhibit evidence of I_P that assist their firing, including producing a high initial firing rate, accelerated firing shortly after recruitment, and self-sustaining firing (ΔF). This extends previous findings of I_P activation in low-threshold TA units (D’Amico et al. 2013; Gorassini et al. 2002a; Stephenson and Maluf 2011; Udina et al. 2010) to much higher threshold units. The low- and high-threshold units, which presumably represent small and large motoneurons, respectively, had similar ΔF values even though the I_P in the lower threshold units may have been recruited well before firing. This indicates that the portion of the I_P that sustains firing is similar for different sized motoneurons, as was previously demonstrated for rats with both ΔI and ΔF measures (Bennett et al. 2001a, 2001b; Li et al. 2004). Because the ΔF (or ΔΙ) estimate of self-sustained firing only estimates the portion of the I_P that is above firing threshold (i.e., tip of the iceberg), the likely subthreshold activation of the I_P in small motoneurons suggests that these neurons may well have larger overall I_P, as detailed further below. Of course, we cannot determine how large the subthreshold I_P is from motor unit firing, but, interestingly, a larger I_P in smaller cells is inconsistent with earlier animals studies (Lee and Heckman 1999). However, we now show that motoneuron size (up to the midrange of sizes, see below) does not affect suprathreshold, self-sustained firing in humans, also consistent with previous animals studies (Bennett et al. 2001a, 2001b; Li et al. 2004).

Motor Units Decomposed from High-Density Surface EMG

There are an estimated 445 motor units in the TA muscle (Feinstein et al. 1955) [although potentially fewer in the older participants (McNeil et al. 2005)], and we were able to decompose 20 of them per participant, on average, from the HDsEMG using convoluted blind source separation. Because 40%, 55%, and 70% of TA motor units are thought to be recruited at 10%, 20%, and 30% of MVC, respectively (Feiereisen et al. 1997), it is possible that we were able to sample 11%, 8%, and 6% of the total population of recruited TA motor units during the three contraction levels, respectively. Given that ≈30% of TA muscle fibers are type II (fast twitch), with pockets located near the surface of the muscle (Henriksson-Larsén et al. 1983; Lexell 1997) where HDsEMG is more likely to decompose larger and superficial units (Farina et al. 2010), it is likely that we decomposed a range of both slow and fast motor units having small and large motoneurons, especially during the 30% MVC contractions where some of the fast superficial motor units may have been activated. However, it is thought that motor units across the TA muscle vary more as a continuum rather than into discrete subtypes. When HDsEMG was used to measure conduction velocity across multiple (≈40) motor units in the TA muscle, motor units recruited at 30% MVC were in the middle of the full range of conduction velocities and estimated fiber diameters (Del Vecchio et al. 2018). Although we likely sampled motor units up to the midrange of conduction velocities and motoneuron size, we did not recruit the largest and fastest motoneurons, which may have different ΔF values from the highest threshold motor units described here (Powers and Heckman 2017). Along with being able to examine multiple motor units, the ability to decompose higher threshold motor units from HDsEMG with high accuracy (≈95%) makes this technique advantageous over intramuscular EMG.

Comparison of Firing Properties of Motor Units from HDsEMG and Intramuscular EMG

The firing profiles of the TA motor units decomposed from the HDsEMG exhibited similarities to motor units isolated from intramuscular EMG activated during triangular or trapezoidal dorsiflexions, suggesting that the identification of the decomposed motor units was accurate (Enoka 2019). The fact that the uniquely and blindly identified motor units within the same contraction had firing rate profiles that were temporally modulated together also suggests that the identification of the units was accurate. This also indicated that there was shared synaptic input to all motor units (Farina et al. 2014; Negro et al. 2016b), which is important for the ΔF analysis. The start (≈8 Hz), maximum (≈15 Hz), and end (≈6 Hz) firing rates of the decomposed TA motor units were similar to the firing rates of TA motor units identified with intramuscular EMG for similar speeds (1–3% MVC/s) and magnitudes (10–30% MVC) of contraction (D’Amico et al. 2013; Stephenson and Maluf 2011; Udina et al. 2010). Motor units were also detected at recruitment thresholds of <1% MVC and >25% MVC for all participants, indicating the ability of the HDsEMG to record TA motor units of varying threshold. As discussed further below, the firing rate profiles generated from the decomposed motor units exhibited features such as secondary and tertiary range firing previously described from intracellular motoneuron recordings in response to well-controlled, triangular current injection.

Secondary Range Firing

Motor units often display a relatively steep increase in firing rate that lasts for a few seconds after the onset of a contraction (secondary range firing; Fig. 3) (Kiehn and Eken 1997; Udina et al. 2010). As shown previously for TA motor units recorded from intramuscular EMG (Erim et al. 1996), this prolonged secondary range may have increased with recruitment order of the motor units, as reflected in the increased slope of the ascending firing rate profile (Fig. 4C). Lower threshold units appeared to have a briefer period of secondary range firing compared with the highest threshold units, where in the latter, the secondary range to produce the higher ascending slopes sometimes comprised most of the ascending firing rate profile. Secondary range firing is likely due to the acceleration in membrane depolarization produced by the I_P during the onset of firing (Li et al. 2004) as depicted in Fig. 1Aiv. The potentially briefer secondary range in the lowest threshold units may be due to the I_P being activated well below firing threshold, so by the time the motoneuron begins to fire, the I_P is past its early slow onset and rapidly completing its final activation (in steep range of its I-V relation; Fig. 1Bi), giving a rapid boost to firing at recruitment (see details below). In contrast, the I_P activation is likely initiated closer to the firing threshold of the higher threshold units to produce an acceleration in discharge at motor unit recruitment over the first few seconds of firing, as the I_P is slowly activated over its full range. Typically, the secondary range in these high threshold units lasts for a few seconds, which likely reflects the known slow onset of the I_P, which in turn reflects the time it takes for the opening probability of the L-type calcium channels to slowly warm up (via channel dimerization), after which these calcium currents activate much more rapidly (leading to steep region of the I-V relation; Fig. 1B) (Binder et al. 2020).

Tertiary Range Firing

Following the secondary range, increases in the firing rate of a motoneuron in response to a continual increase in synaptic input slows down, leading to a linear low-slope (gain) region referred to as the tertiary range (Hultborn et al. 2004; Lee et al. 2003; Li et al. 2004). Tertiary range firing was most prominent in the lowest threshold motor units, because they had a proportionally shorter duration of secondary range firing. Although slowed, the firing rate of the motor units continued to increase linearly during increases in effort (synaptic input) in the tertiary range, with peak firing rates occurring near peak torque. Thus there did not appear to be a large amount of rate saturation or spike accommodation at these speeds (1–3% MVC/s) and magnitudes (10–30% MVC) of contraction. This is in contrast to firing rate profiles of TA motor units that have much weaker (<10% MVC) and slower rates of contraction (<1% MVC/s) (Revill and Fuglevand 2017) or units that are activated for longer periods of time (>10 s) at much higher levels of contraction (>30% MVC) (Erim et al. 1996). Thus use of contractions with moderately slow speeds (1–3% MVC/s) and strengths (10–30% MVC) is likely best to keep the firing rate profiles of the motor units linear with respect to their inputs, a requirement for ΔF methods, especially for the lowest threshold units that fire primarily in their tertiary range.

Despite the relatively linear tertiary range firing, the firing rates on the descending phase of the contraction jumped to a lower offset (or sag) but continued with a similar slope as on the ascending phase of the contraction, especially for the low-threshold control motor units. This sag is often observable in the firing frequency profiles of rat motoneurons in response to triangular current injections (Bennett et al. 2001a) or to sinusoidal stretch (Gorassini et al. 1999) and is a convenient marker of when the synaptic input starts to decrease during the descending phase of the contraction, occurring just after peak torque in the human data. The ionic mechanism of the sag is not known but may result from a rate (direction)-dependent effect of the depolarizing drive on spiking (Kuo et al. 2006; Norton et al. 2008), calcium and sodium I_P inactivation (Lee and Heckman 1999; Powers and Heckman 2017), or the buildup of calcium-activated potassium (SK) currents (Li and Bennett 2007). The influence of sag on the ΔF measures are discussed below.

Composite Control Unit Method to Estimate Self-Sustained Firing Produced by I_P

Because the lowest threshold units had pronounced tertiary range firing that was likely linearly related to the synaptic input profile, we exclusively used them as control units for the ΔF measures. By only using the lowest threshold units as control units, this reduced many underestimation and overestimation errors in the ΔF values as summarized below.

Floor effects.

The lowest threshold test motor units were recruited when the firing rates of their even lower threshold control unit pair were very low. Thus there was little room for the firing rate of the control unit in these cases to decrease when the test unit was derecruited. Using these lowest threshold units only as control and not test units in the composite method helped to reduce the number of very low ΔF values compared with the pairwise method (Fig. 9A).

Nonlinear firing of high-threshold units.

By only using the lowest threshold motor units as control units also helped to reduce the number of underestimated ΔF values by avoiding the use of higher threshold control units with large secondary range firing, which could underestimate synaptic inputs to the test units if they were recruited at the start of the control unit’s secondary range. This likely produced many of the low ΔF values for ΔT recruitment times that were <2 s in the pairwise method. By grouping together the lowest threshold units, the higher threshold test units were typically recruited at a later time when the composite control units were already firing in their linear, tertiary range where synaptic inputs likely were not underestimated.

Overestimation of ΔF values could also occur with the use of higher threshold control units with large accelerations and amplitudes in firing rate at the time of test unit recruitment, indicative of high input-output gain of the motoneuron (Lee and Heckman 1998a, 1999). This was avoided with the composite control method that only employed the firing rate profiles from the lowest threshold (<3% MVC) motor units as a measure of synaptic input. The ascending slope of the firing rate profiles, which was a good indicator of secondary range firing and high gain, was lower in the composite control profile (<1 Hz/s) compared with the earliest recruited higher threshold test units (>>1 Hz/s; Fig. 9B). In addition to the ascending slopes, a high-threshold control unit could have a steep decrease in firing rate (descending slope) indicative of secondary range firing during I_P deactivation. If a test unit was derecruited at this time, it could result in an artificially low estimate of synaptic input, which would also produce an overestimated ΔF (Hassan et al. 2020). These overestimations contributed to the continued variability in ΔF values at ΔT recruitment times >2 s in the pairwise method. In contrast, the shallow, linear ascending and descending slopes of the composite control firing profile occurred throughout the majority of the contraction, when all of the higher threshold test units were being recruited and derecruited, and thus avoided the secondary range nonlinearity. The firing rate slopes of the composite control units were also similar for the ascending and descending phases of the contraction to ensure that the rate of increase and decrease in depolarizing drive was the same. This is important since the rate of depolarizing drive can affect the activation of the sodium component of the I_P (Kuo et al. 2006).

Modulation Depth and ΔF

The minimum to maximum excursion in the firing rate of the composite control unit profile (modulation depth, or CMod) was larger than the ΔF values measured for the test units, especially for the 20% and 30% MVC contractions, where ΔF was typically half of the modulation depth. Thus there was enough sensitivity in the control unit firing rates to reflect changes in synaptic inputs at these higher levels of contraction. Moreover, unlike the pairwise method (see also Hassan et al. 2020; Powers et al. 2008; Stephenson and Maluf 2011), there was no relationship between ΔF and modulation depth for the composite control unit method, especially for the 20% and 30% MVC contractions. These stronger and faster contractions, unlike the 10% MVC trials, likely produced enough synaptic drive so that the composite control motoneurons had a larger excursion of firing rates with linear responses to synaptic inputs in the tertiary range while the test motor units were being recruited and derecruited. In addition, the higher threshold control units with high modulation depths (CMod) that produced equally large (overestimated) ΔF values in the pairwise method were also removed by the composite control method.

The maximum firing rates reached by some of the composite control units could level off between 20% and 30% MVC due to small amounts of rate saturation. However, the firing rate of the composite control units when the test motor units were recruited were ≈2 Hz lower than the maximum firing rates of the composite control units, where rate saturation was less likely. Thus it is recommended that contraction ramps of at least 20–30% MVC over 10 s be used to ensure the modulation depth of the composite control units does not constrain the measurements of ΔF in the test motor units.

Short Ascending Activation Times of Test Units

Another source of error in estimating the I_P values occurred in test units recruited at the top of the triangular force contractions. These high-threshold units were only activated for a couple seconds and likely did not have enough time to fully activate their I_P, and stopped firing rapidly on the descending phase of the contraction with little ΔF (Fig. 8). Animal and human studies have found a similar phenomenon, since the I_P can take seconds to fully activate (Bennett et al. 1998a; Li et al. 2004; Udina et al. 2010), potentially due to warm-up-related effects (Binder et al. 2020). These same units that exhibited a small ΔF at the top of the contraction ramp exhibited a much larger ΔF when given longer times to fire and activate their I_P in stronger contractions. Thus it is important to consider the ascending activation time of a test unit when measuring ΔF values in an individual or experimental condition as test units with low ΔF values and short activation times <2 s should be considered as a separate population, as we did here.

In summary, using a composite control unit profile containing the lowest threshold units with mainly tertiary range firing provided the best representation of synaptic input to the test motor units, and thus a more accurate measure of the self-sustained activation of the motoneuron from the I_P. Although the average ΔF did not change when only the lowest threshold units in the composite control profile were used, compared with using all possible motor units as controls in the pairwise method, the variability of ΔF values was decreased by half, which is important when comparing self-sustained firing across groups or in response to an intervention that might have a small effect size. In this study, we purposefully kept all unit pairs with short ΔT recruitment times and close ΔF and CMod values in both methods to illustrate how the composite method naturally eliminates these problematic pairings. Even so, the pairwise ΔF remained more variable compared with the composite ΔF for unit pairs with ΔT recruitment times >2s because of the overestimation of ΔF from the high-threshold control motor units, which also contributed to the ΔF-CMod correlations. Finally, the composite control motor units had very similar firing rate profiles so that only one of these control units would likely produce similar ΔF values as the entire composite profile. This needs to be studied in the future and will be important to investigate when fewer numbers of very-low-threshold motor units can be decomposed from HDsEMG, as may occur in other muscles (Del Vecchio 2020) and in children (personal observation).

Small Motoneurons May Have a Larger Subthreshold I_P Than Large Motoneurons

While the ΔF estimate alone only provides us with information about the contribution of I_P to cell firing, we next consider how changes in the secondary range might help us assess the subthreshold activation of the I_P in different-sized motor units (motoneurons). Considering our central finding that the portion of the I_P that sustains firing (ΔF) is invariant with motoneuron size, it is odd that the larger higher threshold motoneurons seem to have a more prolonged activation of the I_P after firing onset, as reflected by their prolonged secondary range inferred from the higher ascending slopes. We suggest that this is because these large motoneurons have a smaller overall I_P compared with low-threshold motoneurons, but most of it is activated above the firing threshold, including the early portion of the I_P onset that only slowly turns on due to warm-up as we detail below (Bennett et al. 1998a; Binder et al. 2020; Svirskis and Hounsgaard 1997). Specifically, during ramp contractions, the higher threshold, larger motoneurons start firing at a low frequency relative to where tertiary range firing starts (at blue dot in Fig. 11B, middle trace) and then firing increases relatively steeply but relatively slowly over 2–3 s, presumably as the I_P activates slowly over this time (green trace). This relatively slow I_P activation gives rise to a prolonged secondary range (pink shaded area in Fig. 11B), before tertiary range firing when the I_P is fully activated. Importantly, the calcium portion of the I_P takes seconds to active when it starts from its resting state, due to the slow activation of I_P warm-up (Bennett et al. 1998a; Svirskis and Hounsgaard 1997), likely via channel dimerization (Binder et al. 2020). Thus the slow activation of the I_P in high-threshold human motoneurons (and prolonged secondary range) suggests that these motoneurons are recruited mainly with their I_P starting in the resting state, and then the I_P warms up slowly over the next few seconds during firing, leading to the prolonged secondary range firing (depicted schematically by shaded pink box over I_P activation period in Fig. 11B). This also suggests that there is not an appreciable amount of I_P activation before recruitment (no downward deflection of I_P before firing), and thus the full I_P contributes to the self-sustained firing, making ΔF faithfully reflect the I_P (marked by ΔΙ, length of green arrow in Fig. 11B).

Fig. 11.

Persistent inward calcium and sodium current (I_P) activation and contribution of I_P to self-sustained firing (ΔI) in low- and high-threshold motoneurons. A, top: membrane potential (V_m) of hypothetical low-threshold (small) motoneuron (bottom) during spiking in response to triangular injected current, but used to schematically represent firing in our voluntary ramp contractions. Middle, schematic representation of the synaptic input (I_syn; downward depolarizing current) and I_P current (green trace) activated during the contraction. Purple box marks firing duration where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). A large portion of I_P is activated before cell firing, giving time for the I_P to be warmed up, so the current changes steeply at the onset of firing, leading to only a brief secondary range (light purple rectangle). Only the portion of the I_P activated after firing contributes to the ΔI (length of green arrow). Data adapted from Li et al. (2007) to schematically demonstrate the contribution of the I_P to the self-sustained firing (ΔF) and ΔI. B, top: membrane potential of hypothetical high-threshold (large) motoneuron (bottom) during spiking in response to triangular injected current, as in A; adapted from Li et al. (2007). Middle, firing duration (red box) where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). I_P (green trace) is at rest before cell firing, and this non-warmed up I_P has a slow onset, leading to a prolonged secondary range after onset of firing. The entire I_P contributes to the ΔI (length of green arrow). Overall I_P in high-threshold motoneuron is smaller than in low-threshold motoneuron, but the amount of the I_P contributing to ΔI (and ΔF) is the same.

In contrast, lower threshold, smaller human motoneurons start firing with a relatively higher initial rate, just before or directly in their tertiary range, where the I_P is nearly fully activated and with much briefer secondary range firing (depicted schematically by purple shading in Fig. 11A, middle trace), although this requires direct measurement. The I_P activation during initial firing thus appears to occur more rapidly (during steep I_P slope in Fig. 11A), within the first interspike interval or so (within <1s), leading to the high initial firing rates. In cat motoneurons, warm-up of the I_P by a prior activation (within 6 s) leads to a very similar firing pattern, with I_P activation occurring more rapidly (fully activated near recruitment), with tertiary range firing starting at or soon after recruitment and self-sustained firing still continuing well after the recruitment current (ΔΙ; see Fig. 3 in Bennett et al. 1998a). Thus low-threshold human motoneurons behave as though they are warmed up at recruitment. This is most likely due to a substantial subthreshold I_P activation (note downward deflection of I_P before firing in Fig. 11A) that gives enough time before recruitment for the I_P to warm up, potentially via calcium channel dimerization (Binder et al. 2020). When calcium channels are warmed up, they activate faster, and this leads to a steeper activation of the I_P (at left blue dot in Fig. 11A; steeper I-V relation) so that if a motoneuron is recruited during this steep region, it exhibits much briefer secondary range firing (purple shading in Fig. 11A). The briefer secondary range firing does not necessarily mean there is less I_P activated during firing; instead, the I_P is just activated faster, and cell firing is initiated closer to the end of the I_P accelerated onset. Presumably, if warm-up is indeed important for shaping I_P activation and self-sustained firing in low-threshold motoneurons, then varying the contraction speed and intervals between contractions, using previous methods (Gorassini et al. 2002b; Hornby et al. 2003), should change the degree of secondary range and self-sustained firing, a topic we intend to investigate in future studies.

While we found that the ΔF is similar in small and large human motoneurons, as was found for both ΔF and ΔI values in rats (Bennett et al. 2001a, 2001b; Li et al. 2004), a greater subthreshold I_P activation in small motoneurons suggests that overall these motoneurons may have a larger I_P since only the portion of the I_P activated during firing contributes to the ΔF (see schematic in Fig. 11). This allows the small portion of the I_P that is activated rapidly at and just after recruitment in small motoneurons (Fig. 11A) to be the same size as the entire I_P that is activated slowly during firing in larger motoneurons (Fig. 11B), yielding similar self-sustained firing (ΔF) in small and large motoneurons, though more prolonged secondary range firing in the latter. This highlights a limitation of the ΔF technique in that it can only measure the contribution of the I_P to self-sustained firing during cell firing, and any subthreshold activation of the I_P remains hidden to this measurement. Interestingly, our conclusion that small motoneurons in the human may have larger I_P is opposite to the slightly larger initial I_P peak observed in larger motoneurons of cats (Lee and Heckman 1999) and requires further study. Moreover, direct measurement of the human secondary and tertiary ranges is required to support these conclusions.

Self-Sustained Firing Duration

The SSD provides a functional measure of how much longer I_P keep the motoneuron firing after the synaptic input that initiated the firing is removed. It is not a direct measure of the amplitude of the I_P or the ΔF but only an indication of the proportion of firing that occurs during the self-sustained firing period (the latter defined as firing occurring at levels of synaptic input below that initially needed for recruitment). The amount of self-sustained firing was greater in the higher threshold units that were recruited toward the end of the ascending phase of the contraction (Fig. 10B). These high-threshold units fired briefly (2–3 s) on the ascending phase of the contraction and only had to fire for another 4–6 s on the descending phase of the contraction to produce the comparatively larger SSD values of ≈30% (here, the duration of self-sustained firing is 2–3 s). This is in comparison to the lower threshold units with longer ascending activation times, and thus reduced room to fire for very much longer beyond the synaptic recruitment level before the end of the contraction. Thus the SSD is influenced by the constraints of the triangular contraction profile (and thus not a robust indicator of I_P amplitude) but may still be a useful indication of I_P activation when only the firing rate profile of a single motor unit is being examined.

Limitations and Future Directions

While we conclude that the portion of the I_P that sustains firing is invariant across different-sized motor units up to midrange, this opens up the question of how this occurs as presumably calcium and sodium channel properties have to scale with motoneuron size to achieve this remarkable invariance. Alternatively, the ΔF method may be in some way flawed, and the onus is on future animal and computer modeling studies to sort this issue out.

Although the composite control method is an improvement over the pairwise method, some limitations remain. As mentioned in methods, the fifth-order polynomial line smoothed the firing rate profile so that the peak of the fit line was shifted to the left of the actual peak of the firing rate. However, this did not appreciably affect the estimated control unit frequency at recruitment and derecruitment of the test unit. In the future, we aim to determine a more accurate fitting method to represent the peak firing rate of the units. In addition, instead of using a best straight-line fit to measure the entire ascending and descending slope of the firing rate profile, we intend to separately identify and calculate the slopes of the secondary and tertiary ranges, using a bilinear regression fit, to more accurately measure their amplitudes and durations. The area beneath the secondary range may provide an estimate of the amplitude of the I_P during its suprathreshold activation time. Finally, we plan to examine more closely the frequency drop (sag) during the descending phase of the contraction. The sag in the composite control unit profile may affect the ΔF, but this effect may be small given that the test units also have a similar amount of sag.

General Summary

The multiple motor units decomposed from HDsEMG displayed different firing behaviors whereby the lowest threshold units fired primarily in the tertiary range indicative of appreciable I_P recruitment subthreshold to firing, whereas higher threshold units had more prolonged secondary range firing indicative of continued I_P activation after recruitment. When only the lowest threshold units were used in the composite control unit method, the firing rate profiles provided a more accurate representation of synaptic inputs to the TA motoneuron pool given the more linear and proportional relationship of firing rate to synaptic input in the tertiary range. Thus the composite control unit method avoids under- and overestimation of ΔF values that occur with the use of higher threshold control unit firing profiles with substantial secondary range firing during both recruitment and derecruitment. The composite control profiles had a large enough firing rate modulation to not constrain the ΔF values, but only when the synaptic drive was large enough in the 20% and 30% MVC trials. Contraction rates of 2% and 3% MVC/s over 10 s to these force levels did not produce appreciable firing rate accommodation or saturation. Interestingly, ΔF values were similar across test units of different recruitment thresholds that were activated by small and large motoneurons, respectively, indicating that the portion of the I_P that sustains firing is similar for all motoneurons. These conclusions could not have been reached with the large variability in the conventional pairwise unit analysis and required our new composite control method and elimination of ΔF estimation errors we have detailed. Overall, we recommend that using contraction strengths of 20–30% MVC and firing rates of the lowest threshold units likely provides the best representation of synaptic drive to test motor units for the accurate measurement of ΔF and self-sustained firing mediated by the I_P.

GRANTS

This work was supported by National Institute of Neurological Disorders and Stroke Grant R01 NS-104436 (to K.A.Q.), National Science and Engineering Grant 05205 (to M.A.G.), and postdoctoral fellowships (to B.A.) from the Women and Children’s Health Research Institute and the Neuroscience and Mental Health Institute at the University of Alberta.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

B.A., K.A.Q., and M.A.G. conceived and designed research; B.A., N.M., J.D., K.K.F., and M.A.G. performed experiments; B.A., N.M., J.D., C.K.T., F.N., D.J.B., and M.A.G. analyzed data; B.A., D.J.B., and M.A.G. interpreted results of experiments; B.A., J.D., D.J.B., and M.A.G. prepared figures; B.A., D.J.B., and M.A.G. drafted manuscript; B.A., N.M., K.K.F., C.K.T., F.N., K.A.Q., D.J.B., and M.A.G. edited and revised manuscript; B.A., N.M., K.K.F., C.K.T., F.N., K.A.Q., D.J.B., and M.A.G. approved final version of manuscript.