Numerical Modeling Reveals Improved Organelle Separation for Dielectrophoretic Ratchet Migration

Abstract

Organelle size varies with normal and abnormal cell function. Thus, size-based particle separation techniques are key to assessing the properties of organelle subpopulations differing in size. Recently, insulator-based dielectrophoresis (iDEP) has gained significant interest as a technique to manipulate sub-micrometer-sized particles enabling the assessment of organelle subpopulations. Based on iDEP, we recently reported a ratchet device that successfully demonstrated size-based particle fractionation in combination with continuous flow sample injection. Here, we used a numerical model to optimize the performance with flow rates a factor of three higher than previously and increased the channel volume to improve throughput. We evaluated the amplitude and duration of applied low-frequency DC-biased AC potentials improving separation efficiency. A separation efficiency of nearly 0.99 was achieved with the optimization of key parameters - improved from 0.80 in previous studies (Ortiz et al. Electrophoresis 2022;43:1283–1296.) - demonstrating that fine-tuning the periodical driving forces initiating the ratchet migration under continuous flow conditions can significantly improve the fractionation of organelles of different sizes.

INTRODUCTION

Mitochondria naturally undergo fusion and fission, regulating their size and morphology. The mitochondrial fusion process is mediated by mitofusin protein 1 (Mfn1) [1], whereas the mitochondrial fission process is mediated by dynamin-related protein 1 (Drp1) [2,3]. Compromised fusion and fission lead to size differences in mitochondria [4,5] which may be an indicator of disease. Mitochondria further play a vital role in cell function as a power generator and a cellular signaling center [6,7]. Thus, assessing the size heterogeneity of mitochondria may reveal significant insights into the origin and mechanisms of diseases.

The typical size of mitochondria is approximately 300 – 600 nm, however, the size of mitochondria in cells where fusion is disturbed may be < 300 nm and surmount 1 $\mu$m when fission is compromised [8,9]. This size difference between normal and abnormal mitochondria may allow their separation and purification, enabling a thorough characterization of abnormal mitochondria via biomolecular characterization tools. However, there are currently only limited approaches for fractionating organelles with high separation efficiency and throughput. The few size-based separation techniques reported for mitochondria include free-flow fractionation [10] and capillary electrophoresis [11–13]. Dielectrophoresis (DEP) is another widely studied particle separation technique used for the fractionation of submicrometer-sized particles. DEP refers to a phenomenon of particle migration when dielectric particles experience a non-uniform electric field effectively transporting them in electric field gradients. The strength of the DEP force acting on a particle is determined by the third power of the particle radius according to classical theory [14–16]. Hence, DEP is a powerful technique for the selective manipulation of particles that has been applied from nanometer to micrometer size ranges in microfluidic platforms [16–18]. Various studies demonstrated DEP-based separation of biomolecules and (bio)particles such as bacteria [19–21], DNA [22–26], proteins [27–30], carbon nanotubes [31–33], cells [34,35], fungi [36], and organelles [37,38]. Other advantages of DEP-based particle fractionation are the non-destructive nature, and the capability of achieving high throughput by the integration of continuous flow in microfluidic platforms [39–41]. However, these techniques often suffer from cumbersome sample preparation, complicated fabrication processes, and low separation efficiency.

Previously, we reported a ratchet migration device that utilized insulator-based DEP (iDEP) and micro-posts to achieve size-based mitochondria fractionation [42]. Coupled with continuous flow injection, the tailored device can achieve high throughput separations. The size-based fractionation in the device was achieved via a selective ratchet migration mechanism, able to steer particles of different sizes in opposing directions. The ratchet migration was generated by the combination of DEP and other electrokinetic (EK) forces (electrophoretic and electroosmotic forces). These forces were induced by applying a periodic driving force through tailored electric potentials which allow the selection of size ranges affected by ratchet migration and thus induce separation between certain subpopulations.

However, the continuous flow injection in the ratchet device for processing larger sample volumes has its limitations. When the pressure-driven flow was dominating over the electrokinetic forces in the ratchet migration, the separation efficiency ($P$, following our previous nomenclature) – a measure of how effectively a mixture of particles based on size is separated – was significantly reduced and affected the purity with which organelle subpopulations can be collected [42]. This phenomenon was observed at flow rates larger than 20 nL/min [42,43]. While this is a common challenge in DEP-based particle separation studies with continuous flow [44–46], we hypothesize that the electrical driving forces can be optimized to suppress these limitations induced through continuous injection flows, sustaining higher flow rates, and consequently allowing improved high throughput separation for organelle subpopulations.

Here, we adapted the numerical model built in previous studies [42,47] to investigate the conditions of periodic driving forces to maximize the flow rates allowing high separation efficiencies and throughput. Since our previous model was in excellent agreement with observed experimental data [42,47], we based the current study on this model and focused on revealing the optimum periodic driving parameters (DC and AC amplitudes as well as the duration of the periodic driving signal) to improve separation efficiency. We focused on two particle sizes mimicking large and small mitochondria and assessed the particles collected in the outlet reservoirs of the device after separation. Our study offers a critical understanding of particle manipulation affected by both electrokinetic driving forces, dielectrophoretic trapping, and pressure-driven flow to improve ratchet separation conditions.

MATERIALS AND METHODS

Numerical Modelling

A ratchet device model was built in COMSOL Multiphysics 6.1 based on the modules and physics reported previously [42,47], see the Theory section for more detail on the ratchet mechanism. The schematic illustration of the ratchet device and its geometry used in the numerical model were shown in Figure 1. The device was composed of a main channel containing an array of microposts and two inlet channels which were split from a single inlet and connected to the center of the main channel on each side (see Figure 1A). The channel had two outlets, one on the top and bottom section of the main channel, respectively. The main channel width was 600 μm. The width of the inlet channel was 100 μm (Figure 1B). The length of the main and inlet channels were 1 mm and 500 μm, respectively. Furthermore, the corner between the inlet and the main channel was modified to be round-shaped with a radius of 50 μm to prevent the creation of high electric field regions, which could interfere with the intended ratchet migration mechanism in the post array. Additionally, the width of the particle release line was 40 μm throughout the study.

Figure 1.

A Schematic illustration of the ratchet device (not to scale). B The model geometry used in COMSOL. The main channel width was 600 μm. The inlet channel length was 500 μm and the length of the main channel was 1 mm to reduce computation time. The inset shows the electric field distribution in the device exemplarily.

The numerical model was conducted with a flow rate of 60 nL/min and the opposing ends of the geometry were defined as electrodes. The periodic driving conditions inducing the ratchet migration were applied across the main channel creating non-uniform electric field regions near the posts (see Figure 1B). The particles were released at the particle release line (red line in Figure 1B) located 30 μm before the main channel entrance. The particle properties were adapted for mitochondria of two different sizes. The particle sizes used in the simulation corresponded to the observed average size of mitochondria isolated from Drp-1 knock-out HepG2 cells and Mfn-1 knock-out HepG2 cells. These mitochondria were denoted as Drp and Mfn, respectively. Details of the numerical model were previously published [47]. The properties of the two mitochondria species used in this work is described in the next paragraph. All other parameters were the same as in the previous work [47], except that Brownian motion was not considered as it did not contribute to the separation mechanism.

Mitochondria Properties

The properties of Drp and Mfn relevant to the numerical model were their size and the EK mobility [42,47]. The average size of Drp and Mfn were 1.82 μm and 0.62 μm, respectively. The size was measured by dynamic light scattering (DLS) using a Zetasizer Ultra instrument (Malvern Panalytical Inc. Westborough, MA, USA). The measured EK mobility of Drp and Mfn were $-5.34\times {10}^{-9}$ and $-2.39\times {10}^{-9}{m}^2/(V\bullet s$), respectively, as the EK mobility was previously obtained from the migration velocity of mitochondria in a microfluidic platform with identical surface properties in the same buffer solution [42].

Particle Tracking

The main channel geometry of the device model was divided into subsections with a length of 40 μm starting after the center section of the main channel (see Figure 2). This resulted in 10 subsections each at the top and bottom section of the geometry and allowed counting the number of particles in each subsection using the particle counter function in COMSOL. The physical model of the migration mechanism is described below in detail. Based on this theoretical model, particles with electrokinetic properties and size for both Drp and Mfn mitochondria were released every 0.1 seconds (14 particles respectively per release) for 10 driving periods. After 14 driving periods, only particles that reached the subsection at the top or bottom outlet were counted to trace the particle migration, and the particle count was normalized against the total particles that reached the subsection at each outlet (>90 %). Other particles not reaching the outlet subsection due to a COMSOL artifact were neglected. After 14 periods, no significant change in normalized particle count was observed, thus, there was no need to further increase the length of the simulation.

Figure 2.

Snapshot of particles during separation as obtained from the model after 12 driving periods. The red dots represent Drp and the blue dots represent Mfn particles. Particles that arrived at the outlet subsection (red boxes on top and bottom) were counted for determining the separation efficiency.

Based on the obtained particle counts, we calculated $P$ (separation efficiency) to assess the separation quality according to Equation 1:

$$P=\frac{N_{top,Mfn}}{(N_{top,Drp}+N_{top,Mfn})}\times \frac{N_{bottom,Drp}}{(N_{bottom,Drp}+N_{bottom,Mfn})}$$ (1)

Here, $N_{top/bottom,Drp}$ was the normalized particle count of Drp at either top or bottom outlet and $N_{top/bottom,Mfn}$ was the normalized particle count of Mfn at either top or bottom outlet. A separation efficiency of unity refers to an optimized separation.

THEORY OF RATCHET MIGRATION

The mechanism of the ratchet migration was reported in our previous work (see [42,47] and associated supporting information). Similarly, particles were released into the microfluidic device via pressure-driven flow induced through pressure applied at the inlets; DEP and other EK forces were also generated to induce separation. In the post array, the electrokinetic forces were overlaid with the pressure-driven flow. As illustrated in Figure 3A, the periodic driving signal consisted of two waveforms, A and B. Waveform A represented a biased DC potential with amplitude $U_{ac1}$ and bias $U_{dc}$ that periodically reversed its polarity every half period. Waveform B represented an AC potential $U_{ac2}$ that was superimposed with waveform A during each second-half period. Waveform A induced EK migration of particles along the main channel while the sign of the biased DC potential determined the direction of particle migration. Waveform B induced nDEP trapping around the microposts where the electric field was smallest for the larger particles while the DEP force acting on the small particles was not strong enough to overcome other EK migratory forces. This model did not consider non-linear EK effects as described previously by Khair [48] or concentration polarization electroosmosis [49,50].

Figure 3.

A Components of the periodic driving conditions formed by Waveform A and Waveform B. B Illustration depicting a representative trajectory of Drp (red, large) and Mfn (blue, small) particles for two driving periods (2$t$). The migration of particles during the first half period is shown as an arrow with solid lines and the migration during the second half period as an arrow with dotted lines.

Table 1 summarizes the definitions used for the two waveforms as well as other parameters used in Figure 3A. The period, $t$, and half period, $h_t$, determined the length in which an electrokinetic force was applied to the particles. The $U_{dc}$ bias created a net migration of particles toward one direction i.e., top or bottom outlet. The strength of the DEP force in turn determined the size of the particles to be trapped. Note that $U_{ac2}$ was only applied during the second half period, which is the major factor inducing a ratchet migration mechanism. In addition, a pressure-driven flow was induced to inject particles through the two center inlets in the device. The DEP, EK, and pressure-driven forces adequately described the ratchet migration mechanism, as demonstrated in our previous work [42] and further outlined via the force calculations below.

Table 1.

Summary of the periodic driving parameters studied in the numerical model and their definitions.

Periodic Driving Parameters	Unit	Definition
$U_{ac1}$	V	DC potential amplitude of the periodic driving signal
$U_{dc}$	V	DC offset induces a biased periodic driving signal
$U_{ac2}$	V	AC amplitude of the periodic driving signal
$t$	s	Length of one full driving period
$h_t$	s	First half period of the periodic driving signal

Example particle trajectories induced by the ratchet migration for two driving periods overlaid with the pressure-driven flow are illustrated in Figure 3B, where the larger particle is represented with a red dot and the smaller particle with a blue dot. Both small and large particles migrated toward the bottom outlet in the first half period by electrokinetic forces. In the second half period, smaller particles migrated toward the top outlet due to the reversed electrokinetic force while larger particles were trapped by nDEP forces around the microposts. The region with the lowest electric field was formed at the flat surface of the microposts where the larger particles were trapped by the acting nDEP force. The periodic electrical driving eventually separated particles that were small towards the top outlet and large particles towards the bottom outlet.

Overall, the ratchet migration mechanism is a complex interplay of three major forces. Due to the post array, the forces change their magnitude and the prediction of the resulting trajectories is nontrivial. However, the essential factor responsible for continuously steering the particles into opposing directions is the trapping of larger particles in the second half of the driving period. This can only occur, if the DEP force is the dominating force, i.e. if the DEP force is larger than the other acting forces. We have therefore assessed the DEP force (${\mathit{F}}_{DEP}$), the EK force (${\mathit{F}}_{EK}$) and force due to the pressure-driven flow (${\mathit{F}}_{PD}$) for each particle size according to the following equations:

$${\mathit{F}}_{DEP}=2\pi {\epsilon }_m{\epsilon }_0{r}^{3}f\left(CM\right)\nabla {\mathit{E}}^2$$ (1)

$${\mathit{F}}_{EK}=6\pi \eta r{\mathit{v}}_{EK}=6\pi \eta r{\mu }_{EK}\mathit{E}$$ (2)

$${\mathit{F}}_{PD}=6\pi \eta r\mathit{u}$$ (3)

where ${\epsilon }_m$ is the relative permittivity of water, ${\epsilon }_0$ is the vacuum permittivity, $f\left(CM\right)$ is the Clausius-Mossotti factor, $r$ is the radius of the particle, $\mathit{E}$ is the electric field, ${\mathit{v}}_{EK}$ is the velocity of particles induced by the EK force, ${\mu }_{EK}$ is the apparent electrokinetic mobility and $\mathit{u}$ is the fluid velocity due to pressure-driven flow.

The acting forces were compared in the region of the device where the major responsible process for ratchet migration acts, namely at the flat portions of the posts, where nDEP trapping occurs. This region was used to estimate the magnitude of the three forces as listed in Table 2. As an essential signature of the underlying ratchet mechanism, ${\mathit{F}}_{DEP}$ for the smaller particles in this region is smaller than ${\mathit{F}}_{EK}$, which is to be expected, as trapping does not occur in the second half driving period for the smaller particles. Additionally, ${\mathit{F}}_{PD}$ is smaller than the EK forces, which demonstrates that pressure-driven flow does not significantly influence the separation mechanism. Furthermore, the DEP trapping forces for the larger particles dominate the EK and force due to pressure-driven flow for the larger particle. This assessment demonstrates the suitability of the chosen parameter space to optimize the ratchet mechanism, as we outline further in the Results and Discussion section to achieve optimized separation efficiency.

Table 2.

Forces acting on the small and large particles in the nDEP trapping regions of the ratchet device. Electric field and gradient values were obtained from the COMSOL model, as well as the fluid velocity (about 1 μm above the post to avoid a zero magnitude force at the wall); ${\mu }_{EK}$ (see also section “Mitochondria Properties” and $f\left(CM\right)(=-0.5)$ were from reference [42]. The electric field was obtained in the second half driving period for the case: $U_{ac1}$ = 160 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V, which was resultant from the conditions that gave te best separation efficiency (see Results and Discussion section). The flow rate applied to the inlets was 60 nL/min. The particle size reflects the mean size as obtained from the DLS measurement (see also methods section).

Force acting on the particle	Small particle (0.62 μm)	Large particle (1.82 μm)
$DEP$	$9.1\times {10}^{-15}N$	$2.3\times {10}^{-13}N$
$EK$	$4.7\times {10}^{-14}N$	$1.4\times {10}^{-13}N$
$PD$	$6.0\times {10}^{-15}N$	$1.8\times {10}^{-14}N$

RESULTS AND DISCUSSION

We developed a numerical model to investigate the optimum periodic electrical driving conditions for the ratchet migration of mitochondria in the geometry described in Figure 1. Compared to our previous work, here, we used a wider ratchet array and a narrower inlet channel. In addition, the flow rate for sample injection tripled to 60 nL/min [42]. Particle sizes were 1.82 μm (Drp) and 0.62 μm (Mfn) which represent mitochondria with abnormal fission and fusion in HepG2 cells. The effect of each electrical driving parameter (outlined below) was explored by counting particles that reached the top and bottom outlets and represented as normalized particle counts of both particle sizes (see Figures 4 and 5). Moreover, the separation efficiency, $P$, of each corresponding condition was derived and summarized in Figures 4 and 5.

Figure 4.

Normalized particle count (top and middle panels) and $P$ (bottom panels) as a function of amplitudes used in the COMSOL simulation. A. DC potential amplitude variation (100, 130, and 150 V). B. AC potential amplitude variation (800, 1000, and 1200 V). C. DC offset variation (10, 15, and 20 V). Blue and red bars refer to Mfn and Drp mitochondria, respectively.

Figure 5.

Normalized particle count (top and middle panel) and $P$ (bottom panel) as a function of the length of the driving period used in COMSOL. A. Variation of the duration of the full driving period (8, 10, and 12 s). B. Variation of the duration of the first half driving period (3, 4, and 5 s) for $t$ = 8 s. Blue and red bars refer to Mfn and Drp mitochondria, respectively.

We based the choice of studied parameters on our previous work [42], where a higher magnitude of the applied $U_{ac1}$ and lower magnitude of the $U_{dc}$ bias resulted in improved separation efficiency. Further, the duration of each half period determines the length of particle migration in one direction. Therefore, we explored the lengths of the period $t$ and half period $h_t$ to further improve $P$. In addition, to induce the ratchet effect, larger mitochondria (Drp) must experience DEP trapping. We anticipate that a lower $U_{ac2}$ amplitude is necessary to induce DEP trapping (due to their increased size) and thus evoke the ratchet effect on Drp. We therefore also explored the amplitude of $U_{ac2}$ for optimized separation efficiency of the Mfn and Drp mitochondria.

Summarized in Figure 4 are the studied parameters for $U_{ac1},U_{dc}$, and $U_{ac2}$. According to Figure 4 A, the normalized particle count of Mfn (small mitochondria) at the top outlet was increased (from ~ 0.6 to ~0.8) as $U_{ac1}$ was augmented while the number of Drp (large mitochondria) at the bottom outlet remained nearly constant, i.e., nearly all Drp particles migrated toward the bottom outlet. Higher $U_{ac1}$ generated a stronger EK force that created stronger biased migration of Mfn toward the top outlet. Since the larger Drp were trapped by the DEP force in the second half period, even for increasing $U_{ac1}$ the ratchet migration was only marginally affected for Drp. Overall, as $U_{ac1}$ increased, $P$ was increased from 0.70 to 0.81 with the highest value for $U_{ac1}$ = 150 V.

Figure 4 B demonstrated that a higher $U_{ac2}$ increased the number of Mfn counted at the bottom outlet (from a normalized particle count of ~0.25 to ~0.35). $U_{ac2}$ determined the strength of the DEP force on the particles which is proportional to the particle size, thus, higher $U_{ac2}$ generated a higher DEP force which was strong enough to trap both Mfn and Drp. As a result, a significant number of both Drp and Mfn mitochondria migrated toward the bottom outlets as they were repetitively trapped in the second half period. Thus, Figure 4B demonstrates that $P$ can be improved with low enough $U_{ac2}$ to only induce DEP trapping of the roughly three times larger Drp. In summary, as $U_{ac2}$ was decreased from 1200 V to 800 V, $P$ gradually increased from 0.75 to 0.81. It is interesting to note that the case of $U_{ac2}$ = 800V is similar to the one considered for the force calculation outlined in the Theory section. While our calculations revealed a larger DEP force for the larger particle, it resulted only in a two-fold larger value compared to the EK force. This fact underlines that the ratchet migration mechanism is based on a subtle interplay of all EK forces and that even small force differences are sufficient to induce it. It is somewhat counterintuitive that a larger $U_{ac2}$ amplitude resulted in a lower $P$, as shown in Figure 4B, which justifies the detailed parameter study, as presented here.

Larger $U_{dc}$ created a bias in the net migration of analytes, however, a stronger bias did not result in better separation as shown in Figure 4 C. Varying $U_{dc}$ did not show a clear trend, instead, there was an optimum value of $U_{dc}$. The highest normalized particle count of Mfn at the top outlet (~0.8) was observed when $U_{dc}$ was 15 V. The number of Mfn was lowest at the top outlet when $U_{dc}$ = 10 V ($P$ was lowest), however, nearly an equal number of Mfn was counted at both outlets due to the weak strength of the net migration force. When $U_{dc}$ was ≥ 15 V, the net force acting on analytes was strong enough to induce net migration of Mfn toward the top outlet. Overall, $P$ was highest (0.81) when $U_{dc}$ = 15 V.

The parameters determining the duration of a driving period were also important as they determined the length of particle migration toward a certain direction. According to Figure 5 A, shorter $t$ slightly favored the migration of Mfn toward the top outlet as the normalized particle count of Mfn was highest (~0.8) when $t$ = 8 s. While nearly all Drp was transported toward the bottom outlet in all conditions, the number of Mfn at the top outlet slightly increased as $t$ decreased from 12 s to 8 s (from ~0.7 to ~0.8). This can be explained by shorter $t$ reversing the direction of force more frequently and restricting the effect of pressure-driven flow (maximizing the effect of ratchet migration), thereby, allowing particles to migrate toward the desired direction (Drp to the bottom outlet and Mfn to the top outlet). Overall, $P$ increased as $t$ was shortened from 12 s to 8 s.

Lastly, according to Figure 5 B, pure Drp was collected at the bottom outlet when the first half period was shorter than the second half period ($h_t$ = 3 s when $t$ = 8 s). In the second half period, the direction of particle migration induced was toward the top outlet while Drp was trapped by the acting DEP force. The longer second half period generated a suitable EK force which was strong enough to transport all Mfn toward the top outlet, and for some Drp (~0.3 in normalized particle count) to overcome the DEP force. Subsequently, Drp migrated toward both outlets, unlike the other conditions for $U_{ac1},U_{dc}$ and $U_{ac2}$ summarized in Figures 4 and 5A. Additionally, the longer first-half period ($h_t$ = 5 s when $t$ = 8 s) failed to create biased migration of Mfn toward the top outlet. Instead, Mfn migrated toward both outlets uniformly. A shorter second-half period could not generate sufficient DEP force to trap Drp to induce a separation, which provided the lowest $P$ (of 0.64).

Moreover, Figure 5 B showed a unique trend of particle purity at each outlet between $h_t$ = 3 and 4 s. The purest Drp fraction was observed at the bottom outlet when $h_t$ = 3 s and the purest Mfn fraction was observed at the top outlet when $h_t$ = 4 s, while the purity at the opposite outlet was comparably poor. Based on this, there must be an optimum value between $h_t$ = 3 and 4 s that enables higher $P$ of particles at both outlets.

According to the findings presented in Figures 4 and 5, the highest $P$ achieved was 0.81 with the condition: $U_{ac1}$ = 150 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800V, $t$ = 8 s, and $h_t$ = 4s. Furthermore, Figures 4 and 5 identified three key parameters, $U_{ac1},U_{ac2}$ and $t$, which were most effectively improving $P$. The trend generally observed showed that a higher $P$ was achieved as $U_{ac2}$ and $t$ were decreased, and $U_{ac1}$ was increased. However, there was a limitation in lowering $U_{ac2}$. If $U_{ac2}$ was too low, the induced DEP force became too weak to trap large particles. Hence, the key parameters which were capable of effectively improving $P$ were $U_{ac1}$ and $t$.

We, therefore, studied the influences of $U_{ac1}$ and $t$ in more detail and summarized the findings in Figure 6. In addition, the optimum value of $h_t$ was further assessed since there was an indication of an optimum value of $h_t$ between 3 and 4 s as mentioned above. Condition 1 shows the trend of $P$ as $t$ varied from 4 to 10 s (increment of 2 s) for $U_{ac1}$ = 150 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800V, where the half periods had the same length (black symbols in Figure 6). The electrical driving parameters for this condition were chosen based on the highest $P$ (0.81) in Figures 4 and 5. This study showed that shorter $t$ further improved $P$ (~ 0.92 when $t$ = 4 s), which could be due to the less pronounced influence of the pressure-driven flow as $t$ was shorter.

Figure 6.

Further study to improve $P$. Condition 1: $U_{ac1}$ = 150 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V, $t$ = 8 s (for 14 periods), and the ratio of each half period were 1:1; Condition 2: $U_{ac1}$ = 150 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V, $t$ = 8 s (for 14 periods), and the ratio of each half period were 1:1.3.; Condition 3: $U_{ac1}$ = 160 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V (at 10 kHz), $t$ = 8 s (for 14 periods). The ratio of each half period was 1:1.3.

Next, Condition 2 investigated varying $t$ but different lengths of the two half periods ($h_t$) while other parameters remained unchanged from Condition 1. To optimize the duration of $h_t$, it was varied from 3 s to 4 s while keeping $t$ = 8 s. It was found that the condition $h_t$ = 3.5 s provided the best $P$, which also corresponded to a ratio, $r$, of 1:1.3 for the two half periods with the second half period amounting to the larger value (data not shown). This ratio was thus employed in Condition 2 for varying the length of $t$. As depicted in Figure 6, an asymmetry in the two half periods as studied with Condition 2 could improve the separation efficiency further approaching a value of 0.98 for the smallest period tested ($t$ = 4 s).

Lastly, as a higher $U_{ac1}$ improved $P$, we further increased $U_{ac1}$ to 160 V and studied $P$ while other conditions remained the same as Condition 2. This was plotted in Figure 6 as Condition 3 ($U_{ac1}$ = 160 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800V $r$ = 1:1.3, green symbols). These parameters further improved the separation efficiency for all period lengths studied. Overall, as summarized in Figure 6, $P$ was significantly improved by shorter $t$, higher $U_{ac1}$ and the optimum length of $h_t$.

In conclusion, one of the most effective periodic driving parameters to improve the separation efficiency at higher injection flow rates (60 nL/min) was the period length $t$. Figure 6 demonstrates that for Condition 3 at $t$ = 4 s the maximum $P$ of ~ 0.99 was achieved ($U_{ac1}$ = 160 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V at 10 kHz, $t$ = 4 s, $r$ = 1:1.3 ). We believe that the reason behind this observation is related to shorter $t$ with the concomitantly optimized length of $h_t$ leading to reversing the migration direction of particles after migrating them for a defined period in one direction, so that the selectivity towards one reservoir is optimized for a particular particle size. Consequently, these parameters remarkably weakened dominating pressure-driven flow effects as used here through the continuous injection, even at three times higher inlet flow rates compared to previous continuous ratchet separation [42].

CONCLUDING REMARKS

The separation of normal and abnormal mitochondria defined by size differences motivated this detailed numerical study to understand the effectiveness of driving parameters and pressure-driven flow in a ratchet-based migration device. The particle sizes employed here were based on experimentally obtained mean size distributions from genetically modified mitochondria, with compromised fusion (Mfn) and fission (Drp). To further improve the throughput for organelle fractionation, we explored the optimum condition to minimize the detrimental effects of pressure-driven flow to maximize the ratchet migration mechanism and thus separation. This study identified $t,U_{ac1}$ and $h_t$ as the key parameters which were most effectively improving $P$. The result confirmed that shorter $t$ with higher $U_{ac1}$ and slightly longer $h_t$ in the second half period successfully improved $P$. Based on this study, the highest $P$ of 0.99 was achieved with the condition: $U_{ac1}$ = 160 V, $U_{dc}$ = 15 V, $U_{ac2}$ = 800 V at 10 kHz, $t$ = 4 s, $r$ = 1:1.3. These conditions were found at three times higher flow rates compared to previous studies [42], suggesting there is a potential for scaling up to higher throughput organelle separations while maintaining optimized $P$ within these ratchet devices. Furthermore, the study suggests that fractionation of particles of a specific size from a mixture is possible with this ratchet mechanism by modifying the length of $h_t$.

In summary, we demonstrated that separation based on the presented ratchet mechanism in combination with continuous flow injection has the potential to effectively separate binary particle populations. Future experiments will help evaluate the optimum condition obtained from this numerical model. We further hypothesize that various geometric modifications of the ratchet device, such as asymmetric channel length or micropost size in the top and bottom sections of the device will lead to further improvements of this fractionation device with even higher injection flow rates. Increasing the volume of channels, which minimizes the flow velocity with even higher volumetric flow rates, in combination with asymmetric channel geometry features can also enhance the net ratchet migration, thereby improving $P$. The presented numerical study also suggests that similar ratchet-based separation approaches may be developed for other bioparticles with known electrokinetic and dielectrophoretic properties. Suitable candidates for such separation approaches include organelle types [51–53], extracellular vesicles, bacteria, and viruses.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.