Fast-relaxing cardiomyocytes exert a dominant role in the relaxation behavior of heterogeneous myocardium

Abstract

Substantial variation in relaxation rate exists among cardiomyocytes within small volumes of myocardium; however, it is unknown how this variability affects the overall relaxation mechanics of heart muscle. In this study, we sought to modulate levels of cellular heterogeneity in a computational model, then validate those predictions using an engineered heart tissue platform. We formulated an in silico tissue model composed of half-sarcomeres with varied relaxation rates, incorporating single-cell cardiomyocyte experimental data. These model tissues randomly sampled relaxation parameters from two offset distributions of fast- and slow-relaxing populations of half-sarcomeres. Isometric muscle twitch simulations predicted a complex relationship between relaxation time and the proportion of fast-versus slow-relaxing cells in heterogeneous tissues. Specifically, a 50/50 mixture of fast and slow cells did not lead to relaxation time that was the mean of the relaxation times associated with the two pure cases. Rather, the mean relaxation time was achieved at a ratio of 70:30 slow:fast relaxing cells, suggesting a disproportionate impact of fast-relaxing cells on overall tissue relaxation. To examine whether this behavior persists in vitro, we constructed engineered heart tissues from two lines of fast- and slow-relaxing human iPSC-derived cardiomyocytes. Cell tracking via fluorescent nanocrystals confirmed the presence of both cell populations in the 50/50 mixed tissues at the time of mechanical characterization. Isometric muscle twitch relaxation times of these mixed-population engineered heart tissues showed agreement with the predictions from the model, namely that the measured relaxation rate of 50/50 mixed tissues more closely resembled that of tissues made with 100% fast-relaxing cells. Our observations suggest that cardiomyocyte diversity can play an important role in determining tissue-level relaxation.

Introduction

Research into physiological heterogeneities within healthy myocardium has led to novel insights into how the heart is able to coordinate contraction [1, 2, 3, 4]. Aiding these investigations are computational models that allow for rapid hypothesis testing, multi-scale incorporation of experimental data, and spatiotemporal analyses that are difficult or impossible in vivo or in vitro [5, 6, 7, 8]. These studies cover a range of species, biological scales, and stages of cardiac excitation-contraction coupling. Recently, we found evidence of cell-to-cell relaxation heterogeneity even within well-characterized macroscopic regions of myocardium [9]. The impact of this microscale heterogeneity on tissue-level mechanics remains unclear, yet understanding the link between cellular heterogeneity could have implications for myocardial aging, genetic disorders, gene therapy, and so forth.

Some clues about the source of cell heterogeneity have emerged. In our study on intrinsic cell-to-cell heterogeneity, we identified cardiac troponin I (TnI) phosphorylation as a key differentiator between fast- and slow-relaxing cardiomyocytes [9]. TnI phosphorylation at the Ser23/24 sites decreases myofilament Ca²⁺-sensitivity [10, 11], and a decrease in TnI phosphorylation has been found in failing human hearts [12, 13]. Gene expression, which along with adrenergic stimulation can alter the abundance of phosphorylated TnI in a cardiomyocyte, is known to increase in variability with age and cell population size [14, 15]. This relatively straightforward source of heterogeneity provides an opportunity to make a realistic computational model that predicts the effects of cellular relaxation heterogeneity on tissue-level mechanics.

We report here simulations showing a nonlinear relationship between the ratio of two distinct cell populations mixed together to form tissues, and the relaxation time constant of that generated tissue. To examine whether this behavior could be recapitulated in vitro, we generated engineered heart tissues (EHTs) from fast-relaxing iPSC-derived cardiomyocytes (iPSC-CMs), from slow-relaxing iPSC-CMs, and from an equal proportion mixture of the two aforementioned lines. Functional testing revealed faster relaxation in the 50/50 mixed EHTs compared to the average of the mean relaxation times of the other two groups. These experiments reveal a novel contribution of cellular heterogeneity toward tissue-level relaxation.

Methods

Computational modeling summary

The simulations in this study were based on the kinetic scheme (Fig. 1A) and equations described by Campbell et al., 2018 [16], and implemented in MATLAB (MathWorks, Natick, MA, USA). The model created by Campbell et al. incorporates force-dependent thick filament transitions and Ca²⁺-dependent thin filament activation to simulate force and length responses of a population of half-sarcomeres [16]. We utilized this framework to simulate isometric muscle twitch transients from a connected series of 100 half-sarcomeres. Model parameters for each half-sarcomere component were randomly sampled from a distribution of relaxation properties observed in a prior experimental study [9]. Two populations of fast- and slow-relaxing half-sarcomeres were mixed together in a range of proportions within the simulated muscle to predict the effects of cellular heterogeneity on tissue-level relaxation.

Figure 1. Formulation of computational model based on heterogeneous half-sarcomeres in series.

(A) Three-state kinetic scheme used to fit and simulate half-sarcomere shortening. J terms indicate fluxes between different states. The fluxes J_off and J₁ (outlined in red) were modulated to generate half-sarcomeres of varying PKA phosphorylation. (B) The Ca²⁺ transient (left) of the median RT₅₀ cardiomyocyte from the region of microscale heterogeneity was used as an input into the model of a half-sarcomere to fit to the experimental shortening record of the median cardiomyocyte (right). (C) A heatmap of the parameter space of k₁ (1.4-2.6 s⁻¹) and k_off (40-110 s⁻¹) values. Color indicates the absolute value of the difference between peak half-sarcomere shortening of a given combination of k₁ and k_off values (Peak_short,i) and the peak half-sarcomere shortening of the median RT₅₀ cardiomyocyte (Peak_short,median). The isopleth where the difference is 0 is shown in black. (D) A heatmap of the parameter space of k₁ (1.4-2.6 s⁻¹) and k_off (40-110 s⁻¹) values. Color indicates RT₅₀ (msec) of a given combination of k₁ and k_off values. The isopleth from panel C is superimposed on top of the heatmap in black. (E) The isopleth from panel D is parameterized into a function, ϕ, and plotted against the associated RT₅₀ for that value of ϕ. The inset shows a sample of half-sarcomere shortening records with different values of ϕ resulting in various RT₅₀. (F) (Left) Offset histograms of RT₅₀ to represent populations of fast- (green) and slow-relaxing (red) half-sarcomeres. (Right) 100 connected half-sarcomeres compose an isometric 'tissue', where each half-sarcomere samples its RT₅₀ from the distributions of fast and slow half-sarcomere populations as shown on the left of the panel.

Fitting the model to experimental data

In a previous study, we identified the extent of heterogeneity of relaxation rate (RT₅₀, defined as the time from peak shortening to 50% relaxation) within a macroscopic region of the adult rat myocardium [9]. The frequency of cardiomyocytes (n = 193) that exhibit a range of RT₅₀ from that region of microscale heterogeneity is shown in the green histogram on the left of Fig. 1F. The Ca²⁺ transient of the median cardiomyocyte from that distribution was used as an input into the Ca²⁺-dependent model of a half-sarcomere to fit to the shortening record of the median cardiomyocyte using a constrained particle swarm optimization (Fig. 1B). This yielded a set of half-sarcomere parameters producing the observed median RT₅₀ (Supplemental Table 1). The full description of these parameters can be found in the study that originated this model [16]. The same Ca²⁺ transient was used throughout the computational modeling.

Mimicking variable PKA phosphorylation states

Within our prior study, we identified TnI phosphorylation as a key differential between our fast- and slow-relaxing cells within the region of microscale heterogeneity [9]. Given that phosphorylation of TnI by protein kinase A (PKA) is very well characterized [17], we decided to modulate our half-sarcomere model by varying the anticipated myofilament effects of PKA phosphorylation. Two myofilament proteins are primarily affected by PKA phosphorylation: TnI and cardiac-type myosin-binding protein C (cMyBP-C) [18, 19, 20]. PKA-phosphorylated TnI decreases the sensitivity of the thin filament to Ca²⁺, thus accelerating the detachment rate of Ca²⁺ from troponin C [20]. We mimicked this modulation of Ca²⁺-unbinding by adjusting the Ca²⁺-unbinding rate constant, k_off, within the model. This rate constant is a key coefficient for the flux of available binding sites transitioning from the ON state to the OFF state, defined as

$$J_{off}=k_{off}(N_{on}-N_{bound})\left(1+k_{coop}\left(\frac{N_{overlap}-N_{on}}{N_{overlap}}\right)\right).$$ Equation 1:

PKA phosphorylation of cMyBP-C is thought to enhance the recruitment of cross-bridges to enhance force production in the myofilament [21]. We represented this enhanced recruitment of cross-bridges in our model by adjusting the transition rate of myosin heads from the OFF state to the ON state, k₁. This coefficient alters the flux of myosin as they transition from the OFF state to the ON state, defined as

$$J_1=k_1(1+k_{force}{F}_{total})M_{OFF}.$$ Equation 2:

These two fluxes, J_off (Eq. 1) and J₁ (Eq. 2), are visualized in the kinetic scheme of the model and are outlined in red (Fig. 1A). Next, we had to determine the appropriate relationship between our adjustable parameters, k_off and k₁, and a target RT₅₀ as a simulation of adjusting PKA phosphorylation. We constrained our parameter combinations to those that maintained the same peak sarcomere shortening value as the aforementioned median half-sarcomere, as there was no systematic variation of this metric in the original data set. We examined a parameter space of k₁ (1.4-2.6 s⁻¹) and k_off (40-110 s⁻¹) values to find the isopleth where peak sarcomere shortening remained constant (Fig. 1C). This isopleth was parameterized (ϕ) and projected onto the resultant map of RT₅₀ from the combinations of k_off and k₁ (Fig. 1D). In this way, we could select a desired RT₅₀ for a half-sarcomere, which corresponds to a value of ϕ that determines the unique k_off and k₁ values that will generate that given RT₅₀ (Fig. 1E). This ϕ relationship was decomposed to into a polynomial equation to be utilized in the model for determining k_off for a given RT₅₀,

$$k_{off}=(-2112233)(R{T}_{50}{)}^3+(395240)(R{T}_{50}{)}^2-(25279)(R{T}_{50})+(602.1),$$ Equation 3:

and a polynomial equation for determining k₁ from that derived k_off,

$$k_1=(1.978x{10}^{-6})(k_{off}{)}^3-(2.006x{10}^{-4})(k_{off}{)}^2+(0.01081)(k_{off})+(1.181).$$ Equation 4:

We are able to use this method to simulate a continuous spectrum of half-sarcomeres that have the same peak shortening, but differing RT₅₀ (Fig. 1E, inset).

Generating heterogeneous strips of half-sarcomeres in series

In the absence of an obvious way to reduce cell heterogeneity experimentally, we devised a method of artificially increasing it by combining two cell populations with different median RT₅₀ values. We first offset the distribution of RT₅₀ from the experimental region of microscale heterogeneity to create a 'fast' and 'slow' RT₅₀ population distribution (Fig. 1F, left). We then connected 100 half-sarcomeres in series and randomly sampled values of RT₅₀ from the fast distribution alone to generate a simulated muscle strip of 100% fast half-sarcomeres. By varying the proportion of sampling from the fast and slow populations in steps of 10% down to 0% fast half-sarcomeres (i.e., 100% slow half-sarcomeres), we could artificially change the heterogeneity of the composed tissue (Fig. 1F, right). We imposed fixed end conditions in order to simulate an isometric muscle twitch.

Maintenance and cardiac differentiation of human iPSCs

The human iPSCs used in this study were derived from T cells from an adult female patient diagnosed with hypertrophic cardiomyopathy (HCM), as well as a genome-edited derivative line. A truncating heterozygous cMyBP-C mutation was causing elongated cardiac relaxation within the patient cells. A CRISPR-knockout of the mutant cMyBP-C restored a healthy muscle relaxation phenotype when tested in engineered heart tissues (EHTs; data not shown). In this study, iPSCs were maintained as colonies on growth factor-reduced Matrigel (Corning Life Sciences, Tewksbury, MA) at a 1:60 dilution in mTESR 1 medium (Stemcell Technologies, Vancouver, BC, Canada) and passaged when 70% confluent using enzyme-free ReLeSR reagent (Stemcell Technologies). iPSCs utilized for experiments were between passages 35-55. iPSCs were differentiated into cardiomyocytes using sequential Wnt pathway modulation as previously described [22], using 12.5 μM CHIR99021 (Stemcell Technologies) for 24 h and 5 μM IWP-4 (Tocris Bioscience, Bristol, UK) for 48 h on day 3 after the start of differentiation. Subsequently, the differentiating cultures were maintained in RPMI/B27 (−) insulin (Gibco, Thermo Fisher Scientific, Waltham, MA) until day 11 when spontaneous beating was observed. Media was then changed to RPMI/B27 (+) insulin for 2 days, followed by 4 days of metabolic selection using RPMI with no glucose and 4 mM lactate [23]. iPSC-CMs were then kept in RPMI/B27 (+) insulin for at least two days before seeding into EHTs. iPSC-CMs were loaded with fluorescent nanocrystals 24 hours prior to seeing, as described below.

EHT creation

EHTs made from decellularized porcine myocardium were formed according to our previously published protocol [24, 25]. In short, 150 μm slices were cut from frozen, wild type porcine left ventricular blocks (Fig. 2A). These slices were laser-cut into rectangular scaffolds, clipped into a cassette composed of two Teflon clips within a Teflon frame, and were then decellularized. The decellularized scaffolds were incubated in DMEM (Gibco, Thermo Fisher Scientific) supplemented with 10% fetal bovine serum and 2% penicillin-streptomycin overnight. The iPSC line generated from the HCM patient and the CRISPR-knockout derivative were differentiated into cardiomyocytes (iPSC-CM) as described above (Fig. 2B). iPSC-CMs expressing the truncated cMyBP-C mutation were seeded onto decellularized scaffolds to generate 'slow-relaxing' EHTs, while CRISPR-knockout iPSC-CMs were seeded onto scaffolds to generate 'fast-relaxing' EHTs. Both lines of iPSC-CMs were thoroughly vortexed together in equal proportions to generate '50/50 mixed' EHTs. All EHTs were cultured in RPMI/B27 (+) insulin for 14 days before functional testing.

Figure 2. Process of creating engineered heart tissues with iPSC-CMs.

(A) Decellularized scaffolds were made from porcine myocardium that was cryosectioned into 150 μm slices, laser-cut into consistent rectangles, and clipped into a cassette made of Teflon. (B) iPSCs from a human patient with HCM were either differentiated into cardiomyocytes (cells containing a truncated cMyBP-C mutation) or they were gene-edited using CRISPR to knockout the mutant gene, then differentiated into cardiomyocytes. iPSC-CMs expressing the truncated cMyBP-C mutation were seeded onto decellularized scaffolds to generate 'slow-relaxing' engineered heart tissues (EHTs), while CRISPR-knockout iPSC-CMs were seeded onto scaffolds to generate 'fast-relaxing' EHTs. Both lines of iPSC-CMs were thoroughly vortexed together in equal proportions to generate '50/50 mixed' EHTs.

EHT functional testing

EHT mechanical testing was conducted as previously described by Schwan et al. [24]. Active force measurements were taken under constant perfusion of 35 ± 1°C Tyrode’s solution (containing in mM: 140 NaCl, 5.4 KCl, 1.8 CaCl₂, 1 MgCl₂, 25 Hepes, and 10 glucose; pH 7.3). EHTs were field-stimulated at a constant 100 mA over the range of 1-2 Hz, and measured at lengths ranging from culture length (0%) to 10% stretch. To capture intracellular Ca²⁺ dynamics, some EHTs were incubated in darkness for 20 min at room temperature with Tyrode’s solution supplemented with 17 μM Fura-2AM (EMD Millipore, Burlington, MA, USA), Pluronic F-127 (0.2%, Sigma-Aldrich, St. Louis, MO, USA), and with Kolliphor EL (0.5%, Sigma-Aldrich).

EHT cell tracking and fluorescent imaging

To confirm the presence and distribution of each cell type within each EHT group, fluorescent nanocrystals were loaded into each iPSC-CM line. Approximately 24 hours prior to seeding onto EHT scaffolds, the Qtracker 605 Cell Labeling Kit (Life Technologies, Carlsbad, CA, USA) was utilized to load 4 nM of 605 nm emission (red/orange) Qdot nanocrystals into the iPSC-CMs expressing the truncated cMyBP-C mutation, while the Qtracker 525 Cell Labeling Kit (Life Technologies) was used to load 4 nM of 525 nm emission (green) Qdot nanocrystals into the CRISPR-knockout iPSC-CMs. These Qdots provide a stable fluorescence and remain in the cytoplasm of live cells once absorbed, making them ideal for tracking the presence of our two cell lines in our EHTs. Immediately after functional testing, EHTs were fixed in a 4% paraformaldehyde solution for 1h at room temperature, then stored at 4°C in PBS until imaging. EHTs were stained with the nuclear stain NucBlue Live (Life Technologies) for 30 min prior to imaging. Imaging was performed on a fluorescence microscope (Leica DMi8, Leica Camera AG, Wetzlar, Germany).

Statistical analysis

Data were analyzed using MATLAB (MathWorks), ImageJ (NIH, Bethesda, MD, USA), and Prism (GraphPad Software, San Diego, CA, USA). Comparisons were conducted via one-way ANOVA test or a repeated measures ANOVA, both followed by multiple comparisons (Tukey post hoc analysis). Significance for planned comparisons was defined by a p-value below α = 0.05. Unplanned comparisons after data collection had a significance set to α_adjusted = 0.0167 after Bonferroni correction to account for 3 total post hoc comparisons of EHT RT₂₀ between groups (α_normal = 0.05). All data were presented as mean ± standard error of the mean.

Results

In this study, we investigated the implications of cellular mechanical heterogeneity on tissue-level mechanics. We ran in silico models of 100 half-sarcomeres in series to simulate a tissue-like isometric contraction. A distribution of RT₅₀ values, a metric measuring the time from peak sarcomere shortening to 50% relaxation, obtained from existing experimental data [9] was scaled to create 'fast' and 'slow' populations from which RT₅₀ behavior was randomly sampled and assigned to individual half-sarcomeres. Each simulation sampled values of RT₅₀ from these two populations in varying ratios, from 0% to 100% of RT₅₀ values sampled from the fast population (11 unique percentage categories, 20 simulations per percentage category). Individual half-sarcomere length records were produced from tissue-like simulations, and reveal complex effects of increased mechanical heterogeneity on individual half-sarcomere strain (Fig. 3A). As expected, a 50/50 mixed population model had substantially more stretch and shortening within individual half-sarcomeres than either of the mono-population models.

Figure 3. Simulations of isometric muscle with variable amounts of RT₅₀ heterogeneity.

(A) Representative length changes of 100 half-sarcomeres from simulated muscle isometric twitch for the groups of 100%, 50%, and 0% fast half-sarcomere populations. (B) Simulated muscle isometric twitch force transients normalized by peak force. Each transient is the average of 20 transient simulations for that percentage category of fast half-sarcomeres. Horizontal lines indicate 50% and 80% of the peak normalized force. (C) RT₅₀ of each percentage category of fast half-sarcomeres. (D) RT₂₀ of each percentage category of fast half-sarcomeres. Error bars indicate mean ± SEM.

Cumulative force transients from each percentage category were analyzed to predict the effects on mechanics in a heterogeneous in vitro tissue. Simulations exhibited a conserved time to peak force (TTP) and had a peak force standard deviation within 4% of the mean (Fig. 3B). Notably, the simulations predicted nonlinear behavior in both RT₅₀ (Fig. 3C) and time from peak shortening to 20% relaxation (RT₂₀, Fig. 3D). The predictions showed a steady increase in RT₅₀ that skewed lower than a linear trend between the two extreme groups, then rose sharply between 30-10% fast categories. The trend in RT₂₀ was even more skewed toward a faster early relaxation, with a sharp increase between 30-0% fast categories. These findings suggest that in a tissue composed of an equal number of cells from two populations of fast and slow RT₅₀, the fast-relaxing cells drive an overall faster-relaxing tissue twitch.

We next sought to validate the findings from our model using in vitro experiments. iPSC-CMs were derived from a patient with HCM caused by a truncated cMyBP-C mutation. These iPSC-CMs exhibited prolonged RT₅₀, thus making them a suitable 'slow-relaxing' group. CRISPR/Cas9 manipulation of the mutated cMyBP-C iPSC line was used to eliminate the mutant allele, which resulted in a cell line exhibiting a healthy RT₅₀ phenotype. This CRISPR-knockout line was designated 'fast-relaxing' compared to the unedited line.

Engineered heart tissues (EHTs) were manufactured entirely from the truncated cMyBP-C iPSC-CMs, forming slow-relaxing tissues (n = 8; Fig. 2B). Likewise, EHTs made comprised of only CRISPR-knockout iPSC-CMs formed the fast-relaxing tissues (n = 9). To artificially modulate the heterogeneity of cardiomyocyte relaxation rate within a tissue, the two iPSC-CM lines were thoroughly mixed together in equal proportions and formed the '50/50 mixed' group of tissues (n = 8).

Prior to tissue formation, each cell line was treated with the fluorescent Qdot nanocrystals with different emission wavelengths. This labeling protocol uses a targeting peptide to deliver the Qdot nanocrystals across the cell membrane and into the cytoplasm of living cells. The Qdots are retained in cellular vesicles throughout the duration of the study, and are not able to transfer to other cells except via cell division. Fluorescent microscopy following functional testing confirmed the presence of only mutated-cMyBP-C cardiomyocytes (red) in the slow-relaxing group of EHTs, and only CRISPR-knockout cardiomyocytes (green) in the fast-relaxing EHTs (Fig. 4A). Fluorescence intensity and abundance of each Qdot nanocrystal population was quantified throughout the tissues and normalized by the intensity of DAPI nuclear staining within the tissues (Fig. 4B, left). Both colors of Qdot nanocrystals were present in the mono-populated EHTs in roughly double the relative abundance compared to the 50/50 mixed EHTs following a two-way ANOVA analysis (p ≤ 0.0001 for each color). To estimate the proportion of each cell line in the 50/50 mixed EHTs, normalized fluorescence of each color of Qdot nanocrystals from each mixed EHT was further normalized by the mean normalized fluorescence of the respective mono-population EHT (e.g. red normalized fluorescence for each mixed EHT was divided by the mean normalized fluorescence of the slow EHTs). This demonstrated a ratio of ~12/13 fast/slow cell populations, with no significant difference between relative abundance (Fig. 4B, right). Altogether, these data indicate an equal presence of fast- and slow-relaxing cell types within the 50/50 mixed EHTs at the time of mechanical characterization.

Figure 4. Cell population tracking within EHTs via Qdot nanocrystals.

(A) Representative fluorescent images of each EHT group. Red indicates mutated-cMyBP-C iPSC-CMs, green indicates CRISPR-knockout iPSC-CMs, and blue is a DAPI nuclear stain. (B) (Left) Fluorescence intensity and abundance of each Qdot nanocrystal population was quantified throughout the tissues and normalized by the intensity of DAPI nuclear staining within the tissues. (Right) Normalized fluorescence of each color of Qdot nanocrystals from each mixed EHT was further normalized by the mean normalized fluorescence of the respective mono-population EHT. Statistical significance of means indicated by **** (p ≤ 0.0001). Error bars indicate mean ± SEM.

Intracellular Ca²⁺ measurements were made at the end of two weeks of tissue culture to examine the Ca²⁺-handling properties of each EHT group. In general, measuring Fura-2 emissions from EHTs using our setup can have a moderate noise-to-signal ratio, as shown by representative raw and normalized Ca²⁺ transients (Fig. 5A). Regardless, the general trends of the measured Ca²⁺-handling properties are consistent. Comparisons across all groups were made via one-way ANOVA followed by multiple comparisons using Tukey post hoc analysis. On average, time to peak Ca²⁺ (Ca²⁺ TTP) was shorter for the fast-relaxing EHTs compared to the slow-relaxing EHTs (p ≤ 0.5), with the 50/50 mixed EHTs exhibiting TTP values in between the other two groups (Fig. 5B). Though no significant differences were observed between groups for the properties of peak Ca²⁺, the decay rate of calcium from 80% of the peak (Ca²⁺ Tau₈₀), and the time to 50% decay of peak Ca²⁺ (Ca²⁺ DT₅₀), the 50/50 mixed EHTs had mean values roughly halfway between the means of the two extreme EHT groups (Fig. 5B).

Figure 5. Ca²⁺-handling properties for all EHT groups.

(A) Representative Ca²⁺ transients for the fast-relaxing, slow-relaxing, and 50/50 mixed EHTs. (Left) Raw intracellular Ca²⁺ transients measured via 340/380 nm excitation of Fura-2 loaded into the tissues. (Right) Normalized Ca²⁺ transients for all three EHT groups. (B) Comparison of Ca²⁺-handling properties across each group of EHTs (n = 6 for each group). Statistical significance of means indicated by * (p ≤ 0.05). Error bars indicate mean ± SEM.

Isometric force characteristics were also assessed in EHTs and compared between groups. EHTs were paced from 1-2 Hz and stretched from 0-10% of culture length. It is clear from representative twitch records that the 50/50 mixed EHTs more closely resembled the fast-relaxing EHTs than the slow-relaxing EHTs (Fig. 6A). There was no significant difference in peak force across the three groups, but differences were evident in twitch kinetics (one-way ANOVAs; Fig. 6B). Both EHT TTP and RT₅₀ were slower in the slow-relaxing EHTs relative to the fast-relaxing group (p ≤ 0.05). The twitch kinetic parameters of the 50/50 mixed EHTs were not significantly different from either of the other groups; however, the mean RT₅₀ of the mixed EHTs was less than the midpoint between the means of the two mono-populated EHTs. This is in agreement with our computational modeling predictions (Fig. 3C). Strikingly, the trend in EHT RT₂₀ also matched very well with the model predictions. Originally, we had only planned to measure RT₅₀ as a marker for relaxation. Following mechanical characterization, we noted a further disparity between the early relaxation phases of the 50/50 mixed and the slow EHTs. Following a one-way ANOVA using a Bonferroni post hoc correction for the threshold of significance, both the fast-relaxing EHTs and the 50/50 mixed EHTs had significantly smaller RT₂₀ values than the slow EHTs (p ≤ 0.0167). Interestingly, the more significant impact of fast cells on RT₂₀ than on RT₅₀ in the 50/50 mixed EHT is in keeping with model predictions. The 50/50 mixed EHTs had a similar Frank-Starling response (force-length response) to the fast-relaxing tissues as well, and the sensitivity of peak twitch force to length was significantly higher in these groups than in the slow-relaxing EHTs (p ≤ 0.05; Fig. 6C). The force-frequency response of the EHT groups were not different from each other. These findings suggest that a subpopulation of fast-relaxing cells drive relaxation in heart muscle, particularly early phase relaxation.

Figure 6. Isometric twitch properties for all EHT groups.

(A) Representative isometric twitch force measurements for all EHT groups, shown as raw force measurements (left) and twitches normalized to peak force (right). (B) Comparison of tissue twitch properties across each group of EHTs paced at 1 Hz at culture length. Statistical significance of means for planned comparisons indicated by * (p ≤ 0.05). Statistical significance of means for comparisons made after data collection are indicated by # (p ≤ 0.0167). Error bars indicate mean ± SEM. Horizontal dashed lines indicate the mean of slow-relaxing EHTs, the mean of fast-relaxing EHTs, and the average value between those two means. (C) Force-length and force-frequency responses across each group of EHTs. (Left) Error bars indicate mean ± SEM at each stretch length. Statistical significance of repeated measure means indicated by * (p ≤ 0.05).

Discussion

In this study we have demonstrated how cellular heterogeneity can have substantial effects on tissue-level mechanics. Results from physiologically-derived computational modeling as well as engineered tissue constructs suggest enhanced relaxation rate in mixed-population muscle, particularly in early phase relaxation. Simulations of mixed-population half-sarcomeres in series showed exaggerated displacement of sarcomeres compared to mono-populated simulations. Fluorescence imaging confirmed the presence of both populations of iPSC-CMs in equal proportions within the 50/50 mixed EHTs. Ca²⁺-handling properties in the mixed EHTs had values that were halfway between the values of the mono-populated EHTs, showing a dissociation between the differences in Ca²⁺ in the mixed EHTs and the differences in twitch kinetics. Our findings have significant implications for understanding the effect of individual cardiomyocytes on bulk tissue mechanics.

The agreement between our simulations and in vitro experiments is striking. The model is based on data from a different species of cardiomyocytes than the EHT constructs and is only one-dimensional compared to the three-dimensional EHTs, yet the RT₅₀ and RT₂₀ values of the 50/50 mixed model (Fig. 3C & D) and the 50/50 mixed EHT (Fig. 6B) exhibit the same trends. This is in spite of the fact that the model assumed the same Ca²⁺ transient for all half-sarcomeres, whereas the 50/50 mixed EHTs exhibited overall Ca²⁺-handling properties around the average of the mono-populated EHTs (Fig. 5B). This suggests the enhanced relaxation is due to a mechanical phenomenon occurring within these tissues. The fluorescent imaging confirms the presence of both cell populations within the 50/50 mixed EHTs, with even a slightly higher prevalence of the slow-relaxing iPSC-CMs than the fast-relaxing population (Fig. 4B). Both the Ca²⁺ data and the cell tracking via fluorescence microscopy support the presence of both cell populations in roughly equal proportion at the time of functional characterization. This means there is some mechanism causing this enhanced relaxation in the mixed-population tissues.

One possible explanation for this accelerated relaxation could be enhanced cross-bridge detachment due to increased strain rate. Chung et al. demonstrated this concept using isolated ventricular trabeculae and computational modeling, where they dispelled the theory that relaxation rate is primarily dependent on afterload. Instead, it is driven by end systolic strain rate [26]. Their findings built on observations of biphasic relaxation in isometrically constrained myofibrils [27, 28]. In fact, the rapid re-lengthening of a single sarcomere was shown to cause a sequential rupture of cross-bridges in adjacent half-sarcomeres that propagated in both directions along a myofibril [29]. The increased half-sarcomere strain rates seen in our 50/50 simulation compared to the 0/100 and 100/0 simulations (Fig. 3A) would support the supposition that the mixed EHTs are relaxing more quickly due to increased strain rates. Fast-relaxing half-sarcomeres (or cardiomyocytes within the EHTs) might be causing increased strain on the slower-relaxing half-sarcomeres/cardiomyocytes causing mechanically-induced dissociation of cross-bridges to force relaxation in the latter population. This could also explain the dissociation between the enhanced twitch relaxation rate in the absence of an enhanced Ca²⁺-reuptake rate observed in our EHTs (Fig. 5B), as previous studies have shown Ca²⁺ decay may not control relaxation rate as much as sarcomeric properties [30, 31].

This interpretation suggests that myocardial relaxation is primarily determined by a minority population of the fastest-relaxing cardiomyocytes within the tissue. In our simulations, early phase relaxation enhancement was observed in muscle with as little as 30% fast-relaxing half-sarcomeres (Fig. 3D). Conversely, a loss or reduction in the fastest-relaxing population of cardiomyocytes within the heart could contribute toward delayed ventricular relaxation. In normal hearts, ventricular relaxation rate tends to slow with age [32, 33, 34]. Persistent diastolic dysfunction is recognized to be an important contributor to heart failure with preserved ejection fraction [35, 36]. In rats, this increase in overall relaxation rate with age also correlates with an increase in cardiomyocyte relaxation rate heterogeneity [37]. The transition from clinically healthy or at-risk diastolic function to a heart failure phenotype may involve a loss of the fastest-relaxing cells. This suggests a restoration or replacement of that relatively small population of fast-relaxing cardiomyocytes in aged patients could slow down or prevent the onset of heart failure. Further investigation into the role of cellular functional heterogeneity in the progression of heart disease is needed.

There are some potential limitations of this study that also merit discussion. The simulated muscle strip used murine experimental data, which has notable differences to human muscle in regard to kinetics, ion channels, and myofilament protein isoforms [38, 39]. Additionally, though no significant difference was observed between the peak force of fast- and slow-relaxing EHTs, the slow-relaxing EHTs did exhibit a trend toward a higher mean peak force. The simulated muscle model did not account for the effect this might have on the contractility profile of a heterogenous muscle strip. Furthermore, the model made use of generic means for modulating relaxation rate across the population of cells, rather than a more specific mechanism. This is due in part to gaps that remain to be filled in our understanding of the phenotype displayed by the mutant patient cell line. We speculate that the patient’s truncating MYBPC3 mutation leads in some way to accumulation of excess cMyBP-C (truncated or otherwise) in the sarcomere, where it discourages relaxation through interactions with actin. Experimental work to test this hypothesis is ongoing. Ultimately, additional modeling and EHT experimentation of cardiomyocyte populations with even more disparate contractility metrics and better-defined mechanistic foundations could provide more insight into the combined effect of varied relaxation rate and varied peak force on mixed-population tissues.

Another shortcoming is the moderate noise-to-signal ratio of the Fura-2 Ca²⁺ measurements within the EHTs, which would necessitate a larger sample size than used here to detect any subtle differences in Ca²⁺-handling properties between groups. This level of noise is not exclusive to the cell lines used in this study, as these fluctuations exist across several cell lines in other studies using this EHT platform [24, 25]. Overall however, in spite of the limitations noted here, the close agreement between the rat-based computational model and the data obtained using human iPSC-CM-seeded EHTs suggests that enhancement of relaxation rate the by the presence of a relatively small proportion of fast-relaxing cells is a robust phenomenon.

Based on our observations, cardiac cell-to-cell heterogeneity plays an important role in tissue-level relaxation mechanics. Increased sarcomeric strain rate from fast-relaxation cardiomyocytes seems to increase cross-bridge detachment in early phase tissue relaxation. Both computational modeling using rat single-cell data and engineered heart tissue constructs composed of human iPSC-CMs show faster relaxation rate in heterogeneous muscle than would be expected from bulk statistical analysis. These findings have important implications for our understanding of diastolic heart disease.