Potential impacts of the cardiac troponin I mobile domain on myofilament activation and relaxation

Abstract

The cardiac thin filament is regulated in a Ca²⁺-dependent manner through conformational changes of troponin and tropomyosin (Tm). It has been generally understood that under conditions of low Ca²⁺ the inhibitory peptide domain (IP) of troponin I (TnI) binds to actin and holds Tm over the myosin binding sites on actin to prevent crossbridge formation. More recently, evidence that the C-terminal mobile domain (MD) of TnI also binds actin has made for a more complex scenario. This study uses a computational model to investigate the consequences of assuming that TnI regulates Tm movement via two actin-binding domains rather than one. First, a 16-state model of the cardiac thin filament regulatory unit was created with TnI-IP as the sole regulatory domain. Expansion of this to include TnI-MD formed a 24-state model. Comparison of these models showed that assumption of a second actin-binding site allows the individual domains to have a lower affinity for actin than would be required for IP acting alone. Indeed, setting actin affinities of the IP and MD to 25% of that assumed for the IP in the single-site model was sufficient to achieve precisely the same degree of Ca²⁺ regulation. We also tested the 24-state model’s ability to represent steady-state experimental data in the case of disruption of either the IP or MD. We were able to capture qualitative changes in several properties that matched what was seen in the experimental data. Lastly, simulations were run to examine the effect of disruption of the IP or MD on twitch dynamics. Our results suggest that both domains are required to keep diastolic cross-bridge activity to a minimum and accelerate myofilament relaxation. Overall, our analyses support a paradigm in which two domains of TnI bind with moderate affinity to actin, working in tandem to complete Ca²⁺-dependent regulation of the thin filament.

1. INTRODUCTION

Cardiac troponin I (TnI) acts as a molecular switch for the activation of the cardiac thin filament by coupling Ca²⁺ binding to troponin C (TnC) with the azimuthal movement of tropomyosin (Tm) on the surface of the actin filament. This displacement of Tm reveals the myosin binding sites on the surface of actin, allowing a cross-bridge to form and resulting in force generation (for full review, see Tobacman et al[1]).

Previously, the inhibitory peptide (IP) of TnI was thought to be its dominating regulatory domain. At low Ca²⁺, the IP is bound to the actin filament, stabilizing Tm in position over the myosin binding sites[2], [3]. When Ca²⁺ binds to TnC, a conformational change reveals a hydrophobic patch on its N-terminal lobe. The TnI switch peptide (SP) has a high affinity for this patch, leading to binding of the SP to TnC. The binding of the SP encourages dissociation of the IP from actin[4], which in turn removes the barrier for Tm to shift off the actin binding sites.

More recent studies have introduced the idea that the TnI C-terminal mobile domain (MD) could act as a second site of Ca²⁺-dependent regulation[5]. Although most of the MD is intrinsically disordered[6]–[8], various studies (some recent) offer structural evidence that this region binds to actin[9]. Studies have shown that truncation of the MD results in measurable changes to myofilament Ca²⁺ regulation such as an increase in Ca²⁺ sensitivity[10]–[12] and a decrease, but not elimination of, TnI’s ability to turn off diastolic thin-filament sliding[13].

If there are indeed two domains of TnI that interact with actin in a Ca²⁺-dependent, inhibitory manner, this would have direct implications on our understanding of the Ca²⁺ switch mechanism of the thin filament. In particular, the protein-protein affinity of these regulatory interactions could be drastically different than what might be supposed if the same regulatory function were to be played by a single actor. In other words, the binding affinity of the IP for actin may have been significantly overestimated in previous thin filament models. Our goal in this study was to integrate the available structural information on regulatory domains into a single model. We subsequently used the new model to conduct a quantitative exploration of the consequences that might be expected from the introduction of joint thin filament regulation by IP and MD domains of TnI. Furthermore, the model was used to reproduce in a qualitative manner the functional consequences resulting from disruption of the IP and MD domains of TnI. This ultimately led to insights into the relative binding affinities of the IP vs the MD domains to actin and their roles in regulating cardiac twitch dynamics.

2. METHODS

2.1. Model Design Background

Cardiac thin filament activation is composed of a very complex switch system that involves conformational changes in multiple interacting proteins. We began by considering a new representation of the cardiac thin filament regulatory unit (RU). Each RU consists of 7 actin monomers, 1 Tm, and 1 troponin complex (Figure 1A). Several previous models have taken into account the different states of the thin filament RUs as they relate to Ca²⁺ binding to TnC and the shifting of Tm on the actin surface[14]–[18]. The N-lobe of TnC can be in two states, Ca²⁺ bound or Ca²⁺ unbound, and the Tm can be in three states, blocked (B), closed (C), and open (M)[19], [20]. The B state occurs when TnI is inhibiting the thin filament by keeping Tm positioned over the myosin binding sites. The C state describes a conformation in which TnI has dissociated from actin and Tm has shifted to reveal myosin binding sites. The M state occurs when myosin binds actin, further displacing Tm. In earlier work, we formulated a model of thin filament activation based on these three regulatory states of the thin filament, while also incorporating interactions among neighboring regulatory units via Tm overlap [16]. The model was subsequently expanded to explicitly represent the release of the IP from actin [17] and later to include a more mechanistic and succinct representation of nearest-neighbor Tm interactions.

Figure 1: Model Schematic.

(A) Diagram showing the schema of thin filament structure used to formulate the model; (B) Simplified regulatory unit (RU) with the protein domains relevant to this model: N-lobe of TnC, inhibitory peptide, switch peptide, and mobile domain of TnI, actin filament, tropomyosin, and myosin; (C) Allowed states for each protein domain and their binary encoding in the model; (D) Representative loops from within the Markov chain diagram showing microscopic reversibility of the biasing constants λ, η, and μ; (E) Full Markov chain models for the 16-state and 24 -state models. Transitions with biasing constants applied highlighted in red (λ), green (η), and blue (μ). * some transitions in 24-state model omitted from diagram for clarity; (F) Example of coupled RUs in series in various states to form a thin filament. RUs 1 and 26 remain fixed in the initial state, and neighboring RUs are coupled through Tm position.

Here, we have further expanded the model to include explicit representations of the domains of TnI and their interactions with other thin filament proteins. This model represents the IP, residues 137–148, the SP, residues 149–160, and the most C-terminal end of the MD, residues 193–210 [9], [21], [10]. Specifically, the SP of TnI can exist bound or unbound to the N-lobe of TnC and the IP of TnI can exist bound or unbound to the actin filament. By setting a restriction that Tm cannot transition from B → C without IP release from actin, this produced a 16-state model (Figure 1E). To explore the effect of the MD acting as a second regulatory domain of TnI, we expanded the model again to include the MD which can exist bound or unbound to actin (Figure 1C shows possible states of each domain). This five-component system also included a restriction that Tm cannot transition from B → C without both IP and MD being released from actin. Application of these rules produced a 24-state model (Figure 1E).

In order to impart regulatory behavior to this model, some transitions were made to have a different probability of occurring depending on the position of each domain and its relationship within the switching mechanism. To incorporate these relationships into the model, we applied biasing constants to some of the kinetic rates of the transitions. The λ scaling constant is used to represent coupling between Ca²⁺ binding to TnC and the binding of the TnI SP to TnC. When Ca²⁺ is not bound to TnC, the SP is very unlikely to bind due to the closure of the hydrophobic patch on TnC. On the other hand, the presence of a bound Ca²⁺ ion to TnC stabilizes the SP in complex with TnC, presumably making it less likely to dissociate[22]. Accordingly, λ is chosen to be less than 1 to reflect this dual inhibitory action which discourages any state in the scheme in which the SP would be bound to TnC in the absence of TnC-bound Ca²⁺. The η and μ scaling constants represent the proximity relationship between the regulatory domains (IP and MD) and the SP. Due to the adjacency of these regions, a movement of one may impact the probability of transition of the other. For example, when the SP binds to TnC, it presumably encourages the IP to release from actin. Conversely, when the IP dissociates from actin, we assume that SP binding to TnC is enhanced due to greater mobility of that domain. As such, μ and η were chosen to be greater than 1. This relationship creates an indirect way by which actin binding affinity of IP and MD can be influenced by SP-TnC binding affinity. Biasing constants were incorporated into the model in such a way that microscopic reversibility is satisfied, namely such that the product of rate constants in one direction around a loop equals the product of rate constants around the same loop going in the opposite direction (Figure 1D).

The individual RU models described above (Figure 1E) were in turn embedded in a previously described model of the thin filament, with cooperative coupling between nearest-neighbor RUs[18]. In this scheme, a constant, γ, represents effective stiffness of the chain formed by Tm-Tm overlap that couples adjacent RUs. At γ = 0, the Tm cooperativity of the system is turned off. As γ increases, the weight with which the position of a Tm influences its neighbor increases.

2.2. Markov chain-Monte Carlo simulations

We used a Markov chain-Monte Carlo model to simulate the simultaneous behavior of 26 RUs coupled to form a representative cardiac thin filament during activation (Figure 1F). In order to track the many protein states during simulations, we devised a compact and memory-efficient binary number representation. For the 24-state model, the state of an RU at a given time step (Z_j) was recorded as a 10-bit binary number, with 4 bits encoding the binding of Ca, SP, IP, and MD, 2 bits encoding the Tm position (B, C, M), and 4 bits encoding the Tm positions of the left and right nearest neighbor (LNN, RNN) RUs. The state of TnC, the SP, the IP, and the MD were recorded as 0 or 1, while the state of Tm was recorded using 2 bits for each of its three possible states (Figure 1D). For the 16-state model, the state of an RU at a given time step was recorded as a 9-bit number. It follows the same pattern as the 24-state model but with the removal of the bit encoding the MD.

The initial state of each RU at t = 0 for both steady-state and kinetic simulations was set to have Ca²⁺ and SP unbound from TnC, IP and MD bound to actin, and Tm in the blocked position. To represent deletion of a regulatory domain (in certain simulations), the initial state was set such that only the included regulatory domain was bound (Figure 1E). The scheme of bit encoding, as well as examples of binary numbers representing RU initial conditions are as follows:

$$Z_j=\left[SPIPMDT{m}_{B\leftrightarrow C}T{m}_{C\leftrightarrow M}CaT{m}_{B\leftrightarrow C,LNN}T{m}_{B\leftrightarrow C,LNN}T{m}_{C\mapsto M,RNN}T{m}_{C\leftrightarrow M,RNN}\right]$$

$$\text{Initial}\text{state}\text{with}\text{both}\text{domains:}{Z}_{j_{t=0}}=\left[0110000000\right]$$

$$\text{Initial}\text{state}\text{with}\text{both}\text{domains:}{Z}_{j_{t=0}}=\left[010000000\right]\text{or}\left[001000000\right]$$

To progress the simulation over time, the simulation was broken down into time steps of width Δt, during which a random number r ∈ (0,1) was generated and compared to a set of transition probabilities for the current state. The random number generation was randomly-seeded for each simulation. Transition probabilities are computed by $P_{k_i}=k_i\Delta t$, where k_i is the kinetic rate of transition for one of n possible transitions from the current state. Each state has between 3–4 possible transition for the 16-state model, and 3–5 possible transitions for the 24-state model.

For example, consider an RU that starts in the initial state of the 24-state model. It has n = 4 possible transitions: the SP could bind to TnC, Ca²⁺ could bind to TnC, the IP could release from actin or the MD could release from actin. The probabilities for these are:

$$\begin{gathered} P_1=k_{SP}^{+}\Delta t \\ {P}_2=\left[C{a}_{cytesolic}^{2+}\right]k_{Ca}^{+}\Delta t \\ {P}_3=k_{IP}^{-}\Delta t \\ {P}_4=k_{MD}^{-}\Delta t \end{gathered}$$

The algorithm determines which domain of the RU will transition using the probabilities:

$$transition=\{\begin{array}{cc}SPbinds& 0<r<P_1\\ Cabinds& P_1<r<\left(P_1+P_2\right)\\ IPreleases& \left(P_1+P_2\right)<r<\left(P_1+P_2+P_3\right)\\ MDreleases& \left(P_1+P_2+P_3\right)<r<\left(P_1+P_2+P_3+P_4\right)\\ notransition& \left(P_1+P_2+P_3+P_4\right)<r<1\end{array}$$

This creates a range of probability for each possible transition and leaves a range for no transition to occur at the time step. The algorithm was designed to use a Δt such that no RU state has more than a 50–70% cumulative probability of transitioning to a different state at any given time step. The Δt for these simulations were on the order of 10⁻⁵ to 10⁻⁶ seconds but varied by parameter set in order to guarantee numerical convergence.

If a transition is selected for completion, the algorithm switches the bit of the corresponding domain to update the state of the RU to the new state. This occurs for each RU at that time step, then repeats for each Δt for the length of the simulation. At the beginning of each time step, nearest neighbor Tm states are updated for each RU. The RUs at each end of the thin filament (RU position 1 and 26) were set to the initial state and not permitted to transition to act as set boundary conditions.

When a RU transitions into a state where Tm is in the M state it is recorded as a force-producing event (Figure 1E). For each time step, force is calculated by:

$$F_t=\sum _{j=1}^N{F}_j,F_j=\{\begin{array}{l}0Z_j=[xxxx0xxxxx]\hfill \\ 1Z_j=[xxxx1xxxxx]\hfill \end{array}$$

To get meaningful results from the stochastic model, the simulation time course was repeated H times. The final average force ($\overline{F}$) at each time step was calculated as:

$${\overline{F}}_t=\frac{1}{h}\sum _{h=1}^H{F}_{h,t}$$

where F_h,t is the force at time step t for the hth simulation repetition. For these simulations, H = 1920 repetitions. This was selected to reduce noise and ensure convergence (Figure 2).

Figure 2: Comparison of steady-state convergence.

(A) Average force plotted over time at $\left[C{a}_{cytosolic}^{2+}\right]$ ranging from 7.5 to 4.5. Data shown for repetitions ranging from 32 to 1920. (B) Overlay of the average steady-state force values for each of the 6 simulations from A. ● used for output of model, ▬ used for fit of Hill equation.

The model was scripted, and post-processing was done in MATLAB, while the Markov chain-Monte Carlo algorithm was implemented in CUDA C++ for parallel processing. Simulations were executed on an Nvidia GeForce RTX 2080Ti graphics processing card.

2.3. Simulations

Simulations were run for two scenarios: constant $\left[C{a}_{cytosolic}^{2+}\right]$ to observe steady-state force production, and a $\left[C{a}_{cytosolic}^{2+}\right]$ transient to produce isometric twitch data. Steady-state force at various $\left[C{a}_{cytosolic}^{2+}\right]$ was obtained by simulating a 10 second interval, ensuring attainment of steady-state conditions. The steady-state force was determined by averaging force over a window of the final 25% of each simulation. Steady-state force values at different $\left[C{a}_{cytosolic}^{2+}\right]$ were used to produce force-pCa plots which were fit using the Hill equation. To compare behavior of the 16-state model with the 24-state model, parameters were optimized in the 24-state model to produce steady-state force-pCa curves at γ = 0 such that curves were completely overlapping, while keeping the binding affinity equilibrium of the IP and MD equivalent (Table 1 Sets 2 and 3). With this starting point, γ was increased from 0 to 90 for each model to analyze changes to minimum and maximum force, pCa at 50% of maximum force (pCa50), and Hill coefficients (n_H).

Table 1. Parameter set used in simulations.

(Set 1) 16-state model parameters; (Set 2) 24-state model parameters for overlap with the 16-state model. (Set 3) 24-state model parameters used to fit experimental data.

Parameter	Set 1	Set 2	Set 3
$k_{Ca}^{+}\left(\mu M^{-1}{s}^{-1}\right)$	275	275	275
$k_{Ca}^{-}\left(s^{-1}\right)$	1575	1575	1575
$k_{SP}^{+}\left(s^{-1}\right)$	225	45	225
$k_{SP}^{-}\left(s^{-1}\right)$	292.5	292.5	292.5
$k_{IP}^{+}\left(s^{-1}\right)$	1777.5	888.75	1777.5
$k_{IP}^{-}\left(s^{-1}\right)$	225	446	225
$k_{MD}^{+}\left(s^{-1}\right)$	-	888.75	1462.5
$k_{MD}^{-}\left(s^{-1}\right)$	-	446	225
$k_{\text{ref}}^{BC}\left(s^{-1}\right)$	675	675	675
KBC	2	2	2
fXY(S−1)	225	225	225
δ	0.48	0.48	0.48
λ	0.0001	0.0001	0.0001
η	16	10.25	16
μ	-	10.25	16
γ(mol−1kJ)	0 – 90	0 – 90	70

Experimental data from Kozaili et al[23] and Ghashghaee et al[10] was used to compare steady-state activation of systems with replacement of the IP with a linker sequence and truncation of the MD, respectively. Parameters were optimized based on the behavior of these experimental data sets (Table 1 Set 3). We used change in pCa50 (ΔpCa50) between wild-type and disrupted regulatory domain (IP linker or MD truncation) as our main metric for fitting our model parameters. The ΔpCa50 for the experimental data sets was estimated by subtracting the mean pCa50 between sets and summing the respective SEM from each set to estimate an aggregate error range. Twitch data was run by allowing the system to reach steady-state at diastolic $\left[C{a}_{cytosolic}^{2+}\right]$ of 0.1 μmol. The $\left[C{a}_{cytosolic}^{2+}\right]$ was then allowed to produce a transient by increasing up to 1 μmol based on data from Stull et al[24].

3. RESULTS

We first set out to compare thin filament activation behavior between the 16-state and 24-state models. The goal was to seek any intrinsic differences that might arise from assuming two TnI-actin binding sites rather than one. As a starting point, we sought parameter sets that produced overlapping force-pCa curves from the respective models in the absence of cooperative Tm interactions (γ = 0). Subsequently, γ was increased to compare behavior under increasing Tm cooperativity. To simplify the comparison between models, we kept the kinetic rates and biasing constants for the IP and MD equal in the 24-state model. Since the biasing constants η and μ are multiplied in the model during SP unbinding, it was necessary to change binding affinities of the SP as well to recreate properties of the single domain model. Keeping the binding and unbinding rates of the IP and MD equal to each other, the rates were tuned along with their biasing constants η and μ to produce a steady-state force-pCa curve at γ = 0 that was equivalent to the γ = 0 curve of the 16-state model (Table 1, Sets 1 and 2). From there, γ was increased from 0 to 90 by increments of 10 to see the effect on the force, pCa50, and n_H of each model. Throughout the range of γ values, both models produced identical behavior (Figure 3A).

Figure 3: Comparison of steady-state behavior of 16-state vs. 24-state models.

(A) Steady-state force-pCa plots were produced for the 16-state and 24-state model through a range of γ values to compare behavior. ● used for output of model, ▬ used for fit of Hill equation; (B) Kinetic rates of transition were compared between the single regulatory domain of the 16-state, and the two regulatory domains of the 24-state. Unbinding rates include both when the SP is unbound from TnC and when the SP is bound TnC and the biasing constants η and μ are applied to the rates; (C) Calcium transient used to produce twitch simulations; (D) Normalized force plots of 16-state and 24-state models.

We then ran simulations wherein activation was driven by a Ca²⁺ transient (Figure 3C) for both the 16- and 24-state models to compare twitch properties. Both models produced very similar twitches with no difference in diastolic force, peak force, time from stimulus to peak force (TTP), and time from peak force to 50% relaxation (RT50).

Although the introduction of a second TnI-actin binding interaction into the model did not result in any emergent behavior differences when compared with a single-site model, the parameter changes required to make the models equivalent provide some meaningful insights. For instance, the affinity $\left(\frac{k^{+}}{k^{-}}\right)$ of either the MD or IP for actin in the 24-state model needed only be 25% the strength of the IP-actin affinity assumed in the 16-state model. In other words, the two regulatory sites working together did the same job performed by the single site, but at much lower actin affinities. The strength of coupling between SP and either of the neighboring domains (IP or MD) was also lower in the 24-state model by ~36%. On the other hand, in order to match 24-state model behavior to that of the 16-state model, it was necessary to increase SP-TnC affinity by ~32%.

Having established some of the basic implications of assuming two TnI-actin binding sites, we examined the possibility that IP-actin and MD-actin affinities were something other than equivalent. Initial simulations had assumed parity as a matter of convenience, but clearly this is unlikely to be true in the real system. We therefore attempted to use the 24-state model to recreate behavior of experimental data in which thin filament activation is affected by disruption of the IP or MD of TnI. In the 24-state model, disruption to one or the other of the TnI regulatory domains was represented by setting the transition rates of the domain to zero and setting its associated biasing constant to 1. In effect, this results in the 24-state model converting back to a 16-state model with only one regulatory domain. This process of removing a regulatory domain could then be used to mimic steady-state experimental data in which wild-type data (with both domains) was compared to mutation/truncation data (with only one domain). The model was optimized to fit the following experimental steady-state characteristics: pCa50, the fraction of minimum activation/maximum activation, normalized maximum activation, and n_H.

Kozaili et al[23] replaced 10 amino acids of the IP with a Gly-Ala linker sequence to disrupt functionality of the IP. Measurement of the myosin S1-actin ATPase rate was performed in an NADH-coupled protein assay. Disruption of the IP with the linker sequence led to an increase in pCa50 of 0.3, an increase is max activity by 60%, an increase of min activity/max activity from 0.11 to 0.39, and a non-significant increase in n_H from 2.49 to 2.54. Upon deletion of the IP from the 24-state model, we were able to capture the exact shift in pCa50 of 0.3 (Figure 4C). While we did see an increase in both minimum and maximum force in the model, it was not to the extent that the ATPase rate increased in the experimental data. Normalized maximum force increased by 3% and min activity/max activity increased from 0 to 0.7. There was also a drop in n_H of 3.76 to 2.09 from deletion of the IP which was not seen in the experimental data.

Figure 4: Steady-state comparison of 24-state model and experimental data.

(A) Steady-state force-pCa curves of the 24-state model with both regulatory domains, with the MD deleted, and with the IP deleted. ● used for output of model, ▬ used for fit of Hill equation; (B) Kinetic rate equilibrium constants for the IP and MD both when the SP is unbound from TnC and when the SP is bound TnC and the biasing constants η and μ are applied to the rates; (C) Comparison of steady-state force-pCa curve characteristics (ΔpCa50, maximum activation, ratio of minimum activation and maximum activation, and hill coefficient) for IP disruption between experimental data and the model; (D) Comparison of steady-state force-pCa curve characteristics MD disruption between experimental data and the model.

Ghashghaee et al[10] truncated the last 17 C-terminal amino acids of the TnI MD, leaving residues 1–193 intact. These were exchanged into skinned rat papillary muscle fibers which were then Ca²⁺ activated at different concentrations to measure developed tension. Truncation of the MD led to an increase in pCa50 of 0.1, a non-significant decrease in minimum tension, giving a change in min activity/max activity of 0.08 to 0.05, a non-significant increase of 1% for normalized maximum force and a non-significant increase in n_H from 4.64 to 4.68. Upon deletion of the MD from the 24-state model, we were able to capture the exact shift in pCa50 of 0.1 (Figure 4D). The model showed only small changes to the minimum and maximum force values which is consistent with the experimental data. Normalized maximum force increased by 2% and min activity/max activity increased from 0 to 0.3. There was also a drop in n_H of 3.76 to 2.43 from deletion of the MD which was not seen in the experimental data.

The parameter set used for these simulations had a different binding affinity for IP and MD (Table 1 Set 3). The IP had binding affinities of 0.49 with the SP unbound and 7.9 with the SP bound while the MD had binding affinities of 0.41 with the SP unbound and 6.5 with the SP bound (Figure 4B). This produced different force-pCa curves for the model with both domains, deletion of the IP, and deletion of the MD (Figure 4A).

After optimizing the parameters to get reasonable steady-state behavior, our next step was to use this model to investigate dynamic properties of the 24-state model and how deletion of either of the regulatory domains could affect twitch dynamics. Simulations were run with activation driven by a Ca²⁺ transient (Figure 5A) to produce twitches with both regulatory domains (WT) as well as individual deletions of the IP [(−)IP] and MD [(−)MD] (Figure 4B–C). The WT simulation had an average diastolic force of 0.005 which increased to 0.50 for (−)MD and 1.6 for (−)IP. Peak force increased from 6.8 for the WT to 8.0 for (−)MD and 9.2 for (−)IP. Unlike the other characteristics, TTP decreased from 310 ms for WT to 290 ms for (−)MD and 280 ms for (−)IP. Lastly, RT50 increased from 250 ms for WT to 310 ms for (−)MD and 450 ms for (−)IP (Figure 5B–C).

Figure 5: 24-state model dynamic simulations.

(A) Calcium transient used to produce twitch simulations; (B) Force output of model simulation with both regulatory domains, with the MD deleted [(−) MD], and with the IP deleted [(−) IP]; (C) Normalized force plots; (D) Comparison of twitch characteristics: Diastolic force, peak force, time from stimulus to peak force, time from peak force to 50% relaxation (RT50).

4. DISCUSSION

The objective of this study was to create a model of the cardiac thin filament that incorporates the key regulatory domains of TnI involved in governing thin filament activation. This model was first used to compare regulation by a single actin-binding regulatory domain (IP only) with regulation by two actin-binding regulatory domains (IP and MD). By forcing the two models to share the same steady-state behavior, we expected to gain insight into how regulatory domain affinity to actin and coupling of protein transitions may differ with this change in regulation. The central finding was that addition of a second actin-binding domain results in a more fault-tolerant system: as long as SP-TnC affinity is of sufficient strength, the affinity of the IP and MD domains of TnI can be of a relatively lower affinity. Similarly, SP-IP/SP-MD coupling can be less rigid while still maintaining the same control over contraction as the single-domain system. The notion that contraction is regulated by multiple low-affinity actin-TnI interactions has interesting implications for the evolutionary underpinnings of the thin filament regulatory switch, in that one low-affinity interaction may have arisen first, followed by another that resulted in improved diastolic function and competitive advantage.

In order to investigate how the affinities of the regulatory domains may differ from each other in a more realistic setting, we used experimental data that examined the effect of disruption of one or the other of the regulatory domains. We optimized our model parameters to mimic the changes that occurred when the IP was replaced or when the MD was truncated such as increased diastolic force and increased Ca²⁺ sensitivity. Based on the binding affinities of the IP and MD needed to recreate the experimental data, the IP seems to have the higher binding affinity to actin, resulting in a more severe change in phenotype when it is deleted from the model.

Using these parameters to simulate twitches revealed stark differences in behavior in diastolic and peak force, TTP, and RT50. When considering the mechanism behind this change in behavior, one can consider both regulatory domains acting as independent doorstops, preventing Tm from shifting on actin’s surface. In a system with one regulatory domain, it is easier to remove a single barrier to increase force production, leading to an increase in peak force and a decrease in TTP. However, it also decreases the stability of the off-state of the thin-filament and allows appreciable myosin-based force even during the diastolic interval. The addition of the second regulatory domain encourages the RUs of the thin filament to remain in the off position when one domain is bound to actin even if the other domain is released. This leads to a sharper relaxation when both the IP and MD are acting in the system (Figure 4C). Our results suggest that both the IP and MD of TnI are necessary for the thin filament to deactivate quickly and keep contractile force to low baseline levels. As such, alterations to either domain would likely have negative consequences for diastolic function.

While several of the trends seen in these simulations are similar to those seen in the selected experimental data sets, it is difficult to make direct comparisons because the data describing effects of disrupting the IP and MD were not obtained in equivalent systems. The data used for the IP was a protein assay, with measurements of myosin S1-actin ATPase at steady-state. Meanwhile, the data reporting effects of MD deletion were recorded by measuring developed tension in rat skinned papillary muscles. Furthermore, little data are available regarding how perturbation of the IP or MD domains might affect intact twitch behavior. Nevertheless, looking across multiple studies that have measured the functional consequences of cardiac TnI C-terminal truncation, the consensus seems to be that this (1) increases myofilament Ca²⁺ sensitivity[25]–[27] (2) causes either minimal change or a decrease in maximum steady-state force[25]–[28] and (3) causes a decrease in myofilament cooperativity[25], [26], [28]. The model results are qualitatively consistent with each of these trends.

Another limitation encountered in this study was the fact that with both the IP and MD domains functional, our model did not predict any residual force at low calcium. This was a result of specifying an effective tropomyosin stiffness of sufficient strength to produce cooperativity levels that agreed with data from permeabilized human myocardium (Figure 4A). This steep cooperativity means that nearest-neighbor RUs inhibit one another with great efficiency under low calcium conditions, and residual crossbridge formation is rare. It is conceivable that the model relies too heavily on this form of cooperativity, which is inhibitory in nature. Including cooperativity from other sources, specifically those that are excitatory, would allow the tropomyosin stiffness parameter to be reduced and likely yield a more realistic residual force value.

A major motivation for adding additional mechanistic detail to thin filament models is to enable more insightful analysis of genetic mutations to thin filament proteins and their attendant consequences. Thin filament mutations can lead to hereditary cardiomyopathies such as hypertrophic cardiomyopathy (HCM) [29]–[31]. Previous efforts to enhance model fidelity and reproduce mutation effects in this area have been made by our group and others [18], [32], [33]. Here, we have used experimental data and new structural information to represent new binding interactions that are believed to occur in thin filament regulation. This 24-state model could be used in future work to explore the functional effects of TnI mutations that are positioned to effect its IP, MD, or SP regions, as well as mutations to proteins that interact with these regions (e.g. actin, tropomyosin, or TnC).

Indeed, the simulations presented here already provide some qualitative insight into actions of TnI mutations localized in the IP domain [34], [35]. A simple deletion of the IP in our model captures behavioral trends observed in muscle expressing TnI R145W, such as increased force at maximal calcium, increased calcium sensitivity, and a decrease in n_H. This suggests that more detailed analysis of functional mutation data is both feasible and likely to produce meaningful insight into molecular pathologies.

Highlights.

• Structural investigations of the thin filament suggest that troponin I contains two regulatory domains that bind to actin under low calcium conditions, but previous computational models have only considered one. Assuming two actin-binding sites on troponin I allows each site to have a lower affinity for actin than a single independent site would need to achieve the same level of thin filament regulation

• A computational Markov model that encompasses distinct regulatory domains of troponin I is able to mimic experimental behavior seen upon disruption of those regulatory domains

• Both the inhibitory peptide and mobile domain of troponin I are required to keep diastolic cross-bridge activity to a minimum and accelerate myofilament relaxation

Abbreviations:

IP

Inhibitory Peptide of Troponin I

SP

Switch Peptide of Troponin I

MD

Mobile Domain Troponin I

RU

Regulatory Unit of the Thin Filament