Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere

Abstract

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Keywords: Brownian dynamics; Cardiac contractility; Multiscale modeling; Myosin; Sarcomere.

Figure 1:

(A) Schematic outlining the 5 main states of the Monte Carlo Markov Chain model. States B0 and B1 (red boxes) represent the blocked state of Tm, where 0 represents no Ca²⁺ bound and 1 represents bound Ca²⁺. The C state (yellow box) represents a 25 degree azithumal shift in Tm around the actin filament to comprise the closed state. The green boxes represent the two states where Tm is in the Open state, a 35 degree total shift from the blocked state. M1 represents the pre-powerstroke attached myosin position, and M2 represents the post-powerstroke force producing condition. Transitions from Blocked to Closed to Open states are affected by nearest-neighbor Tm interactions, which is signified by the dotted lines surrounding the transition arrows. (B) For a single steady-State simulation, 1000 3-second timecourses are run and averaged at each pCa value being tested and occupancy of each state is tracked. (C) M2 state occupancy is considered to be directly related to overall force production. The steady-state M2 occupancy at each pCa value is calculated by averaging the final 0.5 s of the simulation. (D) Steady state values of force are normalized to the pCa 4.0 force output and plotted as a function of pCa.

Figure 2:

BrownDye simulations of acto-myosin association were performed to determine the electrostatically-based differences in association rate between ADP- and dADP-bound myosin. A. For each BrownDye trajectory, a myosin monomer was generated randomly on a spherical surface approximately 120 Å from the actin dimer. A timecourse was run on the molecules combining random diffusion and electrostatic forces to determine if the molecules moved close enough to be within the prescribed reaction distance, or if the molecules moved farther away to the q radius and escaped. B. The bound conformation of ADP-myosin (black) or dADP-myosin (cyan) with an actin dimer, visualized using VMD [37]. C. Plot of second-order association rates for actin-myosin binding as a function of prescribed reaction distance. For WT simulations, the association rate was optimized to 0.0025 (μM⁻¹ms⁻¹) which corresponds to a reaction distance of 8.28 Å. Using the same reaction distance, the dATP actin-myosin association rate is determined to be 0.00567 (μM⁻¹ms⁻¹).

Figure 3:

A. Optimized ATP and dATP steady state curves compared to experimental data from Regnier et al. Experimental data are dots with error bars, and solid lines are simulations (black = ATP, cyan = dATP). B. Slack restretch simulations used to calculate k_tr for different parameter sets at pCa = 4.0 (black = ATP, cyan = dATP). Absolute forces were normalized to the maximum ATP force to demonstrate differences in steady state force production. C. absolute forces from (B) were normalized to maximum force of each simulation, to demonstrate differences in tension redevelopment kinetics.

Figure 4:

Steady state force at pCa 4.0 and pCa 5.5 as a function of dATP/ATP ratio (all ATP case displayed as 0% dATP). black: RU-RU Coupling enabled, red: RU-RU coupling disabled (all cooperative coefficients = 1).

Figure 5:

Twitch simulations with experimental calcium transient inputs. A. Force (normalized to maximum ATP case force) as a function of time. The input calcium transient is displayed in the inset, and is digitized from [2]. Solid black line: ATP only. dotted line: 25% dATP. dashed line: 50% dATP. solid cyan: 100% dATP. B. Twitch results for the ATP and dATP curves from (A), normalized to the maximum force for each data set. C. Black line: ATP parameter set twitch with WT calcium transient from Korte et al. Cyan line: 100% dATP twitch with dATP treatment calcium transient from Korte et al, as indicated by the blue line in the inset.