Machine learning meets Monte Carlo methods for models of muscle's molecular machinery to classify mutations

Abstract

The timing and magnitude of force generation by a muscle depend on complex interactions in a compliant, contractile filament lattice. Perturbations in these interactions can result in cardiac muscle diseases. In this study, we address the fundamental challenge of connecting the temporal features of cardiac twitches to underlying rate constants and their perturbations associated with genetic cardiomyopathies. Current state-of-the-art metrics for characterizing the mechanical consequence of cardiac muscle disease do not utilize information embedded in the complete time course of twitch force. We pair dimension reduction techniques and machine learning methods to classify underlying perturbations that shape the timing of twitch force. To do this, we created a large twitch dataset using a spatially explicit Monte Carlo model of muscle contraction. Uniquely, we modified the rate constants of this model in line with mouse models of cardiac muscle disease and varied mutation penetrance. Ultimately, the results of this study show that machine learning models combined with biologically informed dimension reduction techniques can yield excellent classification accuracy of underlying muscle perturbations.

Figure 1.

Sarcomere model is based on lattice geometry, filament compliance, and transition rates. (A) A simplified schematic of the thick filament (red) and binding sites on the thin filament (blue) in a hexagonal pattern. (B) Myosin is modeled as a system of linear (k_R) and torsional (k_θ) springs with a defined myosin rest angle (θ) globular domain length (R). (C) The sarcomere is modeled as an array of springs of different stiffness. During contraction, the myosin heads cycle and the distance between the Z-line (blue, right) and the M-line (red, left) decreases. (D) The model cycles through a coupled thin filament (TF) state transitions and myosin motor head (XB) state transition, where myosin is unable to leave the unbound state (XB1) until it is in range with an actin site that has reached an open state (TF4).

Figure 2.

Isometric twitch simulations. (A) An example of the input calcium trace (blue dashed line) and the resulting single simulated twitch force (black) using baseline model conditions. (B) An average (black) of 100 simulations (gray) for the baseline simulated conditions, demonstrating the stochastic nature of the model. (C) Average twitch trace of 100 independent simulations of control and each of our modifications indicated in the legend. (D) Average control twitch subtracted from average twitch of each of our modifications reveals both magnitude and shape changes.

Figure 3.

SVD of twitches. (A) The first two components of the SVD of the matrix containing force vs. time from 100 of each of our different simulated conditions. (B) The contributions of each mode normalized to the first component shown on linear and logarithmic scales.

Figure 4.

Twitch principal components allow for separation of twitches with similar tension index. (A) Twitches with different underling perturbations may have similar TTI, with a change in the time course of force development. (B) Projections of twitches onto the first two eigenmodes (PC1 and PC2) allows for separation of our twitch data set.

Figure 5.

Classifier Accuracy. The random forest classifier accuracy for 100 twitches from each condition with different input features as indicated along the horizontal axis. The dashed line denotes accuracy for random classifier accuracy (14.3%).

Figure 6.

Confusion matrices of RF classifier accuracy. (A–H) Classifier accuracy for each perturbation by classifier input features. The y axis is the true perturbation class, and the x axis represents classifier prediction. As each of the twitches receives a classifier prediction the sum of a row is 1.0, and each square represents the proportion of twitches that were assigned to the class on the x axis. The darker shades of the heat map correspond to larger proportions of twitches predicted to fall within a given class.