(116f) Investigating Heterogeneous System Performance of Synthetic Myosins Computationally

Myosin motor proteins are ubiquitous in natural biological systems and convert chemical energy into mechanical force.  Myosins often operate in large groups, with their collective interactions contributing to an emergent system performance that varies according to the isoforms present.  These systems are possible to implement in novel myosin-based technologies and the directed design of synthetic myosins could improve system performance.  Empirical studies have demonstrated that myosin behaviors are tunable via alterations of specific molecular structures, but predicting the effects of alterations to individual myosins on system performance is difficult due to the large number of influential variables.  Therefore, we developed a computational method for procedurally designing individual myosins and systems, thus characterizing the influence of each parameter in the design space. Our findings suggest that the considered design parameters affect system performance differently and often in non-intuitive directions.  Additionally, we find that heterogeneous systems (i.e. multiple myosin isoforms working together) have unique and potentially superior performance when compared to homogeneous systems (i.e. single myosin isoforms). The developed approach offers a novel perspective on the complexities of myosin systems and the techniques are extendible for investigating many other biological systems at the interface of chemistry and mechanics.   

Our computational model enables the design of myosin systems from the bottom-up, and predicts the emergent system response to force perturbations.  This approach allows for separate investigation of variables at the levels of individual myosins and the system.  We consider four inputs that represent mechanical or chemical behaviors when configuring myosins and consider discrete numbers of each isoform as the system input. The approach also enables the modeling of heterogeneous systems, which exist in nature but have had little empirical or computational investigation. 

We derive a mechano-chemical model based on the swinging lever arm theory for mapping structures manipulated through synthetic myosin experiments to specific behaviors. The swinging lever arm theory proposes that a myosin chemically attaches to a filament, then mechanically exerts positive force as a linearly elastic element during its power-stroke followed by negative force before detaching chemically.  We consider the configuration of four structures as inputs: (1) the length of the lever arm and (2) the rotation of the converter domain, which influence the mechanical behaviors of a myosin during its power-stroke and the configuration of the (3) loop one and (4) loop two substructures of the myosin head domain, which influence a myosin’s chemical behaviors.

We use differential equations to determine the behavior of each myosin averaged over their entire cycle and then sum the contributions of all myosins to determine the system performance.  The empirically measured force-velocity response of a known myosin isoform is used to validate our model, and considered as a datum myosin design.  We then extrapolate novel myosin designs and compare their performance to the datum.  It is not possible to validate all extrapolated designs, but for the empirical evidence available, our model produces a good fit for maximum system velocity when the lever arm length and detachment rates are extrapolated.

The design of myosins and their numbers in a system are procedurally varied with respect to one variable at a time, which allows for isolating how each parameter affects system performance.  The maximum force of a system, maximum filament velocity, system stability, energy utilized, and volume of a system are all investigated and it is found that no two variables affect the system in the same manner.  We consider systems that have at least two myosins attached on average stable, therefore the system possess a low probability of system dissociation due to diffusion and a high likelihood of consistent filament trajectory.  Robustness of these systems with respect to function (ability to operate under a number of different conditions) is also considered, and it is found that more robust systems generally require more energy use by the system and more volume.

When heterogeneous systems are investigated, it is found that the myosins interacting within the system produce nonlinear performance curves that are not possible to recreate with any homogenous system.  External forces are then applied to systems and the response with respect to each performance parameter is determined numerically.  It is found that when the performance of a system is considered over a range of conditions, that the unique characteristics of heterogeneous systems have increased performance over any possible homogenous system for certain applications.  For instance, one heterogeneous system had decreased energy usage at lower velocities (i.e. greater performance), yet allowed for a higher maximum system velocity with consideration to stability (i.e. greater robustness) in comparison to the optimal homogenous system under the same conditions.  

These results provide novel insights for why nature may favor molecularly heterogeneous systems for functions such as muscular contraction.  An often stated benefit of myosin heterogeneity in muscles is the ability for muscle performance to adapt over time to external stimuli by tweaking myosin concentrations.  However, our findings suggest that the heterogeneity may also provide increased performance for conditions at a specific point in time.  Proving that heterogeneity provides increased performance is difficult through empirical studies, because it is difficult to decouple the influences of each myosin from the system as a whole.  Thus, our computational approach has provided novel insights for how the configuration of individual myosins affects system performance.  Our model has great potential to aid the design of myosin-based technologies, by enabling designers to predict how alterations of individual components as well as the number of each component present affect the performance of a system as a whole. These techniques for decoupling individual molecule behaviors from system performance are crucial for aiding engineers to find the optimal design of the system, and are extendible for investigating heterogeneous biological systems in general, such as the many other classes of motor proteins.