A coarse-grained molecular model for actin-myosin simulation

A coarse-grained approach to model the dynamics of the actomyosin cortex

Background

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions.

Results

Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin.

Conclusions

We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-022-01279-2).

SimGen: A General Simulation Method for Large Systems

SimGen is a stand-alone computer program that reads a script of commands to represent complex macromolecules, including proteins and nucleic acids, in a structural hierarchy that can then be viewed using an integral graphical viewer or animated through a high-level application programming interface in C++. Structural levels in the hierarchy range from α-carbon or phosphate backbones through secondary structure to domains, molecules, and multimers with each level represented in an identical data structure that can be manipulated using the application programming interface. Unlike most coarse-grained simulation approaches, the higher-level objects represented in SimGen can be soft, allowing the lower-level objects that they contain to interact directly. The default motion simulated by SimGen is a Brownian-like diffusion that can be set to occur across all levels of representation in the hierarchy. Links can also be defined between objects, which, when combined with large high-level random movements, result in an effective search strategy for constraint satisfaction, including structure prediction from predicted pairwise distances. The implementation of SimGen makes use of the hierarchic data structure to avoid unnecessary calculation, especially for collision detection, allowing it to be simultaneously run and viewed on a laptop computer while simulating large systems of over 20,000 objects. It has been used previously to model complex molecular interactions including the motion of a myosin-V dimer "walking" on an actin fibre, RNA stem-loop packing, and the simulation of cell motion and aggregation. Several extensions to this original functionality are described.

Coarse-grained force fields for molecular simulations

Molecular dynamics (MD) simulations at the atomic scale are a powerful tool to study the structure and dynamics of model biological systems. However, because of their high computational cost, the time and length scales of atomistic simulations are limited. Biologically important processes, such as protein folding, ion channel gating, signal transduction, and membrane remodeling, are difficult to investigate using atomistic simulations. Coarse-graining reduces the computational cost of calculations by reducing the number of degrees of freedom in the model, allowing simulations of larger systems for longer times. In the first part of this chapter we review briefly some of the coarse-grained models available for proteins, focusing on the specific scope of each model. Then we describe in more detail the MARTINI coarse-grained force field, and we illustrate how to set up and run a simulation of a membrane protein using the Gromacs software package. We explain step-by-step the preparation of the protein and the membrane, the insertion of the protein in the membrane, the equilibration of the system, the simulation itself, and the analysis of the trajectory.

The mechanism of the converter domain rotation in the recovery stroke of myosin motor protein

Upon ATP binding, myosin motor protein is found in two alternative conformations, prerecovery state M* and postrecovery state M**. The transition from one state to the other, known as the recovery stroke, plays a key role in the myosin functional cycle. Despite much recent research, the microscopic details of this transition remain elusive. A critical step in the recovery stroke is the rotation of the converter domain from "up" position in prerecovery state to "down" position in postrecovery state that leads to the swing of the lever arm attached to it. In this work, we demonstrate that the two rotational states of the converter domain are determined by the interactions within a small structural motif in the force-generating region of the protein that can be accurately modeled on computers using atomic representation and explicit solvent. Our simulations show that the transition between the two states is controlled by a small helix (SH1) located next to the relay helix and relay loop. A small translation in the position of SH1 away from the relay helix is seen to trigger the transition from "up" state to "down" state. The transition is driven by a cluster of hydrophobic residues I687, F487, and F506 that make significant contributions to the stability of both states. The proposed mechanism agrees well with the available structural and mutational studies.

Coarse-grained simulation of myosin-V movement

We describe the development of a hierarchic modelling method applied to simulating the processive movement of the myosin-V molecular motor protein along an actin filament track. In the hierarchic model, three different levels of protein structure resolution are represented: secondary structure, domain, and protein, with the level of detail changing according to the degree of interaction among the molecules. The integrity of the system is maintained using a tree of spatially organised bounding volumes and distance constraints. Although applied to an actin-myosin system, the hierarchic framework is general enough so that it may easily be adapted to a number of other large biomolecular systems containing in the order of 100 proteins. We compared the simulation results with biophysical data, and despite the lack of atomic detail in our model, we find good agreement and can even suggest some refinements to the current model of myosin-V motion.

Structural systems biology and multiscale signaling models

We review current advances in experimental as well as computational modeling and simulation approaches to structural systems biology, whose overall aim is to build quantitative models of signaling networks while retaining the crucial elements of molecular specificity. We briefly discuss the current and emerging experimental and computational methods, particularly focusing on hybrid and multiscale methods, and highlight several applications in cell signaling with quantitative and predictive capabilities. The scope of such models range from delineating protein-protein interactions to describing clinical implications.

Interactions between relay helix and Src homology 1 (SH1) domain helix drive the converter domain rotation during the recovery stroke of myosin II

Myosin motor protein exists in two alternative conformations, prerecovery state M* and postrecovery state M**, on adenosine triphosphate binding. The details of the M*-to-M** transition, known as the recovery stroke to reflect its role as the functional opposite of the force-generating power stroke, remain elusive. The defining feature of the postrecovery state is a kink in the relay helix, a key part of the protein involved in force generation. In this article, we determine the interactions that are responsible for the appearance of the kink. We design a series of computational models that contain three other segments, relay loop, converter domain, and Src homology 1 (SH1) domain helix, with which relay helix interacts and determine their structure in accurate replica exchange molecular dynamics simulations in explicit solvent. By conducting an exhaustive combinatorial search among different models, we find that: (1) the converter domain must be attached to the relay helix during the transition, so it does not interfere with other parts of the protein and (2) the structure of the relay helix is controlled by SH1 helix. The kink is strongly coupled to the position of SH1 helix. It arises as a result of direct interactions between SH1 and the relay helix and leads to a rotation of the C-terminal part of the relay helix, which is subsequently transmitted to the converter domain.

Coarse-graining of multiprotein assemblies

Multiscale models are important tools to elucidate how small changes in local subunit conformations may propagate to affect the properties of macromolecular complexes. We review recent advances in coarse-graining methods for poly-protein assemblies, systems that are composed of many copies of relatively few components, with a particular focus on viral capsids and cytoskeletal filaments. These methods are grouped into two broad categories-mapping methods, which use information from one scale of representation to parameterize a lower resolution model, and bridging methods, which repeatedly connect different scales during simulation-and we provide examples of both classes at different levels of complexity. Collectively, these models illustrate the numerous approaches to information transfer between scales and demonstrate that the complexity required of the model depends in general on the nature of the information sought.

Automating the search of molecular motor templates by evolutionary methods

Biological molecular motors are nanoscale devices capable of transforming chemical energy into mechanical work, which are being researched in many scientific disciplines. From a computational point of view, the characteristics and dynamics of these motors are studied at multiple time scales, ranging from very detailed and complex molecular dynamics simulations spanning a few microseconds, to extremely simple and coarse-grained theoretical models of their working cycles. However, this research is performed only in the (relatively few) instances known from molecular biology. In this work, results from elastic network analysis and behaviour-finding methods are applied to explore a subset of the configuration space of template molecular structures that are able to transform chemical energy into directed movement, for a fixed instance of working cycle. While using methods based on elastic networks limits the scope of our results, it enables the implementation of computationally lightweight methods, in a way that evolutionary search techniques can be applied to discover novel molecular motor templates. The results show that molecular motion can be attained from a variety of structural configurations, when a functional working cycle is provided. Additionally, these methods enable a new computational way to test hypotheses about molecular motors.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.