Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

Razo, Mauricio J. del; Dibak, Manuel; Schütte, Christof; Noé, Frank

doi:10.1063/5.0060314

Cited by 16 publications

(8 citation statements)

References 72 publications

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“…Here we develop a coarse-grained model of flexible membrane-bound proteins, diffusing on and interacting with a dynamic membrane. The model is fully particle-based so as to facilitate the integration with particle-based simulations of cellular processes, , and particularly with interacting-particle reaction dynamics (iPRD). − We study the dynamics of protein aggregation and uncover their slow kinetics in large-scale simulations. We present a theoretical coagulation model, which yields information on cluster formation/breakup kinetics as well as the chemical potential governing particle exchange between clusters.…”

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confidence: 99%

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Sadeghi

Noé

2021

J. Phys. Chem. Lett.

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Biomembrane remodeling is essential for cellular trafficking, with membrane-binding peripheral proteins playing a key role in it. Significant membrane remodeling as in endo- and exocytosis is often due to aggregates of many proteins with direct or membrane-mediated interactions. Understanding this process via computer simulations is extremely challenging: protein–membrane systems involve time and length scales that make atomistic simulations impractical, while most coarse-grained models fall short in resolving dynamics and physical effects of protein and membrane flexibility. Here, we develop a coarse-grained model of the bilayer membrane bestrewed with rotationally symmetric flexible proteins, parametrized to reflect local curvatures and lateral dynamics of proteins. We investigate the kinetics, equilibrium distributions, and the free energy landscape governing the formation and breakup of protein clusters on the surface of the membrane. We demonstrate how the flexibility of the proteins as well as their surface concentration play deciding roles in highly selective macroscopic aggregation behavior.

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confidence: 99%

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Sadeghi

Noé

2021

J. Phys. Chem. Lett.

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“…Similar challenges have been noted in MSMs of multimolecular systems. 9,36 To address this issue in our DNA system, we built three distinct SRVs corresponding the DS, the global system comprising both molecules, and S1 and S2, the independent subsystems comprising each molecule individually. Each SRV was trained using identical network hyperparameters of two hidden layers of size 100, a ReLu activation, 50,000 batch size, 10 training epochs, and 0.001 learning rate.…”

Section: Multimolecular Latent Space Simulator (Multi-lss)mentioning

confidence: 99%

“…9 This includes efforts to learn independent components of biomolecular systems 33,34 and couple MSMs via reaction-diffusion dynamics. 35,36 Here, we integrate a novel approach, related to that of del Razo et al, 36 into the LSS pipeline which enables us to independently encode, propagate, and decode molecular subsystems and generate ultralong synthetic trajectories for multimolecular systems. To avoid learning degenerate dynamics, we build separate encoders and latent spaces for each subsystem and use a joint propagator to ensure physically accurate coupling between each system.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown MSMs can be inefficient, ineffective, or misleading when they are applied to multimolecular or partially coupled systems. , Recent work to address the shortcomings has been driven in large part by Noé and co-workers, and progress has been made in the development of so-called Markov field models . This includes efforts to learn independent components of biomolecular systems , and couple MSMs via reaction-diffusion dynamics. , Here, we integrate a novel approach, related to that of del Razo et al, into the LSS pipeline which enables us to independently encode, propagate, and decode molecular subsystems and generate ultralong synthetic trajectories for multimolecular systems. To avoid learning degenerate dynamics, we build separate encoders and latent spaces for each subsystem and use a joint propagator to ensure physically accurate coupling between each system.…”

Section: Introductionmentioning

confidence: 99%

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Molecular Latent Space Simulators for Distributed and Multimolecular Trajectories

Jones

McDargh

Wiewiora³

et al. 2023

J. Phys. Chem. A

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All atom molecular dynamics (MD) simulations offer a powerful tool for molecular modeling, but the short time steps required for numerical stability of the integrator place many interesting molecular events out of reach of unbiased simulations. The popular and powerful Markov state modeling (MSM) approach can extend these time scales by stitching together multiple short discontinuous trajectories into a single long-time kinetic model but necessitates a configurational coarse-graining of the phase space that entails a loss of spatial and temporal resolution and an exponential increase in complexity for multimolecular systems. Latent space simulators (LSS) present an alternative formalism that employs a dynamical, as opposed to configurational, coarse graining comprising three back-to-back learning problems to (i) identify the molecular system’s slowest dynamical processes, (ii) propagate the microscopic system dynamics within this slow subspace, and (iii) generatively reconstruct the trajectory of the system within the molecular phase space. A trained LSS model can generate temporally and spatially continuous synthetic molecular trajectories at orders of magnitude lower cost than MD to improve sampling of rare transition events and metastable states to reduce statistical uncertainties in thermodynamic and kinetic observables. In this work, we extend the LSS formalism to short discontinuous training trajectories generated by distributed computing and to multimolecular systems without incurring exponential scaling in computational cost. First, we develop a distributed LSS model over thousands of short simulations of a 264-residue proteolysis-targeting chimera (PROTAC) complex to generate ultralong continuous trajectories that identify metastable states and collective variables to inform PROTAC therapeutic design and optimization. Second, we develop a multimolecular LSS architecture to generate physically realistic ultralong trajectories of DNA oligomers that can undergo both duplex hybridization and hairpin folding. These trajectories retain thermodynamic and kinetic characteristics of the training data while providing increased precision of folding populations and time scales across simulation temperature and ion concentration.

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“…In order to test the validity of the RK-model and to assess the role of the spatial degrees of freedom, one has to turn to computer simulations in the spatial domain, for which BD is most appropriate given the large size of the system. BD-simulations of patchy particles have been used before to investigate ring formation in solution 23,24 and have also been applied to the case of SAS-6 rings 25 . However, a major limitation of these previous BD-simulations is the absence of ring size variability 25 .…”

Section: Introductionmentioning

confidence: 99%

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface

Melo

Wörthmüller

Gönczy

et al. 2022

Preprint

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The protein SAS-6 forms dimers, which then self-assemble into rings that are critical for the nine-fold symmetry of the centriole organelle. It has recently been shown experimentally that the self-assembly of SAS-6 rings is strongly facilitated on a surface, shifting the reaction equilibrium by four orders of magnitude compared to the bulk. Moreover, a fraction of non-canonical symmetries (i.e., different from nine) was observed. In order to understand which aspects of the system are relevant to ensure efficient self-assembly and selection of the nine-fold symmetry, we have performed Brownian dynamics computer simulation with patchy particles and then compared our results with experimental ones. Adsorption onto the surface was simulated by a Grand Canonical Monte Carlo procedure and Random Sequential Adsorption kinetics. Furthermore, self-assembly was described by Langevin equations with hydrodynamic mobility matrices. We find that as long as the interaction energies are weak, the assembly kinetics can be described well by the coagulation-fragmentation equations in the reaction-limited approximation. By contrast, larger interaction energies lead to kinetic trapping and diffusion-limited assembly. We find that selection of nine-fold symmetry requires a small value for the angular interaction range. These predictions are confirmed by the experimentally observed reaction constant and angle fluctuations. Overall, our simulations suggest that the SAS-6 system works at the crossover between a relatively weak binding energy that avoids kinetic trapping and a small angular range that favors the nine-fold symmetry.

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Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

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Cited by 16 publications

References 72 publications

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Thermodynamics and Kinetics of Aggregation of Flexible Peripheral Membrane Proteins

Molecular Latent Space Simulators for Distributed and Multimolecular Trajectories

Grand canonical Brownian dynamics simulations of adsorption and self-assembly of SAS-6 rings on a surface

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