Assessing the two-body diffusion tensor calculated by the bead models

Wang, Nuo; Huber, Gary L.; McCammon, J. Andrew

doi:10.1063/1.4807590

Cited by 8 publications

(10 citation statements)

References 32 publications

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“…In the case of membrane systems, there is no Rotne-Prager analog available. One possibility for developing membrane simulations analogous to "Brownian Dynamics with Hydrodynamic Interactions" 63 is to numerically tabulate the coupling elements of the diffusion matrix as a function of particle separation to build up a pairwise approximation to the diffusion matrix that can be implemented in simulations, as has been suggested for 3D systems 42 . The RS calculations presented in this work are a natural method to use for such a tabulation and could, perhaps, be supplemented with the lubrication results of Ref.…”

Section: Discussionmentioning

confidence: 99%

Calculating hydrodynamic interactions for membrane-embedded objects

Noruzifar

Camley

Brown

2014

The Journal of Chemical Physics

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A recently introduced numerical scheme for calculating self-diffusion coefficients of solid objects embedded in lipid bilayer membranes is extended to enable calculation of hydrodynamic interactions between multiple objects. The method is used to validate recent analytical predictions by Oppenheimer and Diamant [Biophys. J. 96, 3041 2009] related to the coupled diffusion of membrane embedded proteins and is shown to converge to known near-field lubrication results as objects closely approach one another; however, the present methodology also applies outside of the limiting regimes where analytical results are available. Multiple different examples involving pairs of disk-like objects with various constraints imposed on their relative motions demonstrate the importance of hydrodynamic interactions in the dynamics of proteins and lipid domains on membrane surfaces. It is demonstrated that the relative change in self-diffusion of a membrane embedded object upon perturbation by a similar proximal solid object displays a maximum for object sizes comparable to the Saffman-Delbrück length of the membrane.

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Section: Discussionmentioning

confidence: 99%

Calculating hydrodynamic interactions for membrane-embedded objects

Noruzifar

Camley

Brown

2014

The Journal of Chemical Physics

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“…For two-body systems, we evaluate the 12 × 12 rigid-body mobility matrices (eq 19) for different values of the bodies center-to-center distance. We analyze components of mobility matrices that correspond to relative motions of bodies in directions that are either parallel or perpendicular to the line connecting centers of bodies (Figure 2A).…”

Section: Articlementioning

confidence: 99%

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Długosz

Antosiewicz

2015

J. Phys. Chem. B

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Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.

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“…In the Brownian dynamics simulations of biomolecules with hydrodynamic interactions, the complex molecular system is modeled as multiple (hundreds or thousands) rigid bodies to reduce the numerical “stiffness” due to the local chemical bond type interactions between atoms that cause very high frequency oscillations and subsequently require extremely small step size when marching in time. Instead of a thorough listing of existing literature on the Brownian dynamics models and hydrodynamic interactions, we focus on the “shell-bead” model (see, e.g., [5, 8, 21]) that describes the hydrodynamic forces exerted on a protein.…”

Section: Background and Problem Statementmentioning

confidence: 99%

Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations

Fang¹,

Huang²,

Huber³

et al. 2018

SIAM J. Sci. Comput.

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In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body p consisting of n beads, the 6×3n transformation matrix Z that maps the force on each bead to p’s translational and rotational forces (a 6 × 1 vector), and V the row space of Z, we show how to explicitly construct the (3n – 6) × 3n matrix trueQ˜ consisting of (3n – 6) orthonormal basis vectors of V⊥ (orthogonal complement of V) using only O(nlogn) operations and storage. For applications where only the matrix-vector multiplications Q˜V and trueQ˜TV are needed, we introduce asymptotically optimal O(n) hierarchical algorithms without explicitly forming trueQ˜. Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.

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Assessing the two-body diffusion tensor calculated by the bead models

Cited by 8 publications

References 32 publications

Calculating hydrodynamic interactions for membrane-embedded objects

Calculating hydrodynamic interactions for membrane-embedded objects

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems

Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations

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