Revisiting and parallelizing SHAKE

Weinbach, Yael; Elber, Ron

doi:10.1016/j.jcp.2005.03.015

Cited by 69 publications

(104 citation statements)

References 23 publications

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“…A time-step of 2 fs was used while constraining all bonds to hydrogen atoms using the SHAKE algorithm. 63,64 The temperature was kept constant at 310 K using the Langevin thermostat with a damping coefficient of 0.5 ps −1 . A Nosé-Hoover Langevin piston 65,66 was used to keep the pressure constant at 1 atm with an oscillation period of 200 fs and a damping coefficient of 200 fs.…”

Section: Methodsmentioning

confidence: 99%

Conformational Dynamics of the Human Islet Amyloid Polypeptide in a Membrane Environment: Toward the Aggregation Prone Form

et al. 2016

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Human islet amyloid polypeptide (hIAPP) is a 37-residue peptide hormone, which upon misfolding changes from the physiologically active monomer into pathological amyloid fibril aggregates in the pancreas of type 2 diabetes mellitus patients. During this process, the insulin-producing pancreatic β-cells are damaged; however, the underlying mechanism of this mode of cytotoxicity remains elusive. It is known that anionic lipids accelerate amyloid fibril formation, implicating the importance of the cellular membrane in the process, and that a pH close to the level in the β-cell secretory granules (pH = 5.5) inhibits the amyloid fibril formation. Using all-atom molecular dynamics simulations, we have investigated the membrane-associated monomer state of α-helical hIAPP and analyzed specific interactions of hIAPP with a mixed anionic-zwitterionic lipid membrane, examined the influence of pH on the structure and dynamics of hIAPP and its interaction with the membrane. We find that hIAPP primarily interacts with the membrane by forming favorable interactions between anionic lipids and the positively charged residues in the N-terminal part of the peptide. Rationalizing experimental findings, the simulations show that the N-terminal part of the peptide interacts with the membrane in the lipid head-group region. At neutral pH the C-terminal part of the peptide, which contains the residues that initiate fibril formation, displays a highly dynamic, unfolded state, which interacts significantly less with the membrane than the N-terminal part. Such an unfolded form can be proposed to contribute to the acceleration of fibril formation. At low pH, protonation of His18 mediates a stronger interaction of the C-terminal part with the membrane, resulting in the immobilization of the C-terminal part on the membrane surface which may constitute a mechanism by which low pH inhibits fibril formation.

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Section: Methodsmentioning

confidence: 99%

Conformational Dynamics of the Human Islet Amyloid Polypeptide in a Membrane Environment: Toward the Aggregation Prone Form

et al. 2016

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“…[56] The real space cutoff for the electrostatics and the van der Waals interactions was set to 9.0 Å. In all the simulations we constrain water bond lengths and angle with a matrix version[57] of the SHAKE algorithm[58], and r-RESPA[59] was used to have a dual time stepping; the reciprocal-space component of the Ewald sum was evaluated every 4 fs and the rest of the forces were evaluated every 1 fs.…”

Section: Methodsmentioning

confidence: 99%

Computational study of peptide permeation through membrane: searching for hidden slow variables

Cárdenas

Elber

2013

Molecular Physics

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Atomically detailed molecular dynamics trajectories in conjunction with Milestoning are used to analyze the different contributions of coarse variables to the permeation process of a small peptide (N-acetyl-L-tryptophanamide, NATA) through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) membrane. The peptide reverses its overall orientation as it permeates through the biological bilayer. The large change in orientation is investigated explicitly but is shown to impact the free energy landscape and permeation time only moderately. Nevertheless, a significant difference in permeation properties of the two halves of the membrane suggests the presence of other hidden slow variables. We speculate, based on calculation of the potential of mean force, that a conformational transition of NATA makes significant contribution to these differences. Other candidates for hidden slow variables may include water permeation and collective motions of phospholipids.

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“…Many different ways have been proposed to solve the system of Equations (46), see e.g., [13,[24][25][26][27]. The original, and still commonly used, goes back to Berendsen [3], who called it, again, SHAKE.…”

Section: Verlet Algorithmmentioning

confidence: 99%

“…Practical parallelizations are either approximate or the algorithms are specifically tailored to the problems at hand. An interesting general parallel solution has been worked out by Weinbach and Elber [13]. They take advantage of the fact that the essential step in solving the SHAKE equation…”

Section: Verlet Algorithmmentioning

confidence: 99%

Holonomic Constraints: A Case for Statistical Mechanics of Non-Hamiltonian Systems

Ciccotti

Ferrario

2018

Computation

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Abstract:A dynamical system submitted to holonomic constraints is Hamiltonian only if considered in the reduced phase space of its generalized coordinates and momenta, which need to be defined ad hoc in each particular case. However, specially in molecular simulations, where the number of degrees of freedom is exceedingly high, the representation in generalized coordinates is completely unsuitable, although conceptually unavoidable, to provide a rigorous description of its evolution and statistical properties. In this paper, we first review the state of the art of the numerical approach that defines the way to conserve exactly the constraint conditions (by an algorithm universally known as SHAKE) and permits integrating the equations of motion directly in the phase space of the natural Cartesian coordinates and momenta of the system. We then discuss in detail SHAKE numerical implementations in the notable cases of Verlet and velocity-Verlet algorithms. After discussing in the same framework how constraints modify the properties of the equilibrium ensemble, we show how, at the price of moving to a dynamical system no more (directly) Hamiltonian, it is possible to provide a direct interpretation of the dynamical system and so derive its Statistical Mechanics both at equilibrium and in non-equilibrium conditions. To achieve that, we generalize the statistical treatment to systems no longer conserving the phase space volume (equivalently, we introduce a non-Euclidean invariant measure in phase space) and derive a generalized Liouville equation describing the ensemble even out of equilibrium. As a result, we can extend the response theory of Kubo (linear and nonlinear) to systems subjected to constraints.

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Revisiting and parallelizing SHAKE

Cited by 69 publications

References 23 publications

Conformational Dynamics of the Human Islet Amyloid Polypeptide in a Membrane Environment: Toward the Aggregation Prone Form

Conformational Dynamics of the Human Islet Amyloid Polypeptide in a Membrane Environment: Toward the Aggregation Prone Form

Computational study of peptide permeation through membrane: searching for hidden slow variables

Holonomic Constraints: A Case for Statistical Mechanics of Non-Hamiltonian Systems

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