Numerical solution of AXB=C for (R,S)-symmetric matrices

Li, Jiao‐fen; Hu, Xi-Yan; Peng, Jingjing

doi:10.1007/s12190-013-0677-x

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…77 The energies of water molecules of each system were minimized first, followed by the energy minimization of the entire system with 5000 steps of steepest descent algorithm to minimize the steric clashes in the system. 78 After energy minimization, equilibration was carried out in the NPT ensemble for 20 ns at 1 bar pressure. 79 Subsequently, NVT equilibration was performed for 10 ns for each system.…”

Section: Molecular Dynamics Simulationsmentioning

confidence: 99%

All‐atom simulations of the trimeric spike protein of SARS‐CoV‐2 in aqueous medium: Nature of interactions, conformational stability and free energy diagrams for conformational transition of the protein

2023

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The spike protein of SARS‐CoV‐2 exists in two major conformational states, namely the ‘open’ and ‘closed’ states which are also known as the ‘up’ and ‘down’ states, respectively. In its open state, the receptor binding domain (RBD) of the protein is exposed for binding with ACE2, whereas the spike RBD is inaccessible to ACE2 in the closed state of the protein. In the current work, we have performed all‐atom microsecond simulations of the full‐length trimeric spike protein solvated in explicit aqueous medium with an average system size of ~0.7 million atoms to understand the molecular nature of intra‐ and inter‐chain interactions, water‐bridged interactions between different residues that contribute to the stability of the open and closed states of the protein, and also the free energy landscape for transition between the open and closed states of the protein. We have also examined the changes of such interactions that are associated with switching from one state to the other through both unbiased and biased simulations at all‐atom level with total run length of 4 μs. Interestingly, after about 0.8 μs of unbiased molecular dynamics run of the spike system in the open state, we observed a gradual transition of the monomeric chain (B) from open to its partially closed or down state. Initially the residues at the interface of chain B RBD in the open state spike protein were at non‐hydrogen‐bonding distances from the residues of chain C RBD. However, the two RBDs gradually came closer and finally the residue S459 of the RBD of chain B made a hydrogen bond with F374 of chain C in the last 200 ns of the simulation along with formation of a few more hydrogen bonds involving other residues. Since no transition from closed to the open state of the protein is observed in the present 1 μs unbiased simulation of the closed state protein, the current study seems to suggest that the closed conformational state is preferred for the spike protein of SARS‐CoV‐2 in aqueous medium. Furthermore, calculations of the free energy surface of the conformational transition from open (up) to the closed (down) state using a biased simulation method reveal a free energy barrier of ~3.20 kcal/mol for the transition of RBD from open to the closed state, whereas the barrier for the reverse process is found to be significantly higher.

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Section: Molecular Dynamics Simulationsmentioning

confidence: 99%

All‐atom simulations of the trimeric spike protein of SARS‐CoV‐2 in aqueous medium: Nature of interactions, conformational stability and free energy diagrams for conformational transition of the protein

2023

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“…Many successful techniques have been developed to solve the NLSE. Among them are Painlevé analysis [5][6][7], Hirota method [8], similarity transformation method [10], Lax Pair (LP) and Darboux transformation (DT) method [9,11,12], Miura transformation [13,14], inverse scattering transform and Hamiltonian approach [15], homotopy analysis method [16], Exp-function method [17], the tanh-function method [18,19], the homogeneous balance method [20], and the F-expansion method [21].…”

Section: Introductionmentioning

confidence: 99%

Singular Soliton Molecules of the Nonlinear Schrodinger Equation

Elhadj,

Sakkaf,

Khawaja

et al. 2020

Preprint

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We derive an exact solution to the local nonlinear Schrödinger equation (NLSE) using the Darboux transformation method. The new solution describes the profile and dynamics of a two-soliton molecule. Using an algebraically-decaying seed solution, we obtain a two-soliton solution with diverging peaks, which we denote as singular soliton molecule. We find that the new solution has a finite binding energy. We calculate the force and potential of interaction between the two solitons, which turn out to be of molecular-type. The robustness of the bond between the two solitons is also verified. Furthermore, we obtain a new solution to the nonlocal NLSE using the same method and seed solution. The new solution in this case corresponds to an elastic collision of a soliton, a breather soliton on flat background, and a breather soliton on a background with linear ramp. Finally, we consider an NLSE which is nonlocal in time rather than space. Although we did not find a Lax pair to this equation, we derive three exact solutions.

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“…At the atomistic level, the crazing [105][106][107][108] and the decohesion between carbon filler and polymer matrix [109][110][111][112][113] have been investigated without using the CZ model. First of all, the atomistic simulations have been performed to evaluate the CZ model parameters in crystalline solids [114][115][116][117][118][119][120].…”

Section: Introductionmentioning

confidence: 99%

Multiscale study of influence of interfacial decohesion on piezoresistivity of graphene/polymer nanocomposites

Detrez

Yvonnet

et al. 2019

Modelling Simul. Mater. Sci. Eng.

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A multiscale strategy is proposed to study the role of interfacial decohesion on the piezoresistive properties of graphene/polymer nanocomposite. A cohesive zone model is identified by atomistic simulations. This cohesive zone model enriches imperfect interfaces, which model graphene sheets, at mesoscale in our continuum mechanical model. This nonlinear mechanical model is used to generate deformed representative volume element to study influence of strain and interfacial decohesion on the conductivity of graphene/polymer nanocomposites. The effective conductivity is studied with an electric continuum model at mesoscale that incorporates the tunneling effect. A conductor-insulator transition is observed for elongations above 2% for graphene volume fraction just above the percolation threshold. The transition appears for an elongation of 8% instead of 2%, when the interfacial decohesion is removed.

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Numerical solution of AXB=C for (R,S)-symmetric matrices

Cited by 7 publications

References 24 publications

All‐atom simulations of the trimeric spike protein of SARS‐CoV‐2 in aqueous medium: Nature of interactions, conformational stability and free energy diagrams for conformational transition of the protein

All‐atom simulations of the trimeric spike protein of SARS‐CoV‐2 in aqueous medium: Nature of interactions, conformational stability and free energy diagrams for conformational transition of the protein

Singular Soliton Molecules of the Nonlinear Schrodinger Equation

Multiscale study of influence of interfacial decohesion on piezoresistivity of graphene/polymer nanocomposites

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