Coarse-grained (CG) models of biomolecules have recently attracted considerable interest because they enable the simulation of complex biological systems on length-scales and timescales that are inaccessible for atomistic molecular dynamics simulation. A CG model is defined by a map that transforms an atomically detailed configuration into a CG configuration. For CG models of relatively small biomolecules or in cases that the CG and all-atom models have similar resolution, the construction of this map is relatively straightforward and can be guided by chemical intuition. However, it is more challenging to construct a CG map when large and complex domains of biomolecules have to be represented by relatively few CG sites. This work introduces a new and systematic methodology called essential dynamics coarse-graining (ED-CG). This approach constructs a CG map of the primary sequence at a chosen resolution for an arbitrarily complex biomolecule. In particular, the resulting ED-CG method variationally determines the CG sites that reflect the essential dynamics characterized by principal component analysis of an atomistic molecular dynamics trajectory. Numerical calculations illustrate this approach for the HIV-1 CA protein dimer and ATP-bound G-actin. Importantly, since the CG sites are constructed from the primary sequence of the biomolecule, the resulting ED-CG model may be better suited to appropriately explore protein conformational space than those from other CG methods at the same degree of resolution.

This paper discusses the robust filtering problems for linear discrete-time systems with polytopic parameter uncertainty under the H2 and H , performance. We aim to derive a less conservative design than existing sufficient Iinear matrix inequality (LMI) based conditions. It is shown that a more efficient evaluation of robust HZ or H , performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters give additional freedoms in optimizing the guaranteed H2 or H , performance.The optimization will then lead to a less conservative design. The results will recover the existing robust HZ and H , filtering ones when the additional free parameters are set to be zero. We also propose an iterative algorithm to further refine the suboptimal filter. Examples are given to demonstrate the less conservatism of the proposed approaches.

The multiscale coarse-graining (MS-CG) method obtains CG interactions from atomistic configurations, as demonstrated previously for a variety of soft matter and biological systems. In this article, recent advances in MS-CG algorithms are described, and a recently developed computer program MSCGFM for MS-CG calculations is introduced. The algorithms enhance the efficiency and stability of MS-CG computations, and these algorithms are incorporated into the MSCGFM program. As a result of these efforts, MS-CG calculations on large scale systems such as peptide and proteins can become tractable, and the numerical stability of solutions for ill-posed MS-CG problems can be regularized efficiently. Various parallelization strategies are also discussed.

A solvent free coarse-grained model for a 1:1 mixed dioleoylphosphatidylcholine (DOPC) and a dioleoylphospatidylethanolamine (DOPE) bilayer is developed using the multiscale coarse-graining (MS-CG) approach. B-spline basis functions are implemented instead of the original cubic spline basis functions in the MS-CG method. The new B-spline basis functions are able to dramatically reduce memory requirements and increase computational efficiency of the MS-CG calculation. Various structural properties from the CG simulations are compared with their corresponding all-atom counterpart in order to validate the CG model. The resulting CG structural properties agree well with atomistic results, which shows the MS-CG force field can reasonably approximate the many-body potential of mean force in the coarse-grained coordinates. Fast lipid lateral diffusion in the CG simulations, as a result of smoother free energy landscape, makes the study of phase behavior of the binary mixture possible. Small clusters of distinct lipid composition are identified by analyzing the DOPC/DOPE lipid lateral distribution, indicating a non-uniform distribution for the mixed bilayer. The results of lipid phase behavior are compared to experimental results and connections between the experimental and simulation conclusions are discussed.