Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori−Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Lateral heterogeneities in biomembranes play a crucial role in various physiological functions of the cell. Such heterogeneities lead to demixing of lipid constituents and formation of distinct liquid domains in the membrane. We study lateral heterogeneities in terms of topological rearrangements of lipids to identify the liquid-liquid phase coexistence in model membranes. Using ideas from the physics of amorphous systems and glasses, we calculate the degree of nonaffine deformation associated with individual lipids to characterize the liquid-ordered (L) and liquid-disordered (L) regions in model lipid bilayers. We explore the usage of this method on all-atom and coarse-grained lipid bilayer trajectories. This method is helpful in defining the instantaneous L-L domain boundaries in complex multicomponent bilayer systems. The characterization is also used to highlight the effect of line-active molecules on the phase boundaries and domain mixing. Overall, we propose a framework to explore the molecular origin of spatial and dynamical heterogeneity in biomembrane systems, which can be exploited not only in computer simulations but also in experiments.

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Lipid membrane packing defects are considered to be an essential parameter that regulates specific membrane binding of several peripheral proteins. In the absence of direct experimental characterization, lipid packing defects and their role in the binding of peripheral proteins are generally investigated through computational studies, which have been immensely successful in unraveling the key steps of the membranebinding process. However, packing defects are calculated using two-dimensional (2D) projections and the crucial information on their depths is generally overlooked. Here, we present a simple yet computationally efficient algorithm, which identifies these defects in three dimensions. We validate the algorithm on a number of model membrane systems that are previously studied using 2D defect calculations and find that the defect size and the defect depth may not always be directly correlated. We employ the algorithm to understand the nature of packing defects in flat bilayer membranes exhibiting liquid-ordered (L o ), liquid-disordered (L d ), and co-existing (L o /L d ) phases. Our results indicate the presence of shallower, smaller, and spatially localized defects in the L o phase membranes as compared to the defects in L d and mixed L o /L d phase membranes. Such analyses can elucidate the molecular-scale mechanisms that drive the preferential localization of certain proteins to either of the liquid phases or their interface. We also analyze the membrane sensing and anchoring process of a peptide in terms of the three-dimensional defects, which provides additional insights into the process with respect to depth distributions across the bilayer leaflets.

For mesoscale structural studies of polymers, obtaining maximum level of coarse‐graining that maintains the chemical specificity is highly desirable. Here we present a systematic coarse‐graining study of sulfonated poly(ether ether ketone), sPEEK, and show that a 71:3 coarse‐grained (CG) mapping is the maximum possible map within a CG bead‐spring model. We perform single chain atomistic simulation on the system to collect various structural distributions, against which the CG potentials are optimized using iterative Boltzmann inversion technique. The potentials thus extracted are shown to reproduce the target distributions for larger single chains as well as for multiple chains. The structure at the atomistic level is shown to be preserved when we back‐map the CG system to re‐introduce the atomistic details. By using the same CG mapping for another repeat unit sequence of sPEEK, we show that the nature of the effective interaction at the CG level depends strongly on the polymer sequence and cannot be assumed based on the nature of the corresponding atomistic unit. These CG potentials will be the key to future mesoscopic simulations to study the structure of sPEEK based polymer electrolyte membranes.