Expected and observed effects of volume exclusion on the free en- ergy of rigid and flexible macromolecules in crowded and confined systems, and consequent effects of crowding and confinement on macromolecular reaction rates and equilibria are summarized. Find- ings from relevant theoretical/simulation and experimental literature published from 2004 onward are reviewed. Additional complexity arising from the heterogeneity of local environments in biological media, and the presence of nonspecific interactions between macro- molecules over and above steric repulsion, are discussed. Theoretical and experimental approaches to the characterization of crowding- and confinement-induced effects in systems approaching the com- plexity of living organisms are suggested.

/pdf/macromolecular-crowding-and-confinement-biochemical-4gczqjpbdg.pdf

Macromolecular Crowding and Confinement: Biochemical, Biophysical, and Potential Physiological Consequences*

The “protein folding problem” consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

/pdf/the-protein-folding-problem-je8tdyrxrg.pdf

The Protein Folding Problem

Water is essential for life in many ways, and without it biomolecules might no longer truly be biomolecules. In particular, water is important to the structure, stability, dynamics, and function of biological macromolecules. In protein folding, water mediates the collapse of the chain and the search for the native topology through a funneled energy landscape. Water actively participates in molecular recognition by mediating the interactions between binding partners and contributes to either enthalpic or entropic stabilization. Accordingly, water must be included in recognition and structure prediction codes to capture specificity. Thus water should not be treated as an inert environment, but rather as an integral and active component of biomolecular systems, where it has both dynamic and structural roles. Focusing on water sheds light on the physics and function of biological machinery and self-assembly and may advance our understanding of the natural design of proteins and nucleic acids.

/pdf/water-mediation-in-protein-folding-and-molecular-recognition-24k5x5yaf3.pdf

Water mediation in protein folding and molecular recognition

Characterizing the equilibrium ensemble of folding pathways, including their relative probability, is one of the major challenges in protein folding theory today. Although this information is in principle accessible via all-atom molecular dynamics simulations, it is difficult to compute in practice because protein folding is a rare event and the affordable simulation length is typically not sufficient to observe an appreciable number of folding events, unless very simplified protein models are used. Here we present an approach that allows for the reconstruction of the full ensemble of folding pathways from simulations that are much shorter than the folding time. This approach can be applied to all-atom protein simulations in explicit solvent. It does not use a predefined reaction coordinate but is based on partitioning the state space into small conformational states and constructing a Markov model between them. A theory is presented that allows for the extraction of the full ensemble of transition pathways from the unfolded to the folded configurations. The approach is applied to the folding of a PinWW domain in explicit solvent where the folding time is two orders of magnitude larger than the length of individual simulations. The results are in good agreement with kinetic experimental data and give detailed insights about the nature of the folding process which is shown to be surprisingly complex and parallel. The analysis reveals the existence of misfolded trap states outside the network of efficient folding intermediates that significantly reduce the folding speed.

https://www.pnas.org/content/pnas/106/45/19011.full.pdf

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Everything you wanted to know about Markov State Models but were afraid to ask.

Although most experimental and theoretical studies of protein folding involve proteins in vitro, the effects of spatial confinement may complicate protein folding in vivo. In this study, we examine the folding dynamics of villin (a small fast folding protein) with explicit solvent confined to an inert nanopore. We have calculated the probability of folding before unfolding (Pfold) under various confinement regimes. Using Pfold correlation techniques, we observed two competing effects. Confining protein alone promotes folding by destabilizing the unfolded state. In contrast, confining both protein and solvent gives rise to a solvent-mediated effect that destabilizes the native state. When both protein and solvent are confined we see unfolding to a compact unfolded state different from the unfolded state seen in bulk. Thus, we demonstrate that the confinement of solvent has a significant impact on protein kinetics and thermodynamics. We conclude with a discussion of the implications of these results for folding in confined environments such as the chaperonin cavity in vivo.

https://www.pnas.org/content/pnas/104/25/10430.full.pdf

Protein folding under confinement: A role for solvent

Commercial graphics processors (GPUs) have high compute capacity at very low cost, which makes them attractive for general purpose scientic computing In this poster we show how graphics processors can be used for N-body simulations to obtain large improvements in performance over current generation CPUs We have developed a highly optimized algorithm for performing the O(N^2) force calculations that constitute the major part of stellar and molecular dynamics simulations In the calculations, we achieve sustained performance of nearly 100 GFlops on an ATI X1900XTX The performance on GPUs 25x an Intel Pentium4, and 2x specialized hardware such as GRAPE-6A, but at a fraction of the cost Furthermore, the wide availability of GPUs has signicant implications for cluster computing and distributed computing efforts like Folding@Home

N-Body simulation on GPUs

Does native state topology determine the RNA folding mechanism

Here, we present a novel computational approach for describing the formation of oligomeric assemblies at experimental concentrations and timescales. We propose an extension to the Markovian state model approach, where one includes low concentration oligomeric states analytically. This allows simulation on long timescales (seconds timescale) and at arbitrarily low concentrations (e.g., the micromolar concentrations found in experiments), while still using an all-atom model for protein and solvent. As a proof of concept, we apply this methodology to the oligomerization of an Abeta peptide fragment (Abeta(21-43)). Abeta oligomers are now widely recognized as the primary neurotoxic structures leading to Alzheimer's disease. Our computational methods predict that Abeta trimers form at micromolar concentrations in 10 ms, while tetramers form 1000 times more slowly. Moreover, the simulation results predict specific intermonomer contacts present in the oligomer ensemble as well as putative structures for small molecular weight oligomers. Based on our simulations and statistical models, we propose a novel mutation to stabilize the trimeric form of Abeta in an experimentally verifiable manner.

Simulating oligomerization at experimental concentrations and long timescales: A Markov state model approach.

Local structure formation in simulations of two small proteins.

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