Connecting protein and mRNA burst distributions for stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distribution. Additionally, if gene expression is repressed such that observed protein bursts arise only from single mRNAs, we show how observations of protein burst distributions (repressed and unrepressed) can be used to completely determine the mRNA burst distribution. Assuming independent contributions from individual bursts, we derive analytical expressions connecting means and variances for burst and steady-state protein distributions. Finally, we validate our general analytical results by considering a specific reaction scheme involving regulation of protein bursts by small RNAs. For a range of parameters, we derive analytical expressions for regulated protein distributions that are validated using stochastic simulations. The analytical results obtained in this work can thus serve as useful inputs for a broad range of studies focusing on stochasticity in gene expression

Accelerating Electrostatic Surface Potential Calculation with Multiscale Approximation on Graphics Processing Units

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. This paper demonstrates how one can take advantage of graphic processing units (GPUs) available in today’s typical desktop computer, together with a multiscale approximation method, to significantly speedup such computations. Specifically, the electrostatic potential computation, using an analytical linearized Poisson Boltzmann (ALPB) method, is implemented on an ATI Radeon 4870 GPU in combination with the hierarchical charge partitioning (HCP) multiscale approximation. This implementation delivers a combined 1800-fold speedup for a 476,040 atom viral capsid

Calculation and visualization of atomistic mechanical stresses in nanomaterials and biomolecules.

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications

Modulation of nucleosomal DNA accessibility via charge-altering post-translational modifications in histone core

Abstract Background Controlled modulation of nucleosomal DNA accessibility via post-translational modifications (PTM) is a critical component to many cellular functions. Charge-altering PTMs in the globular histone core—including acetylation, phosphorylation, crotonylation, propionylation, butyrylation, formylation, and citrullination—can alter the strong electrostatic interactions between the oppositely charged nucleosomal DNA and the histone proteins and thus modulate accessibility of the nucleosomal DNA, affecting processes that depend on access to the genetic information, such as transcription. However, direct experimental investigation of the effects of these PTMs is very difficult. Theoretical models can rationalize existing observations, suggest working hypotheses for future experiments, and provide a unifying framework for connecting PTMs with the observed effects. Results A physics-based framework is proposed that predicts the effect of charge-altering PTMs in the histone core, quantitatively for several types of lysine charge-neutralizing PTMs including acetylation, and qualitatively for all phosphorylations, on the nucleosome stability and subsequent changes in DNA accessibility, making a connection to resulting biological phenotypes. The framework takes into account multiple partially assembled states of the nucleosome at the atomic resolution. The framework is validated against experimentally known nucleosome stability changes due to the acetylation of specific lysines, and their effect on transcription. The predicted effect of charge-altering PTMs on DNA accessibility can vary dramatically, from virtually none to a strong, region-dependent increase in accessibility of the nucleosomal DNA; in some cases, e.g., H4K44, H2AK75, and H2BK57, the effect is significantly stronger than that of the extensively studied acetylation sites such H3K56, H3K115 or H3K122. Proximity to the DNA is suggestive of the strength of the PTM effect, but there are many exceptions. For the vast majority of charge-altering PTMs, the predicted increase in the DNA accessibility should be large enough to result in a measurable modulation of transcription. However, a few possible PTMs, such as acetylation of H4K77, counterintuitively decrease the DNA accessibility, suggestive of the repressed chromatin. A structural explanation for the phenomenon is provided. For the majority of charge-altering PTMs, the effect on DNA accessibility is simply additive (noncooperative), but there are exceptions, e.g., simultaneous acetylation of H4K79 and H3K122, where the combined effect is amplified. The amplification is a direct consequence of the nucleosome–DNA complex having more than two structural states. The effect of individual PTMs is classified based on changes in the accessibility of various regions throughout the nucleosomal DNA. The PTM’s resulting imprint on the DNA accessibility, “PTMprint,” is used to predict effects of many yet unexplored PTMs. For example, acetylation of H4K44 yields a PTMprint similar to the PTMprint of H3K56, and thus acetylation of H4K44 is predicted to lead to a wide range of strong biological effects. Conclusion Charge-altering post-translational modifications in the relatively unexplored globular histone core may provide a precision mechanism for controlling accessibility to the nucleosomal DNA

The SAMPL4 host-guest blind prediction challenge: an overview.

Prospective validation of methods for computing binding affinities can help assess their predictive power and thus set reasonable expectations for their performance in drug design applications. Supramolecular host-guest systems are excellent model systems for testing such affinity prediction methods, because their small size and limited conformational flexibility, relative to proteins, allows higher throughput and better numerical convergence. The SAMPL4 prediction challenge therefore included a series of host-guest systems, based on two hosts, cucurbit[7]uril and octa-acid. Binding affinities in aqueous solution were measured experimentally for a total of 23 guest molecules. Participants submitted 35 sets of computational predictions for these host-guest systems, based on methods ranging from simple docking, to extensive free energy simulations, to quantum mechanical calculations. Over half of the predictions provided better correlations with experiment than two simple null models, but most methods underperformed the null models in terms of root mean squared error and linear regression slope. Interestingly, the overall performance across all SAMPL4 submissions was similar to that for the prior SAMPL3 host-guest challenge, although the experimentalists took steps to simplify the current challenge. While some methods performed fairly consistently across both hosts, no single approach emerged as consistent top performer, and the nonsystematic nature of the various submissions made it impossible to draw definitive conclusions regarding the best choices of energy models or sampling algorithms. Salt effects emerged as an issue in the calculation of absolute binding affinities of cucurbit[7]uril-guest systems, but were not expected to affect the relative affinities significantly. Useful directions for future rounds of the challenge might involve encouraging participants to carry out some calculations that replicate each others' studies, and to systematically explore parameter options