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In order to grow and replicate, living cells must express a diverse array of proteins, but the process by which proteins are made includes a great deal of inherent randomness. Understanding this randomness-whether it arises from the discrete stochastic nature of chemical reactivity ("intrinsic" noise), or from cell-to-cell variability in the concentrations of molecules involved in gene expression, or from the timings of important cell-cycle events like DNA replication and cell division ("extrinsic" noise)-remains a challenge. In this article we analyze a model of gene expression that accounts for several extrinsic sources of noise, including those associated with chromosomal replication, cell division, and variability in the numbers of RNA polymerase, ribonuclease E, and ribosomes. We then attempt to fit our model to a large proteomics and transcriptomics data set and find that only through the introduction of a few key correlations among the extrinsic noise sources can we accurately recapitulate the experimental data. These include significant correlations between the rate of mRNA degradation (mediated by ribonuclease E) and the rates of both transcription (RNA polymerase) and translation (ribosomes) and, strikingly, an anticorrelation between the transcription and the translation rates themselves.

A molecular dynamics calculation of the amino acid polar requirement is used to score the canonical genetic code. Monte Carlo simulation shows that this computational polar requirement has been optimized by the canonical genetic code, an order of magnitude more than any previously known measure, effectively ruling out a vertical evolution dynamics. The sensitivity of the optimization to the precise metric used in code scoring is consistent with code evolution having proceeded through the communal dynamics of statistical proteins using horizontal gene transfer, as recently proposed. The extreme optimization of the genetic code therefore strongly supports the idea that the genetic code evolved from a communal state of life prior to the last universal common ancestor.

Background: Since the publication of the first draft of the human genome in 2000, bioinformatic data have been accumulating at an overwhelming pace. Currently, more than 3 million sequences and 35 thousand structures of proteins and nucleic acids are available in public databases. Finding correlations in and between these data to answer critical research questions is extremely challenging. This problem needs to be approached from several directions: information science to organize and search the data; information visualization to assist in recognizing correlations; mathematics to formulate statistical inferences; and biology to analyze chemical and physical properties in terms of sequence and structure changes., Results: Here we present MultiSeq, a unified bioinformatics analysis environment that allows one to organize, display, align and analyze both sequence and structure data for proteins and nucleic acids. While special emphasis is placed on analyzing the data within the framework of evolutionary biology, the environment is also flexible enough to accommodate other usage patterns. The evolutionary approach is supported by the use of predefined metadata, adherence to standard ontological mappings, and the ability for the user to adjust these classifications using an electronic notebook. MultiSeq contains a new algorithm to generate complete evolutionary profiles that represent the topology of the molecular phylogenetic tree of a homologous group of distantly related proteins. The method, based on the multidimensional QR factorization of multiple sequence and structure alignments, removes redundancy from the alignments and orders the protein sequences by increasing linear dependence, resulting in the identification of a minimal basis set of sequences that spans the evolutionary space of the homologous group of proteins., Conclusion: MultiSeq is a major extension of the Multiple Alignment tool that is provided as part of VMD, a structural visualization program for analyzing molecular dynamics simulations. Both are freely distributed by the NIH Resource for Macromolecular Modeling and Bioinformatics and MultiSeq is included with VMD starting with version 1.8.5. The MultiSeq website has details on how to download and use the software: http://www.scs.uiuc.edu/~schulten/multiseq/

An important part of protein structure characterization is the determination of excluded space such as fissures in contact interfaces, pores, inaccessible cavities, and catalytic pockets. We introduce a general tessellation method for visualizing the dual space around, within, and between biological molecules. Using Delaunay triangulation, a three-dimensional graph is constructed to provide a displayable discretization of the continuous volume. This graph structure is also used to compare the dual space of a system in two different states. Tessellator, a cross-platform implementation of the algorithm, is used to analyze the cavities within myoglobin, the protein-RNA docking interface between aspartyl-tRNA synthetase and tRNA(Asp), and the ammonia channel in the hisH-hisF complex of imidazole glycerol phosphate synthase.

Multiple Alignment is a new interface for performing and analyzing multiple protein structure alignments. It enables viewing levels of sequence and structure similarity on the aligned structures and performing a variety of evolutionary and bioinformatic tasks, including the construction of structure-based phylogenetic trees and minimal basis sets of structures that best represent the topology of the phylogenetic tree. It is implemented as a plugin for VMD (Visual Molecular Dynamics), which is distributed by the NIH Resource for Macromolecular Modeling and Bioinformatics at the University of Illinois.

We present a new algorithm, based on the multidimensional QR factorization, to remove redundancy from a multiple structural alignment by choosing representative protein structures that best preserve the phylogenetic tree topology of the homologous group. The classical QR factorization with pivoting, developed as a fast numerical solution to eigenvalue and linear least-squares problems of the form Ax=b, was designed to re-order the columns of A by increasing linear dependence. Removing the most linear dependent columns from A leads to the formation of a minimal basis set which well spans the phase space of the problem at hand. By recasting the problem of redundancy in multiple structural alignments into this framework, in which the matrix A now describes the multiple alignment, we adapted the QR factorization to produce a minimal basis set of protein structures which best spans the evolutionary (phase) space. The non-redundant and representative profiles obtained from this procedure, termed evolutionary profiles, are shown in initial results to outperform well-tested profiles in homology detection searches over a large sequence database. A measure of structural similarity between homologous proteins, Q(H), is presented. By properly accounting for the effect and presence of gaps, a phylogenetic tree computed using this metric is shown to be congruent with the maximum-likelihood sequence-based phylogeny. The results indicate that evolutionary information is indeed recoverable from the comparative analysis of protein structure alone. Applications of the QR ordering and this structural similarity metric to analyze the evolution of structure among key, universally distributed proteins involved in translation, and to the selection of representatives from an ensemble of NMR structures are also discussed.

Proteins have evolved to use water to help guide folding. A physically motivated, nonpairwise-additive model of water-mediated interactions added to a protein structure prediction Hamiltonian yields marked improvement in the quality of structure prediction for larger proteins. Free energy profile analysis suggests that long-range water-mediated potentials guide folding and smooth the underlying folding funnel. Analyzing simulation trajectories gives direct evidence that water-mediated interactions facilitate native-like packing of supersecondary structural elements. Long-range pairing of hydrophilic groups is an integral part of protein architecture. Specific water-mediated interactions are a universal feature of biomolecular recognition landscapes in both folding and binding.

Steady progress has been made in the field of ab initio protein folding. A variety of methods now allow the prediction of low-resolution structures of small proteins or protein fragments up to approximately 100 amino acid residues in length. Such low-resolution structures may be sufficient for the functional annotation of protein sequences on a genome-wide scale. Although no consistently reliable algorithm is currently available, the essential challenges to developing a general theory or approach to protein structure prediction are better understood. The energy landscapes resulting from the structure prediction algorithms are only partially funneled to the native state of the protein. This review focuses on two areas of recent advances in ab initio structure prediction-improvements in the energy functions and strategies to search the caldera region of the energy landscapes.

We investigate the use of a Mayer cluster expansion to quantify changes to the energy landscape of an ab initio protein structure prediction Hamiltonian as side-chain excluded volume radii are increased. The expansion is generalized so that the effect of other changes in the Hamiltonian, which would alone be best treated with a cumulant expansion, can be evaluated simultaneously. The effect of changing the excluded volume radii on various thermodynamic quantities, in particular the free energy and glass transition temperature, is calculated with the expansion and compared to results from simulation. The expansion is found to be sufficiently accurate at the second-order level to be useful for calculating values of the excluded volume radii that refine the energy landscape for structure prediction. This is explicitly checked by a free energy profile analysis and examining the quality of predictions before and after the optimization. A useful method to test whether equilibrium has been attained during molecular dynamics sampling is also described. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We discuss how protein structure prediction schemes may be refined via a cumulant expansion approach using optimization criteria motivated by energy landscape ideas. The approach is advantageously combined with a free energy profile analysis based on multiple histogram sampling methods, which enables a quantitative assessment of the effects of refinement on the energy landscape to be made. The approach is widely applicable, but is illustrated here for a previously described prediction scheme intended for use in the absence of any known homology information. The relationship to previous optimization schemes is discussed. [ABSTRACT FROM AUTHOR]

Proposes a reduced model of proteins and simulates folding of a designed three helix bundle protein with 54 residues, the dynamics of a random heteropolymer, and the helix formation of a short peptide. Solvent effects; Hydrogen bond strength; Model of hydrophobic force.

It is well known that stochasticity in gene expression is an important source of noise that can have profound effects on the fate of a living cell. In the galactose genetic switch in yeast, the unbinding of a transcription repressor is induced by high concentrations of sugar particles activating gene expression of sugar transporters. This response results in high propensity for all reactions involving interactions with the metabolite. The reactions for gene expression, feedback loops and transport are typically described by chemical master equations (CME). Sampling the CME using the stochastic simulation algorithm (SSA) results in large computational costs as each reaction event is evaluated explicitly. To improve the computational efficiency of cell simulations involving high particle number systems, the authors have implemented a hybrid stochastic–deterministic (CME–ODE) method into the publically available, GPU‐based lattice microbes (LM) software suite and its python interface pyLM. LM and pyLM provide a convenient way to simulate complex cellular systems and interface with high‐performance RDME/CME/ODE solvers. As a test of the implementation, the authors apply the hybrid CME‐ODE method to the galactose switch in Saccharomyces cerevisiae, gaining a 10–50× speedup while yielding protein distributions and species traces similar to the pure SSA CME. [ABSTRACT FROM AUTHOR]

Using protein counts sampled from single cell proteomics distributions to constrain fluxes through a genome-scale model of metabolism, Population flux balance analysis (Population FBA) successfully described metabolic heterogeneity in a population of independent Escherichia coli cells growing in a defined medium. We extend the methodology to account for correlations in protein expression arising from the co-regulation of genes and apply it to study the growth of independent Saccharomyces cerevisiae cells in two different growth media. We find the partitioning of flux between fermentation and respiration predicted by our model agrees with recent 13C fluxomics experiments, and that our model largely recovers the Crabtree effect (the experimentally known bias among certain yeast species toward fermentation with the production of ethanol even in the presence of oxygen), while FBA without proteomics constraints predicts respirative metabolism almost exclusively. The comparisons to the 13C study showed improvement upon inclusion of the correlations and motivated a technique to systematically identify inconsistent kinetic parameters in the literature. The minor secretion fluxes for glycerol and acetate are underestimated by our method, which indicate a need for further refinements to the metabolic model. For yeast cells grown in synthetic defined (SD) medium, the calculated broad distribution of growth rates matches experimental observations from single cell studies, and we characterize several metabolic phenotypes within our modeled populations that make use of diverse pathways. Fast growing yeast cells are predicted to perform significant amount of respiration, use serine-glycine cycle and produce ethanol in mitochondria as opposed to slow growing cells. We use a genetic algorithm to determine the proteomics constraints necessary to reproduce the growth rate distributions seen experimentally. We find that a core set of 51 constraints are essential but that additional constraints are still necessary to recover the observed growth rate distribution in SD medium. [ABSTRACT FROM AUTHOR]

Ribosomal signatures, idiosyncrasies in the ribosomal RNA (rRNA) and/or proteins, are characteristic of the individual domains of life. As such, insight into the early evolution of the domains can be gained from a comparative analysis of their respective signatures in the translational apparatus. In this work, we identify signatures in both the sequence and structure of the rRNA and analyze their contributions to the universal phylogenetic tree using both sequence- and structure-based methods. Domain-specific ribosomal proteins can be considered signatures in their own right. Although it is commonly assumed that they developed after the universal ribosomal proteins, we present evidence that at least one may have been present before the divergence of the organismal lineages. We find correlations between the rRNA signatures and signatures in the ribosomal proteins showing that the rRNA signatures coevolved with both domain-specific and universal ribosomal proteins. Finally, we show that the genomic organization of the universal ribosomal components contains these signatures as well. From these studies, we propose the ribosomal signatures are remnants of an evolutionary-phase transition that occurred as the cell lineages began to coalesce and so should be reflected in corresponding signatures throughout the fabric of the cell and its genome. [ABSTRACT FROM AUTHOR]

Provides information on the use of protein energy landscape theory to obtain optimal energy functions for protein structure prediction via stimulated annealing, with focus on science. Relationship between folding dynamics and characteristic energy scales that control the collapse of proteins and modulate rigidity of short-range interactions; Indications of the findings.

We have combined equilibrium and steered molecular dynamics (SMD) simulations with principal component and correlation analyses to probe the mechanism of allosteric regulation in imidazole glycerol phosphate (IGP) synthase. An evolutionary analysis of IGP synthase revealed a conserved network of interactions leading from the effector binding site to the glutaminase active site, forming conserved communication pathways between the remote active sites. SMD simulations of the undocking of the ribonucleotide effector N¹-[(5′-phosphoribulosyl)-formino]-5′-aminoimidazole carboxamide ribonucleotide (PRFAR) resulted in a large scale hinge-opening motion at the interface. Principal component analysis and a correlation analysis of the equilibration protein motion indicate that the dynamics involved in the allosteric transition are mediated by coupled motion between sites that are more than 25 Å apart. Furthermore, conserved residues at the substrate-binding site, within the barrel, and at the interface were found to exhibit highly correlated motion during the allosteric transition. The coupled motion between PRFAR unbinding and the directed opening of the interface is interpreted in combination with kinetic assays for the wild-type and mutant systems to develop a model of allosteric regulation in IGP synthase that is monitored and investigated with atomic resolution. [ABSTRACT FROM AUTHOR]