Spatial organization is a characteristic of all cells, achieved in eukaryotic cells by utilizing both membrane-bound and membrane-less organelles. One of the key processes in eukaryotes is RNA splicing, which readies mRNA for translation. This complex and highly dynamical chemical process involves assembly and disassembly of many molecules in multiple cellular compartments and their transport among compartments. Our goal is to model the effect of spatial organization of membrane-less organelles (specifically nuclear speckles) and of organelle heterogeneity on splicing particle biogenesis in mammalian cells. Based on multiple sources of complementary experimental data, we constructed a spatial model of a HeLa cell to capture intracellular crowding effects. We then developed chemical reaction networks to describe the formation of RNA splicing machinery complexes and splicing processes within nuclear speckles (specific type of non-membrane-bound organelles). We incorporated these networks into our spatially-resolved human cell model and performed stochastic simulations for up to 15 minutes of biological time, the longest thus far for a eukaryotic cell. We find that an increase (decrease) in the number of nuclear pore complexes increases (decreases) the number of assembled splicing particles; and that compartmentalization is critical for the yield of correctly-assembled particles. We also show that a slight increase of splicing particle localization into nuclear speckles leads to a disproportionate enhancement of mRNA splicing and a reduction in the noise of generated mRNA. Our model also predicts that the distance between genes and speckles has a considerable effect on the mRNA production rate, with genes located closer to speckles producing mRNA at higher levels, emphasizing the importance of genome organization around speckles. The HeLa cell model, including organelles and sub-compartments, provides a flexible foundation to study other cellular processes that are strongly modulated by spatiotemporal heterogeneity.

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.

Simulation of in vivo cellular processes with the reaction–diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel efficiency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.

SUMMARY: NetworkView is an application for the display and analysis of protein·RNA interaction networks derived from structure and/or dynamics. These networks typically model individual protein residues and nucleic acid monomers as nodes and their pairwise contacts as edges with associated weights. NetworkView projects the network onto the underlying 3D molecular structure so that visualization and analysis of the network can be coupled to physical and biological properties. NetworkView is implemented as a plugin to the molecular visualization software VMD. AVAILABILITY AND IMPLEMENTATION: NetworkView is included with VMD, which is available at http://www.ks.uiuc.edu/Research/vmd/. Documentation, tutorials and supporting programs are available at http://www.scs.illinois.edu/schulten/software/. CONTACT: [email protected]

Stochastic expression of genes produces heterogeneity in clonal populations of bacteria under identical conditions. We analyze and compare the behavior of the inducible lac genetic switch using well-stirred and spatially resolved simulations for Escherichia coli cells modeled under fast and slow-growth conditions. Our new kinetic model describing the switching of the lac operon from one phenotype to the other incorporates parameters obtained from recently published in vivo single-molecule fluorescence experiments along with in vitro rate constants. For the well-stirred system, investigation of the intrinsic noise in the circuit as a function of the inducer concentration and in the presence/absence of the feedback mechanism reveals that the noise peaks near the switching threshold. Applying maximum likelihood estimation, we show that the analytic two-state model of gene expression can be used to extract stochastic rates from the simulation data. The simulations also provide mRNA-protein probability landscapes, which demonstrate that switching is the result of crossing both mRNA and protein thresholds. Using cryoelectron tomography of an E. coli cell and data from proteomics studies, we construct spatial in vivo models of cells and quantify the noise contributions and effects on repressor rebinding due to cell structure and crowding in the cytoplasm. Compared to systems without spatial heterogeneity, the model for the fast-growth cells predicts a slight decrease in the overall noise and an increase in the repressors rebinding rate due to anomalous subdiffusion. The tomograms for E. coli grown under slow-growth conditions identify the positions of the ribosomes and the condensed nucleoid. The smaller slow-growth cells have increased mRNA localization and a larger internal inducer concentration, leading to a significant decrease in the lifetime of the repressor-operator complex and an increase in the frequency of transcriptional bursts.

To address the problem of performing long time simulations of biochemical pathways under in vivo cellular conditions, we have developed a lattice-based, reaction-diffusion model that uses the graphics processing unit (GPU) as a computational co-processor. The method has been specifically designed from the beginning to take advantage of the GPU's capacity to perform massively parallel calculations by not only executing a core set of mathematical calculations, but also running much of the underlying algorithmic logic on the GPU. In this study we present our three-dimensional model for in vivo diffusion that exploits the calculation capabilities of the GPU. The implementation of the diffusion operator on the GPU is subject to architectural constraints, and we discuss its structure and the trade-offs made to accommodate the GPU hardware.

Abstract 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. Availability: Both binary and source code downloads for VMD 1.83, which includes Multiple Alignment, are available from . The Multidimensional QR factorization algorithm is available at Contact: [email protected]

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/