Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in a percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times but anomalous diffusion at intermediate times. The effective exponents for square distance vs time usually are below one at these intermediate times, but they can also be larger than one for high barrier concentrations. Thus, we observe sub- and superdiffusion in a crowded environment.     

Protein-Protein Interactions in a Crowded Environment: An Analysis via Cross-Docking Simulations and Evolutionary Information

Large-scale analyses of protein-protein interactions based on coarse-grain molecular docking simulations and binding site predictions resulting from evolutionary sequence analysis, are possible and realizable on hundreds of proteins with variate structures and interfaces. We demonstrated this on the 168 proteins of the Mintseris Benchmark 2.0. On the one hand, we evaluated the quality of the interaction signal and the contribution of docking information compared to evolutionary information showing that the combination of the two improves partner identification. On the other hand, since protein interactions usually occur in crowded environments with several competing partners, we realized a thorough analysis of the interactions of proteins with true partners but also with non-partners to evaluate whether proteins in the environment, competing with the true partner, affect its identification. We found three populations of proteins: strongly competing, never competing, and interacting with different levels of strength. Populations and levels of strength are numerically characterized and provide a signature for the behavior of a protein in the crowded environment. We showed that partner identification, to some extent, does not depend on the competing partners present in the environment, that certain biochemical classes of proteins are intrinsically easier to analyze than others, and that small proteins are not more promiscuous than large ones. Our approach brings to light that the knowledge of the binding site can be used to reduce the high computational cost of docking simulations with no consequence in the quality of the results, demonstrating the possibility to apply coarse-grain docking to datasets made of thousands of proteins. Comparison with all available large-scale analyses aimed to partner predictions is realized. We release the complete decoys set issued by coarse-grain docking simulations of both true and false interacting partners, and their evolutionary sequence analysis leading to binding site predictions. Download site: http://www.lgm.upmc.fr/CCDMintseris/     

Crowded Cell-like Environment Accelerates the Nucleation Step of Amyloidogenic Protein Misfolding

To understand the role of a crowded physiological environment in the pathogenesis of neurodegenerative diseases, we report the following. 1) The formation of fibrous aggregates of the human Tau fragment Tau-(244–441), when hyperphosphorylated by glycogen synthase kinase-3β, is dramatically facilitated by the addition of crowding agents. 2) Fibril formation of nonphosphorylated Tau-(244–441) is only promoted moderately by macromolecular crowding. 3) Macromolecular crowding dramatically accelerates amyloid formation by human prion protein. A sigmoidal equation has been used to fit these kinetic data, including published data of human α-synuclein, yielding lag times and apparent rate constants for the growth of fibrils for these amyloidogenic proteins. These biochemical data indicate that crowded cell-like environments significantly accelerate the nucleation step of fibril formation of human Tau fragment/human prion protein/human α-synuclein (a significant decrease in the lag time). These results can in principle be predicted based on some known data concerning protein concentration effects on fibril formation both in vitro and in vivo. Furthermore, macromolecular crowding causes human prion protein to form short fibrils and nonfibrillar particles with lower conformational stability and higher protease resistance activity, compared with those formed in dilute solutions. Our data demonstrate that a crowded physiological environment could play an important role in the pathogenesis of neurodegenerative diseases by accelerating amyloidogenic protein misfolding and inducing human prion fibril fragmentation, which is considered to be an essential step in prion replication.Amyloid fibrils associated with neurodegenerative diseases such as Alzheimer disease, Parkinson disease, Huntington disease, and transmissible spongiform encephalopathy (TSE)³ (1–5) can be considered biologically relevant failures of the cellular protein quality control mechanisms (6) consisting of molecular chaperones and proteases (7). Up to now, about 20 different proteins with unrelated sequences and tertiary structures are known to form fibrous aggregates associated with various neurodegenerative diseases. These amyloidogenic proteins include both natively unfolded proteins, such as human Tau protein (3) and human α-synuclein (8), and folded globular proteins such as human prion protein (4). There are two faces of protein misfolding in neurodegeneration as follows: a gain of toxic function and a loss of physiological function, which can even occur in combination (9).Human Tau protein, a marker for Alzheimer disease, forms filaments in the brains of patients with Alzheimer disease (3, 10, 11). It has been found that hyperphosphorylation of Tau reduces the binding affinity between Tau and tubulin and contributes to the self-association of Tau and the formation of Tau paired helical filaments (3, 11–13). It has been proposed that glycogen synthase kinase-3β (GSK-3β) hyperphosphorylation of Tau plays an important role in Alzheimer disease (14, 15), and GSK-3β induces an Alzheimer disease-like hyperphosphorylation of Tau when overexpressed in cultured human neurons (16).A large body of data strongly suggests Creutzfeldt-Jakob disease, bovine spongiform encephalopathy, and other TSEs are caused by prions (4). Prions are infectious proteins that can transmit biological information by propagating protein misfolding and aggregation (17). The infectious agent is believed to consist entirely of the prion protein (PrP) and is devoid of nucleic acid (4, 17). Prion biogenesis is associated with the normal protease-sensitive form of the protein (cellular PrP molecule, PrP^C) undergoing structural change into an abnormal, protease-resistant, disease-causing isoform of prion protein (PrP^Sc) (4, 17). Although the mechanism by which PrP^C is converted to PrP^Sc in TSE-infected cells and in vivo is not clear, data from cell-free reactions suggest this process is akin to autocatalytic polymerization (18).Misfolding of Tau and prion proteins has been traditionally and widely studied in dilute solutions (10, 19–21). However, the physiological environment is poorly modeled by such dilute solutions, and biochemical reactions in vivo differ greatly from those in dilute solutions (22). The proteins associated with neurodegenerative diseases form fibrils in a physiological environment crowded with other background macromolecules (22–26), such as proteins, glycosaminoglycans, and proteoglycans (23). Crowding is not confined to cellular interiors but also occurs in the extracellular matrix of tissues (24) and takes place at membrane surfaces (27). For example, blood plasma contains ∼80 g/liter protein, a concentration sufficient to cause significant crowding effects (24). Polysaccharides also contribute to crowding, especially in the extracellular matrix of tissues such as collagen (23, 26). The conversion of PrP from a normal soluble conformation PrP^C to its pathogenic conformation PrP^Sc is believed to occur on the cell surface, in the endocytic vesicles, or in the crowded extracellular matrix (18). Thus, macromolecular crowding on the cell surface and in the extracellular matrix may play an important role in the conformational transition and amyloid formation of PrP in vivo, which have not been fully characterized yet. In vitro, such a crowded environment can be achieved experimentally by adding high concentrations of single or mixed nonspecific crowding agents to the system (23–31). Recently, it has been demonstrated that macromolecular crowding significantly enhances the rate of amyloid formation of α-synuclein (32, 33), amyloid-β peptides (27), and human apolipoprotein C-II (34). However, the role of the crowded physiological environment in the pathogenesis of neurodegenerative diseases is poorly understood so far.To address the contributions of crowded physiological environments on the pathogenesis of neurodegenerative diseases, we report here that macromolecular crowding dramatically accelerates fibril formation by human Tau fragment and by human prion protein under physiological conditions. Our results indicate that macromolecular crowding significantly accelerates the nucleation step of fibril formation of human Tau fragment/human prion protein/human α-synuclein by fitting the data to a sigmoidal equation (35, 36). Furthermore, macromolecular crowding causes human prion protein to form short fibrils and nonfibrillar particles with lower conformational stability and higher protease resistance activity, compared with those formed in dilute solutions.     

Properties of Polycrystalline Diamond: Multiscale Modeling Approach

Abstract

Two modeling techniques to characterize fracture behavior of polycrystalline diamond films are discussed. The first technique is a multiscale modeling method in which first-principles local density approximation calculations on selected structures are combined with an analytic mesoscale model to obtain energies and cleavage fracture energies for symmetric ?001? tilt grain boundaries (GBs) over the entire misorientation range. The second technique is large-scale atomistic simulation of the dynamics of failure in notched polycrystalline diamond samples under an applied strain. Electronic characteristics of selected ?001? symmetrical tilt GBs calculated with a semiempirical tight-binding Hamiltonian are also presented, and the possible role of graphitic defects on field emission from polycrystalline diamond is briefly discussed.     

Mechanism of the Exchange Reaction in HRAS from Multiscale Modeling

HRAS regulates cell growth promoting signaling processes by cycling between active (GTP-bound) and inactive (GDP-bound) states. Understanding the transition mechanism is central for the design of small molecules to inhibit the formation of RAS-driven tumors. Using a multiscale approach involving coarse-grained (CG) simulations, all-atom classical molecular dynamics (CMD; total of 3.02 µs), and steered molecular dynamics (SMD) in combination with Principal Component Analysis (PCA), we identified the structural features that determine the nucleotide (GDP) exchange reaction. We show that weakening the coupling between the SwitchI (residues 25–40) and SwitchII (residues 59–75) accelerates the opening of SwitchI; however, an open conformation of SwitchI is unstable in the absence of guanine nucleotide exchange factors (GEFs) and rises up towards the bound nucleotide to close the nucleotide pocket. Both I21 and Y32, play a crucial role in SwitchI transition. We show that an open SwitchI conformation is not necessary for GDP destabilization but is required for GDP/Mg escape from the HRAS. Further, we present the first simulation study showing displacement of GDP/Mg away from the nucleotide pocket. Both SwitchI and SwitchII, delays the escape of displaced GDP/Mg in the absence of GEF. Based on these results, a model for the mechanism of GEF in accelerating the exchange process is hypothesized.     

Multiscale Metabolic Modeling: Dynamic Flux Balance Analysis on a Whole-Plant Scale

Plant metabolism is characterized by a unique complexity on the cellular, tissue, and organ levels. On a whole-plant scale, changing source and sink relations accompanying plant development add another level of complexity to metabolism. With the aim of achieving a spatiotemporal resolution of source-sink interactions in crop plant metabolism, a multiscale metabolic modeling (MMM) approach was applied that integrates static organ-specific models with a whole-plant dynamic model. Allowing for a dynamic flux balance analysis on a whole-plant scale, the MMM approach was used to decipher the metabolic behavior of source and sink organs during the generative phase of the barley (Hordeum vulgare) plant. It reveals a sink-to-source shift of the barley stem caused by the senescence-related decrease in leaf source capacity, which is not sufficient to meet the nutrient requirements of sink organs such as the growing seed. The MMM platform represents a novel approach for the in silico analysis of metabolism on a whole-plant level, allowing for a systemic, spatiotemporally resolved understanding of metabolic processes involved in carbon partitioning, thus providing a novel tool for studying yield stability and crop improvement.Plants are of vital significance as a source of food (Grusak and DellaPenna, 1999; Rogalski and Carrer, 2011), feed (Lu et al., 2011), energy (Tilman et al., 2006; Parmar et al., 2011), and feedstocks for the chemical industry (Metzger and Bornscheuer, 2006; Kinghorn et al., 2011). Given the close connection between plant metabolism and the usability of plant products, there is a growing interest in understanding and predicting the behavior and regulation of plant metabolic processes. In order to increase crop quality and yield, there is a need for methods guiding the rational redesign of the plant metabolic network (Schwender, 2009).Mathematical modeling of plant metabolism offers new approaches to understand, predict, and modify complex plant metabolic processes. In plant research, the issue of metabolic modeling is constantly gaining attention, and different modeling approaches applied to plant metabolism exist, ranging from highly detailed quantitative to less complex qualitative approaches (for review, see Giersch, 2000; Morgan and Rhodes, 2002; Poolman et al., 2004; Rios-Estepa and Lange, 2007).A widely used modeling approach is flux balance analysis (FBA), which allows the prediction of metabolic capabilities and steady-state fluxes under different environmental and genetic backgrounds using (non)linear optimization (Orth et al., 2010). Assuming steady-state conditions, FBA has the advantage of not requiring the knowledge of kinetic parameters and, therefore, can be applied to model detailed, large-scale systems. In recent years, the FBA approach has been applied to several different plant species, such as maize (Zea mays; Dal’Molin et al., 2010; Saha et al., 2011), barley (Hordeum vulgare; Grafahrend-Belau et al., 2009b; Melkus et al., 2011; Rolletschek et al., 2011), rice (Oryza sativa; Lakshmanan et al., 2013), Arabidopsis (Arabidopsis thaliana; Poolman et al., 2009; de Oliveira Dal’Molin et al., 2010; Radrich et al., 2010; Williams et al., 2010; Mintz-Oron et al., 2012; Cheung et al., 2013), and rapeseed (Brassica napus; Hay and Schwender, 2011a, 2011b; Pilalis et al., 2011), as well as algae (Boyle and Morgan, 2009; Cogne et al., 2011; Dal’Molin et al., 2011) and photoautotrophic bacteria (Knoop et al., 2010; Montagud et al., 2010; Boyle and Morgan, 2011). These models have been used to study different aspects of metabolism, including the prediction of optimal metabolic yields and energy efficiencies (Dal’Molin et al., 2010; Boyle and Morgan, 2011), changes in flux under different environmental and genetic backgrounds (Grafahrend-Belau et al., 2009b; Dal’Molin et al., 2010; Melkus et al., 2011), and nonintuitive metabolic pathways that merit subsequent experimental investigations (Poolman et al., 2009; Knoop et al., 2010; Rolletschek et al., 2011). Although FBA of plant metabolic models was shown to be capable of reproducing experimentally determined flux distributions (Williams et al., 2010; Hay and Schwender, 2011b) and generating new insights into metabolic behavior, capacities, and efficiencies (Sweetlove and Ratcliffe, 2011), challenges remain to advance the utility and predictive power of the models.Given that many plant metabolic functions are based on interactions between different subcellular compartments, cell types, tissues, and organs, the reconstruction of organ-specific models and the integration of these models into interacting multiorgan and/or whole-plant models is a prerequisite to get insight into complex plant metabolic processes organized on a whole-plant scale (e.g. source-sink interactions). Almost all FBA models of plant metabolism are restricted to one cell type (Boyle and Morgan, 2009; Knoop et al., 2010; Montagud et al., 2010; Cogne et al., 2011; Dal’Molin et al., 2011), one tissue or one organ (Grafahrend-Belau et al., 2009b; Hay and Schwender, 2011a, 2011b; Pilalis et al., 2011; Mintz-Oron et al., 2012), and only one model exists taking into account the interaction between two cell types by specifying the interaction between mesophyll and bundle sheath cells in C4 photosynthesis (Dal’Molin et al., 2010). So far, no model representing metabolism at the whole-plant scale exists.Considering whole-plant metabolism raises the problem of taking into account temporal and environmental changes in metabolism during plant development and growth. Although classical static FBA is unable to predict the dynamics of metabolic processes, as the network analysis is based on steady-state solutions, time-dependent processes can be taken into account by extending the classical static FBA to a dynamic flux balance analysis (dFBA), as proposed by Mahadevan et al. (2002). The static (SOA) and dynamic optimization approaches introduced in this work provide a framework for analyzing the transience of metabolism by integrating kinetic expressions to dynamically constrain exchange fluxes. Due to the requirement of knowing or estimating a large number of kinetic parameters, so far dFBA has only been applied to a plant metabolic model once, to study the photosynthetic metabolism in the chloroplasts of C3 plants by a simplified model of five biochemical reactions (Luo et al., 2009). Integrating a dynamic model into a static FBA model is an alternative approach to perform dFBA.In this study, a multiscale metabolic modeling (MMM) approach was applied with the aim of achieving a spatiotemporal resolution of cereal crop plant metabolism. To provide a framework for the in silico analysis of the metabolic dynamics of barley on a whole-plant scale, the MMM approach integrates a static multiorgan FBA model and a dynamic whole-plant multiscale functional plant model (FPM) to perform dFBA. The performance of the novel whole-plant MMM approach was tested by studying source-sink interactions during the seed developmental phase of barley plants.     

On the Origins of a Crowded Cytoplasm

Contemporary cells show a highly crowded macromolecular content, the processes which originated this state being largely unknown. We propose that a driving force leading to the crowded cellular state could be the increase in growth rate produced by an enhanced cytoplasmic protein concentration. Briefly, in a diluted scenario, an increase in protein concentration has two opposing effects on growth rate. The favorable effect is the increase in the activity per unit volume of the component proteins and the disadvantageous effect is the concomitant increase in the protein mass per unit volume which has to be produced. In this work we show that the first effect is quantitatively more important, resulting in an overall increase in growth rate. This result was obtained with a model of E. coli and using nonmechanistic physiological arguments. The proposed driving force operates even at low protein concentrations, where the nonspecific interactions of macromolecular crowding are not significant, and could be as ancient as the first protocells. Experimental measurement of this cytoplasmic protein concentration effect in present organisms is hindered by the prevailing nonspecific interactions, product of long-term evolution. However, chemical/biochemical systems, built up to mimic properties of living cells, could be an adequate tool to test this effect. [Reviewing Editor: Dr. Antony Dean]     

Multiscale Measurements Distinguish Cellular and Interstitial Hindrances to Diffusion In Vivo

Molecular cancer therapy relies on interstitial diffusion for drug distribution in solid tumors. A mechanistic understanding of how tumor components affect diffusion is necessary to advance cancer drug development. Yet, because of limitations in current techniques, it is unclear how individual tissue components hinder diffusion. We developed multiscale fluorescence recovery after photobleaching (MS-FRAP) to address this deficiency. Diffusion measurements facilitated by MS-FRAP distinguish the diffusive hindrance of the interstitial versus cellular constituents in living tissue. Using multiscale diffusion measurements in vivo, we resolved the contributions of these two major tissue components toward impeding diffusive transport in solid tumors and subcutaneous tissue in mice. We further used MS-FRAP in interstitial matrix-mimetic gels and in vivo to show the influence of physical interactions between collagen and hyaluronan on diffusive hindrance through the interstitium. Through these studies, we show that interstitial hyaluronan paradoxically improves diffusion and that reducing cellularity enhances diffusive macromolecular transport in solid tumors.     

Trypanosome Motion Represents an Adaptation to the Crowded Environment of the Vertebrate Bloodstream

Blood is a remarkable habitat: it is highly viscous, contains a dense packaging of cells and perpetually flows at velocities varying over three orders of magnitude. Only few pathogens endure the harsh physical conditions within the vertebrate bloodstream and prosper despite being constantly attacked by host antibodies. African trypanosomes are strictly extracellular blood parasites, which evade the immune response through a system of antigenic variation and incessant motility. How the flagellates actually swim in blood remains to be elucidated. Here, we show that the mode and dynamics of trypanosome locomotion are a trait of life within a crowded environment. Using high-speed fluorescence microscopy and ordered micro-pillar arrays we show that the parasites mode of motility is adapted to the density of cells in blood. Trypanosomes are pulled forward by the planar beat of the single flagellum. Hydrodynamic flow across the asymmetrically shaped cell body translates into its rotational movement. Importantly, the presence of particles with the shape, size and spacing of blood cells is required and sufficient for trypanosomes to reach maximum forward velocity. If the density of obstacles, however, is further increased to resemble collagen networks or tissue spaces, the parasites reverse their flagellar beat and consequently swim backwards, in this way avoiding getting trapped. In the absence of obstacles, this flagellar beat reversal occurs randomly resulting in irregular waveforms and apparent cell tumbling. Thus, the swimming behavior of trypanosomes is a surprising example of micro-adaptation to life at low Reynolds numbers. For a precise physical interpretation, we compare our high-resolution microscopic data to results from a simulation technique that combines the method of multi-particle collision dynamics with a triangulated surface model. The simulation produces a rotating cell body and a helical swimming path, providing a functioning simulation method for a microorganism with a complex swimming strategy.     

用于生理组学协同研究的跨层次建模标记语言(M3L)

根据生理组学多领域多层次协同研究的需求,针对中国生理组学研究的特点,设计了一种跨层次建模标记语言(Mul-tiscale Modeling Markup Language,简称M3L),规范研究过程中的信息描述方法,实现了数学模型和计算数据的开放式共享和重用。M3L包含结构化模型机制、数据存档机制、信息交互与重用机制、数学描述机制、可视化模型及附件描述机制。M3L中针对人体和小动物解剖结构数据的特殊设计实现了结构与功能信息的关联,促进了中国生理组学研究中模型和数据的标准化描述;M3L以跨层次结构化的方式描述模型,符合生理组学研究模型的特点,满足了协同开发的需求。     

Control of Gaseous Environment of Organisms using a Diffusion Column Technique

A technique based on the theory of steady-state diffusion ofgases in a long column provides a simple means of controllingthe gas concentration in biological experiments. The diffusioncolumn consists of a sand-filled tube with side-arms along itslength. Selected gas concentrations are applied at both endsof the column and maintain a predictable concentration gradientalong the column. The gas composition at each side-arm is thusknown and can be adjusted by alteration of the controlling concentrationsat the ends of the column. The response to gas concentrationof small bodies such as seeds and micro-organisms can be testedby placing them in small cuvettes attached to the side-arms.The technique is well suited for experiments needing a closelygraded series of gaseous concentrations. The design and useof an electrode to monitor oxygen concentration is also described.     

Novel Multiscale Modeling Tool Applied to Pseudomonas aeruginosa Biofilm Formation

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.     

Modeling the Role of Diffusion Coefficients on Turing Instability in a Reaction-diffusion Prey-predator System

The paper is concerned with the effect of variable dispersal rates on Turing instability of a non-Lotka-Volterra reaction-diffusion system. In ecological applications, the dispersal rates of different species tends to oscillate in time. This oscillation is modeled by temporal variation in the diffusion coefficient with large as well as small periodicity. The case of large periodicity is analyzed using the theory of Floquet multipliers and that of the small periodicity by using Hill's equation. The effect of such variation on the resulting Turing space is studied. A comparative analysis of the Turing spaces with constant diffusivity and variable diffusivities is performed. Numerical simulations are carried out to support analytical findings.     

Bottom-Up Meets Top-Down: The Crossroads of Multiscale Chromatin Modeling

Chromatin can be viewed as a hierarchically structured fiber that regulates gene expression. It consists of a complex network of DNA and proteins whose characteristic dynamical modes facilitate compaction and rearrangement in the cell nucleus. These modes stem from chromatin’s fundamental unit, the nucleosome, and their effects are propagated across length scales. Understanding the effects of nucleosome dynamics on the chromatin fiber, primarily through post-translational modifications that occur on the histones, is of central importance to epigenetics. Within the last decade, imaging and chromosome conformation capture techniques have revealed a number of structural and statistical features of the packaged chromatin fiber at a hitherto unavailable level of resolution. Such experiments have led to increased efforts to develop polymer models that aim to reproduce, explain, and predict the contact probability scaling and density heterogeneity. At nanometer scales, available models have focused on the role of the nucleosome and epigenetic marks on local chromatin structure. At micrometer scales, existing models have sought to explain scaling laws and density heterogeneity. Less work, however, has been done to reconcile these two approaches: bottom-up and top-down models of chromatin. In this perspective, we highlight the multiscale simulation models that are driving toward an understanding of chromatin structure and function, from the nanometer to the micron scale, and we highlight areas of opportunity and some of the prospects for new frameworks that bridge these two scales. Taken together, experimental and modeling advances over the last few years have established a robust platform for the study of chromatin fiber structure and dynamics, which will be of considerable use to the chromatin community in developing an understanding of the interplay between epigenomic regulation and molecular structure.