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Realistic vOlumetric-Approach to Simulate Transcranial Electric Stimulation -- ROAST -- a fully automated open-source pipeline

Research in the area of transcranial electrical stimulation (TES) often relies on computational models of current flow in the brain. Models are built based on the magnetic resonance images (MRI) of the human head to capture detailed individual anatomy. To simulate current flow on an individual, the subjects MRI is segmented, virtual electrodes are placed on this anatomical model, the volume is tessellated into a mesh, and a finite element model (FEM) is solved numerically to estimate the current flow. Various software tools are available for each step, as well as processing pipelines that connect these tools for automated or semi-automated processing. The goal of the present tool - ROAST - is to provide an end-to-end pipeline that can automatically process individual heads with realistic volumetric anatomy leveraging open-source software and custom scripts to improve segmentation and execute electrode placement. The electric field estimated with the open-source tools used by ROAST differ little from the results obtained with commercial meshing and FEM solving software. We also do not find large differences between the various automated segmentation methods used by ROAST and SimNIBS, a well-established open-source modeling pipeline. However, we do find large differences when volumetric segmentation are converted into surfaces that are used in SimNIBS to generate volumetric meshes. Evaluation on intracranial recordings from human subjects suggests that ROAST outperforms newer versions of SimNIBS in predicting field distribution and magnitudes, but that an older version of SimNIBS performs similarly. We hope that the detailed comparisons presented here of various choices in this modeling pipeline can provide guidance for future tool development. We release ROAST as an open-source, easy-to-install and fully-automated pipeline for individualized TES modeling at https://www.parralab.org/roast/.

biophysics

A semi-quantitative analysis of lupus arthritis using contrasted high-field MRI

ObjectiveArthritis in systemic lupus erythematosus is poorly described and there is no objective measure for quantification of the arthritis. We aim to develop MRI as a research tool for the quantification of lupus arthritis.\n\nMethodsPatients were eligible for entry into the study if they were evaluated at the MUSC Lupus Center and determined by their treating physician to have active hand arthritis due to SLE. Standard of care lupus activity measures were collected along with a detailed physical exam. MRI images were obtained using standard musculoskeletal sequences with gadolinium contrast. Semi-quantitative scoring of the images used the OMERACT RAMRIS system.\n\nResultsRAMRIS demonstrates large amounts of synovitis, tenosynovitis, bone marrow edema and erosive disease in only a minority of patients. Some patients were not scored as having any synovitis or tenosynovits. We describe potential features of lupus arthritis that are not captured in the RAMRIS scores and may be contributing to symptoms.\n\nConclusionLupus arthritis is an entity separate from rheumatoid arthritis and requires the development of new quantitative methods to describe it. MRI findings suggest the inadequacy of a typical lupus musculoskeletal measures and even swollen/tender joint counts to assess the level of disease activity.

biophysics

New routes for PTP1B allosteric inhibition by multitemperature crystallography, fragment screening and covalent tethering

Allostery is an inherent feature of proteins and provides alternative routes to regulating function. Small-molecule allosteric inhibitors are often desirable; however, it remains challenging to identify surface sites in proteins which can bind small molecules and modulate function. We identified new allosteric sites in protein tyrosine phosphatase 1B (PTP1B) by combining multiple-temperature X-ray crystallography experiments and structure determination from hundreds of individual small-molecule fragment soaks. New modeling approaches reveal \"hidden\" low-occupancy conformational states for protein and ligands. Our results converge on a new allosteric site that is conformationally coupled to the active-site WPD loop, a hotspot for fragment binding, not conserved in the closest homolog, and distinct from other recently reported allosteric sites in PTP1B. Targeting this site with covalently tethered molecules allosterically inhibits enzyme activity. Overall, this work demonstrates how the ensemble nature of macromolecular structure revealed by multitemperature crystallography can be exploited for developing allosteric modulators.

biophysics

Bringing Diffuse X-ray Scattering Into Focus

X-ray crystallography is experiencing a renaissance as a method for probing the protein conformational ensemble. The inherent limitations of Bragg analysis, however, which only reveals the mean structure, have given way to a surge in interest in diffuse scattering, which is caused by structure variations. Diffuse scattering is present in all macromolecular crystallography experiments. Recent studies are shedding light on the origins of diffuse scattering in protein crystallography, and provide clues for leveraging diffuse scattering to model protein motions with atomic detail.

biophysics

Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, Mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation, and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

biophysics

Combining optical imaging of cleared tissue with mathematical modelling to predict drug delivery and therapeutic response

Understanding how drugs are delivered to diseased tissue, and their subsequent spatial and temporal distribution, is a key factor in the development of effective, targeted therapies. However, the interaction between the pathophysiology of diseased tissue and individual therapeutic agents can be complex, and can vary significantly between individuals. In cancer, suboptimal dosing resulting from poor delivery can cause reduced treatment efficacy, upregulation of resistance mechanisms and can even stimulate growth. Preclinical tools to better understand drug delivery are therefore urgently required, which incorporate the inherent variability and heterogeneity of human disease. To meet this need, we have combined multiscale mathematical modelling, high-resolution optical imaging of intact, optically-cleared tumour tissue from animal models, and in vivo magnetic resonance imaging (MRI). Our framework, named REANIMATE (REAlistic Numerical Image-based Modelling of biologicAl Tissue substratEs) allows large tissue samples to be investigated as if it were a living sample, in detailed, highly controlled, computational experiments. Specifically, we show that REANIMATE can be used to predict the heterogeneous delivery of specific therapeutic agents, in disparate two murine xenograft models of human colorectal carcinoma. Given the wide adoption of optical clearing equipment in biomedical research laboratories, REANIMATE enables a new paradigm in cancer drug development, which could also be applied to other disease areas.

biophysics

Dissecting single cell molecular spatiotemporal mobility and clustering at Focal Adhesions in polarised cells by fluorescence fluctuation spectroscopy methods

Quantitative fluorescence fluctuation spectroscopy from optical microscopy datasets is a very powerful tool to resolve multiple spatiotemporal cellular and subcellular processes at the molecular level. In particular, raster image correlation spectroscopy (RICS) and number and brightness analyses (N&B) yield molecular mobility and clustering dynamic information extracted from real-time cellular processes. This quantitative information can be inferred in a highly flexibly and detailed manner, i.e. 1) at the localisation level: from full-frame datasets and multiple regions of interest within; and 2) at the temporal level: not only from full-frame and multiple regions, but also intermediate temporal events. Here we build on previous research in deciphering the molecular dynamics of paxillin, a main component of focal adhesions. Cells use focal adhesions to attach to the extracellular matrix and interact with their local environment. Through focal adhesions and other adhesion structures, cells sense their local environment and respond accordingly; due to this continuous communication, these structures can be highly dynamic depending on the extracellular characteristics. By using a previously well-characterised model like paxillin, we examine powerful sensitivity characteristics and some limitations of RICS and N&B analyses. We show that cells upon contact to different surfaces show differential self-assembly dynamics in terms of molecular diffusion and oligomerisation. In addition, single-cell studies show that these dynamics change gradually following an antero-posterior gradient.

biophysics

Conversion between parallel and antiparallel β-sheets in wild-type and Iowa mutant fibrils

Using a variant of Hamilton-Replica-Exchange we study for wild type and Iowa mutant A{beta}40 the conversion between fibrils with antiparallel {beta}-sheets, and such with parallel {beta}-sheets. We show that wild type and mutant form distinct salt bridges that in turn stabilize different fibril organizations. The conversion between the two fibril forms leads to the release of small aggregates that in the Iowa mutant may shift the equilibrium from fibrils to more toxic oligomers.

biophysics

Mechanical changes in proteins with large-scale motions highlight the formation of structural locks

Protein function depends just as much on flexibility as on structure, and in numerous cases, a proteins biological activity involves transitions that will impact both its conformation and its mechanical properties. Here, we use a coarse-grain approach to investigate the impact of structural changes on protein flexibility. More particularly, we focus our study on proteins presenting large-scale motions. We show how calculating directional force constants within residue pairs, and investigating their variation upon protein closure, can lead to the detection of a limited set of residues that form a structural lock in the proteins closed conformation. This lock, which is composed of residues whose side-chains are tightly interacting, highlights a new class of residues that are important for protein function by stabilizing the closed structure, and that cannot be detected using earlier tools like local rigidity profiles or distance variations maps, or alternative bioinformatics approaches, such as coevolution scores.

biophysics

Dynamics of a Form-Fitting Protein in a Nanopore: Avidin in ClyA

We probe the molecular dynamics of a protein, avidin, as it is captured and trapped in a nanopore, ClyA, with time-resolved single-molecule electrical conductance measurements, and we present a method for visualizing this process from the data. The case of avidin in ClyA has rich time-dependent conductance spectra of discrete levels that correlate with different configurations of the protein in the pore. One is very long-lasting, stable and noise-free, and portends the use of this system as a platform for more general studies of proteins and other molecules, where avidin acts as a shuttle that ferries analytes into the pore for probing. We demonstrate this by the sensitive detection of a biotin molecule attached to avidin captured by the pore. We also present an approach to determining the nanopore size based on a 3D printed model of the pore.

biophysics

Flex ddG: Rosetta ensemble-based estimation of changes in protein-protein binding affinity upon mutation

Computationally modeling changes in binding free energies upon mutation (interface {Delta}{Delta}G) allows large-scale prediction and perturbation of protein-protein interactions. Additionally, methods that consider and sample relevant conformational plasticity should be able to achieve higher prediction accuracy over methods that do not. To test this hypothesis, we developed a method within the Rosetta macromolecular modeling suite (flex ddG) that samples conformational diversity using \"backrub\" to generate an ensemble of models, then applying torsion minimization, side chain repacking and averaging across this ensemble to estimate interface {Delta}{Delta}G values. We tested our method on a curated benchmark set of 1240 mutants, and found the method outperformed existing methods that sampled conformational space to a lesser degree. We observed considerable improvements with flex ddG over existing methods on the subset of small side chain to large side chain mutations, as well as for multiple simultaneous non-alanine mutations, stabilizing mutations, and mutations in antibody-antigen interfaces. Finally, we applied a generalized additive model (GAM) approach to the Rosetta energy function; the resulting non-linear reweighting model improved agreement with experimentally determined interface DDG values, but also highlights the necessity of future energy function improvements.

biophysics

Denaturants alter the flux through multiple pathways in the folding of PDZ domain

Although we understand many aspects of how small proteins (number of residues less than about hundred) fold, it is a major challenge to understand how large proteins self-assemble. To partially overcome this challenge, we performed simulations using the Self-Organized Polymer model with Side Chains (SOP-SC) in guanidinium chloride (GdmCl), using the Molecular Transfer Model (MTM), to describe the folding of the 110-residue PDZ3 domain. The simulations reproduce the folding thermodynamics accurately including the melting temperature (Tm), the stability of the folded state with respect to the unfolded state. We show that the calculated dependence of ln kobs (kobs is the relaxation rate) has the characteristic Chevron shape. The slopes of the Chevron plots are in good agreement with experiments. We show that PDZ3 folds by four major pathways populating two metastable intermediates, in accord with the kinetic partitioning mechanism. The structure of one of the intermediates, populated after polypeptide chain collapse, is structurally similar to an equilibrium intermediate. Surprisingly, the connectivities between the intermediates and hence, the fluxes through the pathways depend on the concentration of GdmCl. The results are used to predict possible outcomes for unfolding of PDZ domain subject to mechanical forces. Our study demonstrates that, irrespective of the size or topology, simulations based on MTM and SOP-SC offer a framework for describing the folding of proteins, mimicking precisely the conditions used in experiments.

biophysics

Efficient Flexible Backbone Protein-Protein Docking for Challenging Targets

Computational prediction of protein-protein complex structures facilitates a fundamental understanding of biological mechanisms and enables therapeutics design. Binding-induced conformational changes challenge all current computational docking algorithms by exponentially increasing the conformational space to be explored. To restrict this search to relevant space, some computational docking algorithms exploit the inherent flexibility of the protein monomers to simulate conformational selection from pre-generated ensembles. As the ensemble size expands with increased protein flexibility, these methods struggle with efficiency and high false positive rates. Here, we develop and benchmark a method that efficiently samples large conformational ensembles of flexible proteins and docks them using a novel, six-dimensional, coarse-grained score function. A strong discriminative ability allows an eight-fold higher enrichment of nearnative candidate structures in the coarse-grained phase compared to a previous method. Further, the method adapts to the diversity of backbone conformations in the ensemble by modulating sampling rates. It samples 100 conformations each of the ligand and the receptor backbone while increasing computational time by only 20-80%. In a benchmark set of 88 proteins of varying degrees of flexibility, the expected success rate for blind predictions after resampling is 77% for rigid complexes, 49% for moderately flexible complexes, and 31% for highly flexible complexes. These success rates on flexible complexes are a substantial step forward from all existing methods. Additionally, for highly flexible proteins, we demonstrate that when a suitable conformer generation method exists, RosettaDock 4.0 can dock the complex successfully.\n\nSignificancePredicting binding-induced conformational plasticity in protein backbones remains a principal challenge in computational protein-protein docking. To date, there are no methods that can reliably dock proteins that undergo more than 1 [A] root-mean-squared-deviation of the backbones of the interface residues upon binding. Here, we present a method that samples backbone motions and scores conformations rapidly, obtaining-for the first time-successful docking of nearly 50% of flexible target complexes with backbone conformational change up to 2.2 [A] RMSD. This method will be applicable to a broader range of protein docking problems, which in turn will help us understand biomolecular assembly and protein function.

biophysics

Regulatory mechanisms are revealed by the distribution of transcription initiation times in single microbial cells

Transcription is the dominant point of control of gene expression. Biochemical studies have revealed key molecular components of transcription and their interactions, but the dynamics of transcription initiation in cells is still poorly understood. This state of affairs is being remedied with experiments that observe transcriptional dynamics in single cells using fluorescent reporters. Quantitative information about transcription initiation dynamics can also be extracted from experiments that use electron micrographs of RNA polymerases caught in the act of transcribing a gene (Miller spreads). Inspired by these data we analyze a general stochastic model of transcription initiation and elongation, and compute the distribution of transcription initiation times. We show that different mechanisms of initiation leave distinct signatures in the distribution of initiation times that can be compared to experiments. We analyze published micrographs of RNA polymerases transcribing ribosomal RNA genes in E.coli and compare the observed distributions of inter-polymerase distances with the predictions from previously hypothesized mechanisms for the regulation of these genes. Our analysis demonstrates the potential of measuring the distribution of time intervals between initiation events as a probe for dissecting mechanisms of transcription initiation in live cells.

biophysics

Architecture of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

By incorporating the information of human chromosome inferred from Hi-C experiments into a heteropolymer model of chromatin chain, we generate a conformational ensemble to investigate its spatiotemporal dynamics. The heterogeneous loci interactions result in hierarchical organization of chromatin chain, which obeys compact space-filling (SF) statistics at intermediate length scale. Remarkably, the higher order architecture of the chromatin, characterized by the single universal Flory exponent ({nu} = 1/3) for condensed homopolymers, provides quantitative account of the dynamical properties of the chromosome. The local chromosome structures, exemplified by topologically associated domains (~ 0.1 - 1 Mb), display dynamics with fast relaxation time ([lsim] 50 sec), whereas the long-range spatial reorganization of the entire chromatin [Formula] occurs on a much longer time scale ({gtrsim} hour), suggestive of glass-like behavior. This key finding provides the dynamic basis of cell-to-cell variability. Active forces, modeled using stronger isotropic white noises, accelerate the relaxation dynamics of chromatin domain described by the low frequency modes. Surprisingly, they do not significantly change the local scale dynamics from those under passive condition. By linking the spatiotemporal dynamics of chromosome with its organization, our study highlights the importance of physical constraints in chromosome architecture on the sluggish dynamics.\n\nSignificance StatementChromosomes are giant chain molecules made of hundreds of megabase-long DNA intercalated with proteins. Structure and dynamics of interphase chromatin in space and time hold the key to understanding the cell type-dependent gene regulation. In this study, we establish that the crumpled and space-filling organization of chromatin fiber in the chromosome territory, characterized by a single universal exponent used to describe polymer sizes, is sufficient to explain the complex spatiotemporal hierarchy in chromatin dynamics as well as the subdiffusive motion of the chromatin loci. While seemingly a daunting problem at a first glance, our study shows that relatively simple principles, rooted in polymer physics, can be used to grasp the essence of dynamical properties of the interphase chromatin.

biophysics

A hidden Markov model approach to characterizing the photo-switching behavior of fluorophores

Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.

biophysics

Is chaos making a difference? Synchronization transitions in chaotic and non-chaotic neuronal networks

Chaotic dynamics of neural oscillations has been shown at the single neuron and network levels, both in experimental data and numerical simulations. Theoretical studies over the last twenty years have demonstrated an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to relevant network behavior and whether the dynamical richness of neural networks are sensitive to the dynamics of isolated neurons, still remain open questions. We investigated transition dynamics of a medium-sized heterogeneous neural network of neurons connected by electrical coupling in a small world topology. We make use of an oscillatory neuron model (HB+Ih) that exhibits either chaotic or non-chaotic behavior at different combinations of conductance parameters. Measuring order parameter as a measure of synchrony, we find that the heterogeneity of firing rate and types of firing patterns make a greater contribution than chaos to the steepness of synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in process of network synchronization transitions. Moreover, the macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as the multi-stable behavior, where the network dynamically switches between a number of different semi-synchronized, metastable states.

biophysics

Nonequilibrium entropic bounds for Darwinian replicators

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constrains for these systems remain an open question. This is largely due to the lack of a general theory of out of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements in non-equilibrium physics, under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Finally, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics.

biophysics