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From deep TLS validation to ensembles of atomic models built from elemental motions

The widely used Translation Libration Screw (TLS) approximation describes concerted motions of atomic groups in X-ray refinement. TLS refinement often provides a better interpretation of diffraction data and the resulting rigid body motions may subsequently be assigned biochemical significance. In TLS refinement, three matrices (T, L and S) describe harmonic vibration, libration and their correlation. Because these matrices describe specific motions, they impose a number of conditions on their elements. Ignoring these conditions while refining the matrix elements may result in matrices that cannot be interpreted in terms of physically realistic motions. We describe a mathematical framework and the computational tools to analyze refined TLS matrices through their decomposition into descriptors of underlying motions. This allows for straightforward validation and identification of implausible TLS parameters. An algorithm for the generation of structural ensembles that are consistent with given TLS parameters, implemented as a part of the Phenix project, is also described.\n\nSynopsisProcedures for the decomposition of TLS matrices into elementary vibrations and librations indicates possible errors in the definition of these matrices and corrects them when possible. The program outputs the corresponding vibration-libration parameters and generates structural ensembles.

Biophysics

Predicting X-ray Diffuse Scattering from Translation Libration Screw Structural Ensembles

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. While Bragg diffraction describes the average positional distribution of crystalline atoms, many different models can fit this distribution equally well. Diffuse X-ray scattering can reduce this degeneracy by directly reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guiniers equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to Translation-Libration-Screw (TLS) refinement, which models rigid body displacement for segments of the macromolecule. To enable calculation of diffuse scattering from TLS refined structures, phenix.tls_models builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how X-ray diffuse scattering can extend macromolecular structural refinement, validation, and analysis.\n\nSynopsisA method of simulating X-ray diffuse scattering from multi-model PDB files is presented. Despite similar agreement with Bragg data, different Translation-Libration-Screw refinement strategies produce unique diffuse intensity patterns.

Biophysics

Public good diffusion limits microbial mutualism

Standard game theory cannot describe microbial interactions mediated by diffusible molecules. Nevertheless, we show that one can still model microbial dynamics using game theory with parameters renormalized by diffusion. Contrary to expectations, greater sharing of metabolites reduces the strength of cooperation and leads to species extinction via a nonequilibrium phase transition. We report analytic results for the critical diffusivity and the length scale of species intermixing. We also show that fitness nonlinearities suppress mutualism and favor the species producing slower nutrients.\n\nPACS numbers: 87.23.Cc, 87.23.Kg, 87.15.Zg, 64.60.ah

Biophysics

A population density and moment-based approach to modeling domain Ca-mediated inactivation of L-type Ca channels

We present a population density and moment-based description of the stochastic dynamics of domain Ca2+-mediated inactivation of L-type Ca2+ channels. Our approach accounts for the effect of heterogeneity of local Ca2+ signals on whole cell Ca2+ currents; however, in contrast with prior work, e.g., Sherman et al. (1990), we do not assume that Ca2+ domain formation and collapse are fast compared to channel gating. We demonstrate the population density and moment-based modeling approaches using a 12-state Markov chain model of an L-type Ca2+ channel introduced by Greenstein and Winslow (2002). Simulated whole cell voltage clamp responses yield an inactivation function for the whole cell Ca2+ current that agrees with the traditional approach when domain dynamics are fast. We analyze the voltage-dependence of Ca2+ inactivation that may occur via slow heterogeneous domains. Next, we find that when channel permeability is held constant, Ca2+-mediated inactivation of L-type channel increases as the domain time constant increases, because a slow domain collapse rate leads to increased mean domain [Ca2+] near open channels; conversely, when the maximum domain [Ca2+] is held constant, inactivation decreases as the domain time constant increases. Comparison of simulation results using population densities and moment equations confirms the computational efficiency of the moment-based approach, and enables the validation of two distinct methods of truncating and closing the open system of moment equations. In general, a slow domain time constant requires higher order moment truncation for agreement between moment-based and population density simulations.

Biophysics

Quantifying transport in crowded biochemical environments

Transport of cells and biochemical molecules often takes place in crowded, heterogeneous environments. As such, it is important we understand how to quantify crowded transport phenomena, and the possibilities of extracting transport coefficients from limited observations. We employ a volume-excluding random walk model on a square lattice where different fractions of lattice sites are filled with inert, immobile obstacles to investigate whether it is possible to estimate parameters associated with transport when crowding is present. By collecting and analysing data obtained on multiple spatial scales we demonstrate that commonly used models of motility within crowded environments can be used to reliably predict our random walk data. However, infeasibly large amounts of data are needed to estimate transport parameters, and quantitative estimates may differ depending on the spatial scale on which they are collected. We also demonstrate that in models of crowded environments there is a relatively large region of the parameter space within which it is difficult to distinguish between the \"best fit\" parameter values. This suggests commonly used descriptions of transport within crowded systems may not be appropriate, and that we should be careful in choosing models to represent the effects of crowding upon motility within biochemical systems.

Biophysics

Side-chain-directed model and map validation for 3D Electron Cryomicroscopy

Advances in electron cryomicroscopy allow for the building of de novo atomic models into high resolution Coulomb potential maps. While established validation metrics independently assess map quality and model geometry, methods to assess the precise fitting of an atomic model into the map and to validate the interpretation of high resolution features are less well developed. Here, we present EMRinger, which tests model-to-map agreement using side-chain dihedral-directed map density measurements. These measurements reveal local map density peaks and show that peaks located at rotameric angles are a sensitive marker of whether the backbone is correctly positioned. The EMRinger Score can be improved by model refinement, suggesting its utility as an effective model-to-map validation metric. Additionally, EMRinger sampling identifies how radiation damage alters scattering from negatively charged amino acids during data collection. EMRinger will be useful in assessing how advances in cryo-EM increase the ability to resolve and model high-resolution features.

Biophysics

Low cost, high performance processing of single particle cryo-electron microscopy data in the cloud

The advent of a new generation of electron microscopes and direct electron detectors has realized the potential of single particle cryo-electron microscopy (cryo-EM) as a technique to generate high-resolution structures. However, calculating these structures requires high performance computing clusters, a resource that may be limiting to many likely cryo-EM users. To address this limitation and facilitate the spread of cryo-EM, we developed a publicly available off-the-shelf computing environment on Amazons elastic cloud computing infrastructure. This environment provides users with single particle cryo-EM software packages and the ability to create computing clusters that can range in size from 16 to 480+ CPUs. Importantly, these computing clusters are also cost-effective, as we illustrate here by determining a near-atomic resolution structure of the 80S yeast ribosome for $28.89 USD in ~10 hours.

Biophysics

Mapping the Conformational Landscape of a Dynamic Enzyme by XFEL and Multitemperature Crystallography

Determining the interconverting conformations of dynamic proteins in atomic detail is a major challenge for structural biology. Conformational heterogeneity in the active site of the dynamic enzyme cyclophilin A (CypA) has been previously linked to its catalytic function, but the extent to which the different conformations of these residues are correlated is unclear. Here we compare the conformational ensembles of CypA by multitemperature synchrotron crystallography and fixed-target X-ray free electron laser (XFEL) crystallography. The \"diffraction-before-destruction\" nature of XFEL experiments provides a radiation-damage-free view of the functionally important alternative conformations of CypA, confirming earlier synchrotron-based results. We monitored the temperature dependences of these alternative conformations with eight synchrotron datasets spanning 100-310 K. Multiconformer models show that many alternative conformations in CypA are populated only at 240 K and above, yet others remain populated or become populated at 180 K and below. These results point to a complex evolution of conformational heterogeneity between 180-240 K that involves both thermal deactivation and solvent-driven arrest of protein motions in the crystal. The lack of a single shared conformational response to temperature within the dynamic active-site network provides evidence for a conformation shuffling model, in which exchange between rotamer states for a large aromatic ring in the middle of the network shifts the conformational ensemble for the other residues in the network. Together, our multitemperature analyses and XFEL data motivate a new generation of temperature- and time-resolved experiments to structurally characterize the dynamic underpinnings of protein function.

Biophysics

Interventional Nerve Visualization via the Intrinsic Anisotropic Optical Properties of the Nerves

We present an optical concept to visualize nerves during surgical interventions. The concept relies on the anisotropic optical properties of the nerves which allows for specific switching of the optical reflection by the nervous-tissue. Using a low magnification polarized imaging system we are able to visualize the on and off switching of the optical reflection of the nervous-tissue, enabling a non-invasive nerve specific real-time nerve visualization during surgery.

Biophysics

A Novel Mechanism for Color Vision: Pupil Shape and Chromatic Aberration Can Provide Spectral Discrimination for Color Blind Organisms.

We present a mechanism by which organisms with only a single photoreceptor, that have a monochromatic view of the world, can achieve color discrimination. The combination of an off-axis pupil and the principle of chromatic aberration (where light of different colors focus at different distances behind a lens) can combine to provide \"color-blind\" animals with a way to distinguish colors. As a specific example we constructed a computer model of the visual system of cephalopods, (octopus, squid, and cuttlefish) that have a single unfiltered photoreceptor type. Nevertheless, cephalopods dramatically change color both to produce chromatically-matched camouflage and to signal conspecifics. This presents a paradox - an apparent ability to determine color in organisms with a monochromatic visual system - that has been a long-standing puzzle. We demonstrate that chromatic blurring dominates the visual acuity in these animals, and we quantitatively show how chromatic aberration can be exploited, especially through non-axial pupils that are characteristic of cephalopods, to obtain spectral information. This mechanism is consistent with the extensive suite of visual/behavioral and physiological data that have been obtained from cephalopod studies, and resolves the apparent paradox of vivid chromatic behaviors in \"color-blind\" animals. Moreover, this proposed mechanism has potential applicability in any organisms with limited photoreceptor complements, such as spiders and dolphins.

Biophysics

Pluripotency Conversion of Gene Studied from Quantum Folding Theory

The chemically and physically induced pluripotency in a stem cell is studied from the point of quantum transition between differentiation and pluripotency states in genes. The quantum folding theory of a macromolecule is briefly reviewed. The relation of protein folding rate with the number N of torsion modes participating in the quantum transition (coherence degree) is discussed and a simple statistical relationship is obtained. As a unifying approach to conformational quantum transition the folding rate formula can be generalized from protein to nucleic acid. It is found that the formula of folding rate versus N well fits RNA folding data. Then the quantum folding theory is applied to study the pluripotency conversion in stem cell. We proved that the acquisition of pluripotency is essentially a quantum-stochastic event of small-probability through the comparison of the rate with protein folding. Due to the large coherence degree of DNA and the uphill nature of torsion transition the pluripotency-acquisition rate should be small. By establishing the reaction network of the conformational change of the pluripotency genes the characteristic time of the chemical reprogramming is calculated and the result is consistent with experiments. The dependence of the transition rate on physical factors such as temperature, PH value and the volume and shape of the coherent domain of the gene is analyzed from the rate equation. Based on these studies an approach to the physically induced pluripotency with higher rate is proposed.

Biophysics

Exposing hidden alternative backbone conformations in X-ray crystallography using qFit

Proteins must move between different conformations of their native ensemble to perform their functions. Crystal structures obtained from high-resolution X-ray diffraction data reflect this heterogeneity as a spatial and temporal conformational average. Although movement between natively populated alternative conformations can be critical for characterizing molecular mechanisms, it is challenging to identify these conformations within electron density maps. Alternative side chain conformations are generally well separated into distinct rotameric conformations, but alternative backbone conformations can overlap at several atomic positions. Our model building program qFit uses mixed integer quadratic programming (MIQP) to evaluate an extremely large number of combinations of sidechain conformers and backbone fragments to locally explain the electron density. Here, we describe two major modeling enhancements to qFit: peptide flips and alternative glycine conformations. We find that peptide flips fall into four stereotypical clusters and are enriched in glycine residues at the n+1 position. The potential for insights uncovered by new peptide flips and glycine conformations is exemplified by HIV protease, where different inhibitors are associated with peptide flips in the \"flap\" regions adjacent to the inhibitor binding site. Our results paint a picture of peptide flips as conformational switches, often enabled by glycine flexibility, that result in dramatic local rearrangements. Our results furthermore demonstrate the power of large-scale computational analysis to provide new insights into conformational heterogeneity. Overall, improved modeling of backbone heterogeneity with high-resolution X-ray data will connect dynamics to the structure-function relationship and help drive new design strategies for inhibitors of biomedically important systems.\n\nAuthor SummaryDescribing the multiple conformations of proteins is important for understanding the relationship between molecular flexibility and function. However, most methods for interpreting data from X-ray crystallography focus on building a single structure of the protein, which limits the potential for biological insights. Here we introduce an improved algorithm for using crystallographic data to model these multiple conformations that addresses two previously overlooked types of protein backbone flexibility: peptide flips and glycine movements. The method successfully models known examples of these types of multiple conformations, and also identifies new cases that were previously unrecognized but are well supported by the experimental data. For example, we discover glycine-driven peptide flips in the inhibitor-gating \"flaps\" of the drug target HIV protease that were not modeled in the original structures. Automatically modeling \"hidden\" multiple conformations of proteins using our algorithm may help drive biomedically relevant insights in structural biology pertaining to, e.g., drug discovery for HIV-1 protease and other therapeutic targets.

Biophysics

Obstructions in Vascular Networks. Critical vs Non-critical Topological Sites for Blood Supply

We relate vascular network structure to hemodynamics after vessel obstructions. We consider tree-like networks with a viscoelastic fluid with the rheological characteristics of blood. We analyze the network hemodynamic response, which is a function of the frequencies involved in the driving, and a measurement of the resistance to flow. This response function allows the study of the hemodynamics of the system, without the knowledge of a particular pressure gradient. We find analytical expressions for the network response, that explicitly show the roles played by the network structure, the degree of obstruction, and the geometrical place in which obstructions occur. Notably, we find that the sequence of resistances of the network without occlusions, strongly determines the tendencies that the response function has with the anatomical place where obstructions are located. We identify anatomical sites in a network that are critical for its overall capacity to supply blood to a tissue after obstructions. We demonstrate that relatively small obstructions in such critical sites are able to cause a much larger decrease on flow than larger obstructions placed in non-critical sites. Our results indicate that, to a large extent, the response of the network is determined locally. That is, it depends on the structure that the vasculature has around the place where occlusions are found. This result is manifest in a network that follows Murrays law, which is in reasonable agreement with several mammalian vasculatures. For this one, occlusions in early generation vessels have a radically different effect than occlusions in late generation vessels occluding the same percentage of area available to flow. This locality implies that whenever there is a tissue irrigated by a tree-like in-vivo vasculature, our model is able to interpret how important obstructions are for the irrigation of such tissue.

Biophysics

Perspectives on Quorum sensing in Fungi

Keeping a pace with Quorum sensing, analyzing communication shows the close co-evolution of fungi with organisms present in their environment giving insights into multispecies communication. Subsequently, many examples of cell density dependent regulation by extracellular factors have been found in diverse microorganisms. The widespread incidence of diverse quorum-sensing systems strongly suggests that regulation in accordance with cell density is important for the success of microbes in many environments. The paper includes the basic autoregulatory quorum sensing molecules that has been perceived. Although fungal quorum sensing research is still in its infancy, its discovery has changed our views about the fungal kingdom and could eventually lead to the development of new antifungal therapeutics.

Biophysics

The case for absolute ligand discrimination : modeling information processing and decision by immune T cells

1. Introduction 1. Introduction 2. Theoretical approaches for... 3. Biologically realistic models... 4. Ligand recognition by... 5. Wrapping up References Cells within the body are constantly bombarded with a large repertoire of molecules that must be dealt with as potential stimuli. Most of the time, these molecular inputs are measured by receptors at the surface of the cells. State of these receptors are thus informative on the outside world, and experimental and theoretical biophysicists [50] have extensively used information theory to estimate how much information (in the Shannon sense [45]) can be encoded at this stage. This information can be used and processed by the cells, and again transmission of information between Inputs and Outputs have been well studied (see e ...

Biophysics

CTFFIND4: Fast and accurate defocus estimation from electron micrographs

CTFFIND is a widely-used program for the estimation of objective lens defocus parameters from transmission electron micrographs. Defocus parameters are estimated by fitting a model of the microscopes contrast transfer function (CTF) to an images amplitude spectrum. Here we describe modifications to the algorithm which make it significantly faster and more suitable for use with images collected using modern technologies such as dose fractionation and phase plates. We show that this new version preserves the accuracy of the original algorithm while allowing for higher throughput. We also describe a measure of the quality of the fit as a function of spatial frequency and suggest this can be used to define the highest resolution at which CTF oscillations were successfully modeled.

Biophysics

Mitotic chromosome compaction via active loop extrusion

During cell division chromosomes are compacted in length by more than a hundred-fold. A wide range of experiments demonstrated that in their compacted state, mammalian chromosomes form arrays of closely stacked consecutive [~]100Kb loops. The mechanism underlying the active process of chromosome compaction into a stack of loops is unknown. Here we test the hypothesis that chromosomes are compacted by enzymatic machines that actively extrude chromatin loops. When such loop-extruding factors (LEF) bind to chromosomes, they progressively bridge sites that are further away along the chromosome, thus extruding a loop. We demonstrate that collective action of LEFs leads to formation of a dynamic array of consecutive loops. Simulations and an analytically solved model identify two distinct steady states: a sparse state where loops are highly dynamic but provide little compaction, and a dense state with more stable loops and dramatic chromosome compaction. We find that human chromosomes operate at the border of the dense steady state. Our analysis also shows how the macroscopic characteristics of the loop array are determined by the microscopic properties of LEFs and their abundance. When number of LEFs are used that match experimentally based estimates, the model can quantitatively reproduce the average loop length, the degree of compaction, and the general loop-array morphology of compact human chromosomes. Our study demonstrates that efficient chromosome compaction can be achieved solely by an active loop-extrusion process.\n\nSignificance StatementDuring cell division chromosomes are compacted in length more than a hundred-fold and are folded in arrays of loops. The mechanism underlying this essential biological process is unknown. Here we test whether chromosome compaction can be performed by molecular machines that actively extrude chromatin loops. These machines bind to DNA and progressively bridge sites that are further and further away along the chromosome. We demonstrate that the collective action of loop-extruding machines can fold a chromosome into a dynamic array of loops. Simulated chromosome agrees with compact human chromosomes in its degree of compaction, loop size and the general loop-array morphology. Our study demonstrates that efficient chromosome compaction can be achieved solely by such active loop-extrusion process.

Biophysics

A simple method for automated equilibration detection in molecular simulations

Molecular simulations intended to compute equilibrium properties are often initiated from configurations that are highly atypical of equilibrium samples, a practice which can generate a distinct initial transient in mechanical observables computed from the simulation trajectory. Traditional practice in simulation data analysis recommends this initial portion be discarded to equilibration, but no simple, general, and automated procedure for this process exists. Here, we suggest a conceptually simple automated procedure that does not make strict assumptions about the distribution of the observable of interest, in which the equilibration time is chosen to maximize the number of effectively uncorrelated samples in the production timespan used to compute equilibrium averages. We present a simple Python reference implementation of this procedure, and demonstrate its utility on typical molecular simulation data.

Biophysics