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Causality, Transfer Entropy and Allosteric Communication Landscapes inProteins with Harmonic Interactions

A fast and approximate method of generating allosteric communication landscapes is presented by using Schreiber's entropy transfer concept in combination with the Gaussian Network Model of proteins. Predictions of the model and the allosteric communication landscapes generated show that information transfer in proteins does not necessarily take place along a single path, but through an ensemble of pathways. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations has to be introduced, which leads to the presence of causality in proteins. The model provides a simple tool for mapping entropy sink-source relations into pairs of residues. Residues that should be manipulated to control protein activity may be determined with this approach. This should be of great importance for allosteric drug design and for understanding the effects of mutations on protein function. The model is applied to determine allosteric communication in two proteins, Ubiquitin and Pyruvate Kinase. Predictions are in agreement with detailed molecular dynamics simulations and experimental evidence.\n\nSignificanceProteins perform their function by an exchange of information within themselves and with their environments through correlated fluctuations of their atoms. Fluctuations of one atom may drive the fluctuations of another. Information transmitted in this way leads to allosteric communication which is described as the process in which action at one site of the protein is transmitted to another site at which the protein performs its activity. Disruption of allosteric communication by mutation for example leads to disease. The present paper incorporates information theoretic concepts into the well known Gaussian Network Model of proteins and allows for rapid characterization of allosteric communication landscapes for normal functioning as well as malfunctioning proteins.

biophysics

Multispot single-molecule FRET: high-throughput analysis of freely diffusing molecules

We describe an 8-spot confocal setup for high-throughput smFRET assays and illustrate its performance with two characteristic experiments. First, measurements on a series of freely diffusing doubly-labeled dsDNA samples allow us to demonstrate that data acquired in multiple spots in parallel can be properly corrected and result in measured sample characteristics identical to those obtained with a standard single-spot setup. We then take advantage of the higher throughput provided by parallel acquisition to address an outstanding question about the kinetics of the initial steps of bacterial RNA transcription. Our real-time kinetic analysis of promoter escape by bacterial RNA polymerase confirms results obtained by a more indirect route, shedding additional light on the initial steps of transcription.\n\nFinally, we discuss the advantages of our multispot setup, while pointing potential limitations of the current single laser excitation design, as well as analysis challenges and their solutions.

biophysics

Folding Principle of Chromosome Emerges from Mapping of Genome Features onto its 3D Structure

How chromosomes fold into 3D structures and how genome functions are affected or even controlled by their spatial organization remain challenging questions. Hi-C experiment has provided important structural insights for chromosome, and Hi-C data are used here to construct the 3D chromatin structure which are characterized by two spatially segregated chromatin compartments A and B. By mapping a plethora of genome features onto the constructed 3D chromatin model, we show vividly the close connection between genome properties and the spatial organization of chromatin. We are able to dissect the whole chromatin into two types of chromatin domains which have clearly different Hi-C contact patterns as well as different sizes of chromatin loops. The two chromatin types can be respectively regarded as the basic units of chromatin compartments A and B, and also spatially segregate from each other as the two chromatin compartments. Therefore, the chromatin loops segregate in the space according to their sizes, suggesting the excluded volume or entropic effect in chromatin compartmentalization as well as chromosome positioning. Taken together, these results provide clues to the folding principles of chromosomes, their spatial organization, and the resulted clustering of many genome features in the 3D space.

biophysics

A looping-based model for quenching repression

We model the regulatory role of proteins bound to looped DNA using a simulation in which dsDNA is represented as a self-avoiding chain, and proteins as spherical protrusions. We simu-late long self-avoiding chains using a sequential importance sampling Monte-Carlo algorithm, and compute the probabilities for chain looping with and without a protrusion. We find that a protrusion near one of the chains termini reduces the probability of looping, even for chains much longer than the protrusion-chain-terminus distance. This effect increases with protrusion size, and decreases with protrusion-terminus distance. The reduced probability of looping can be explained via an eclipse-like model, which provides a novel inhibitory mechanism. We test the eclipse model on two possible transcription-factor occupancy states of the eve 3/7 enhancer, and show that it provides a possible explanation for the experimentally-observed eve stripe 3 and 7 expression patterns.\n\nThe authors declare no conflict of interests

biophysics

Using the Volta phase plate with defocus for cryo-EM single particle analysis

Previously, we reported an in-focus data acquisition method for cryo-EM single particle analysis with the Volta phase plate (VPP) (Danev and Baumeister, 2016). Here, we extend the technique to include a small amount of defocus which enables contrast transfer function measurement and correction. This hybrid approach simplifies the experiment and increases the data acquisition speed. It also enables 3D reconstructions with resolutions in the 2 [A] range, demonstrating that, in practice, there are no resolution limitations imposed by the VPP.

biophysics

Gentle, fast and effective crystal soaking by acoustic dispensing

SynopsisA high-throughput method is described for crystal soaking using acoustic droplet ejection, and its effectiveness demonstrated.\n\nAbstractBright light sources, agile robotics, and fast detectors are continually reducing the time it takes to perform an X-ray diffraction experiment, making high throughput experiments more feasible than ever. But this is also pushing the upstream bottleneck towards sample preparation, even for robust and well characterised crystal systems. Crystal soaking is routinely used to generate protein-ligand complex structures, yet protein crystals are often sensitive to changes in solvent composition, and frequently require gentle or careful stepwise soaking techniques, limiting overall throughput. Here, we describe the use of acoustic droplet ejection for soaking of protein crystals with small molecules, and show that it is both gentle on crystals and allows very high throughput, with 1000 unique soaks easily performed in under 10 minutes. In addition to having very low compound consumption (tens of nanolitres per sample), the positional precision of acoustic droplet ejection enables targeted placement of the compound/solvent away from crystals and towards drop edges, allowing for gradual diffusion of solvent across the drop. This ensures both an improvement in reproducibility of X-ray diffraction and an increased solvent tolerance of the crystals, thus enabling higher effective compound soaking concentrations. We detail the technique here with examples from the protein target JMJD2D, a histone lysine demethylase, having roles in cancer and the focus of active structure based drug design efforts.

biophysics

Histone code and higher-order chromatin folding: A hypothesis

Histone modifications alone or in combination are thought to modulate chromatin structure and function; a concept termed histone code. By combining evidence from several studies, we investigated if the histone code can play a role in higher-order folding of chromatin. Firstly using genomic data, we analyzed associations between histone modifications at the nucleosome level. We could dissect the composition of individual nucleosomes into five predicted clusters of histone modifications. Secondly, by assembling the raw reads of histone modifications at various length scales, we noticed that the histone mark relationships that exist at nucleosome level tend to be maintained at the higher orders of chromatin folding. Recently, a high-resolution imaging study showed that histone marks belonging to three of the five predicted clusters show structurally distinct and anti-correlated chromatin domains at the level of chromosomes. This made us think that the histone code can have a significant impact in the overall compaction of DNA: at the level of nucleosomes, at the level of genes, and finally at the level of chromosomes. As a result, in this article, we put forward a theory where the histone code drives not only the functionality but also the higher-order folding and compaction of chromatin.

biophysics

Flowtrace: simple visualization of coherent structures in biological fluid flows

1We present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results to more experimentally-diffcult and mathematically-sophisticated techniques for identifying patterns in fluid flows, and suggest that our tool represents an essential \"middle ground\" allowing experimentalists to easily determine whether a system exhibits interesting flow patterns and coherent structures without the need to resort to more intensive techniques. In addition to being informative, the visualizations generated by our tool are often striking and elegant, illustrating coherent structures directly from videos without the need for computational overlays. Our tool is available as fully-documented open-source code available for MATLAB, Python, or ImageJ at www.flowtrace.org.

biophysics

Bridging microscopic and macroscopic mechanisms of p53-MDM2 binding using molecular simulations and kinetic network models

Under normal cellular conditions, the tumor suppressor protein p53 is kept at a low levels in part due to ubiquitination by MDM2, a process initiated by binding of MDM2 to the intrinsically disordered transactivation domain (TAD) of p53. Although many experimental and simulation studies suggest that disordered domains such as p53 TAD bind their targets nonspecifically before folding to a tightly-associated conformation, the molecular details are unclear. Toward a detailed prediction of binding mechanism, pathways and rates, we have performed large-scale unbiased all-atom simulations of p53-MDM2 binding. Markov State Models (MSMs) constructed from the trajectory data predict p53 TAD peptide binding pathways and on-rates in good agreement with experiment. The MSM reveals that two key bound intermediates, each with a non-native arrangement of hydrophobic residues in the MDM2 binding cleft, control the overall on-rate. Using microscopic rate information from the MSM, we parameterize a simple four-state kinetic model to (1) determine that induced-fit pathways dominate the binding flux over a large range of concentrations, and (2) predict how modulation of residual p53 helicity affects binding, in good agreement with experiment. These results suggest new ways in which microscopic models of bound-state ensembles can be used to understand biological function on a macroscopic scale.\n\nAUTHOR SUMMARYMany cell signaling pathways involve protein-protein interactions in which an intrinsically disordered peptide folds upon binding its target. Determining the molecular mechanisms that control these binding rates is important for understanding how such systems are regulated. In this paper, we show how extensive all-atom simulations combined with kinetic network models provide a detailed mechanistic understanding of how tumor suppressor protein p53 binds to MDM2, an important target of new cancer therapeutics. A simple four-state model parameterized from the simulations shows a binding-then-folding mechanism, and recapitulates experiments in which residual helicity boosts binding. This work goes beyond previous simulations of small-molecule binding, to achieve pathways and binding rates for a large peptide, in good agreement with experiment.

biophysics

A Critical-like Collective State Leads to Long-range Cell Communication in Dictyostelium discoideum Aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe wide-ranging behaviors from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell-cell communication and hence aggregation, we analyzed cell-cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cellcell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.\n\nAuthor SummaryCells are often coupled to each other in cell collectives, such as aggregates during early development, tissues in the developed organism, and tumors in disease. How do cells communicate over macroscopic distances much larger than the typical cell-cell distance to decide how they should behave? Here, we developed a multiscale model of social amoeba, spanning behavior from individuals to thousands of cells. We show that local cell-cell coupling via secreted chemicals may be tuned to a critical value, resulting in emergent long-range communication and heightened sensitivity. Hence, these aggregates are remarkably similar to bacterial biofilms and neuronal networks, all communicating in a pulse-like fashion. Similar organizing principles may also aid our understanding of the remarkable robustness in cancer development.

biophysics

Computing structure-based lipid accessibility of membrane proteins with mp_lipid_acc in RosettaMP

BackgroundMembrane proteins are vastly underrepresented in structural databases, which has led to a lack of computational tools and the corresponding inappropriate use of tools designed for soluble proteins. For membrane proteins, lipid accessibility is an essential property. Even though programs are available for sequence-based prediction of lipid accessibility and structure-based identification of solvent-accessible surface area, the latter does not distinguish between water accessible and lipid accessible residues in membrane proteins.\n\nResultsHere we present mp_lipid_acc, the first method to identify lipid accessible residues from the protein structure, implemented in the RosettaMP framework and available as a webserver. Our method uses protein structures transformed in membrane coordinates, for instance from PDBTM or OPM databases, and a defined membrane thickness to classify lipid accessibility of residues. mp_lipid_acc is applicable to both -helical and {beta}-barrel membrane proteins of diverse architectures with or without water-filled pores and uses a concave hull algorithm for classification. We further provide a manually curated benchmark dataset, on which our method achieves prediction accuracies of 90%.\n\nConclusionWe present a novel tool to classify lipid accessibility from the protein structure, which is applicable to proteins of diverse architectures and achieves prediction accuracies of 90% on a manually curated database. mp_lipid_acc is part of the Rosetta software suite, available at www.rosettacommons.org. The webserver is available at http://rosie.graylab.jhu.edu/mp_lipid_acc/submit and the benchmark dataset is available at http://tinyurl.com/mp-lipid-acc-dataset.\n\nSupplementary informationSupplementary information is available at BMC Bioinformatics.

biophysics

Balance of microtubule stiffness and cortical tension determines the size of blood cells with marginal band across species

The fast blood stream of animals is associated with large shear stresses. Consequently, blood cells have evolved a special morphology and a specific internal architecture allowing them to maintain their integrity over several weeks. For instance, non-mammalian red blood cells, mammalian erythroblasts and platelets have a peripheral ring of microtubules, called the marginal band, that flattens the overall cell morphology by pushing on the cell cortex. In this article, we model how the shape of these cells stems from the balance between marginal band elasticity and cortical tension. We predict that the diameter of the cell scales with the total microtubule polymer, and verify the predicted law across a wide range of species. Our analysis also shows that the combination of the marginal band rigidity and cortical tension increases the ability of the cell to withstand forces without deformation. Finally, we model the marginal band coiling that occurs during the disc-to-sphere transition observed for instance at the onset of blood platelet activation. We show that when cortical tension increases faster than crosslinkers can unbind, the marginal band will coil, whereas if the tension increases slower, the marginal band may shorten as microtubules slide relative to each other.\n\nSignificance StatementMany blood cells have a discoidal shape, which is essential for them to function properly within the organism. For some cells, such as blood platelets, this shape is due to the interplay between the elasticity of the marginal band, which is a closed ring of stiff filaments called microtubules, and the tension of the cell cortex, a polymer scaffold associated with the plasma membrane. Dmitrieff et al. examined how cell size is determined by the mechanical balance between these two components. Remarkably, the theory is confirmed over nearly three orders of magnitudes, by data collected from 25 species. The theory also shows how the composite structure is adapted to resist transient mechanical challenges, as encountered in the blood stream.

biophysics

Refractive index tomograms and dynamic membrane fluctuations of red blood cells from patients with diabetes mellitus

In this paper we present the optical characterisations of diabetic red blood cells (RBCs) in a non-invasive manner employing three-dimensional (3-D) quantitative phase imaging. By measuring 3-D refractive index tomograms and 2-D time-series phase images, the morphological (volume, surface area and sphericity), biochemical (haemoglobin concentration and content) and mechanical (membrane fluctuation) parameters were quantitatively retrieved at the individual cell level. With simultaneous measurements of individual cell properties, systematic correlative analyses on retrieved RBC parameters were also performed. Our measurements show that diabetic patients had RBCs of reduced cell sphericity and elevated intracellular haemoglobin concentration and content compared to healthy (non-diabetic) subjects. Furthermore, membrane deformability of diabetic RBCs is significantly lower than that of healthy, non-diabetic RBCs. Interestingly, non-diabetic RBCs exhibit strong correlations between the elevated glycated haemoglobin in RBC cytoplasm and decreased cell deformability, whereas diabetic RBCs do not show correlations. Our observations strongly support the idea that slow and irreversible glycation of haemoglobin and membrane proteins of RBCs by hyperglycaemia significantly compromises RBC deformability in diabetic patients.

biophysics

Cryo-EM structure of haemoglobin at 3.2 A determined with the Volta phase plate

With the advent of direct electron detectors, the perspectives of cryo-electron microscopy (cryo-EM) have changed in a profound way1. These cameras are superior to previous detectors in coping with the intrinsically low contrast of radiation-sensitive organic materials embedded in amorphous ice, and so they have enabled the structure determination of several macromolecular assemblies to atomic or near-atomic resolution. According to one theoretical estimation, a few thousand images should suffice for calculating the structure of proteins as small as 17 kDa at 3 [A] resolution2. In practice, however, we are still far away from this theoretical ideal. Thus far, protein complexes that have been successfully reconstructed to high-resolution by single particle analysis (SPA) have molecular weights of ~100 kDa or larger3. Here, we report the use of Volta phase plate in determining the structure of human haemoglobin (64 kDa) at 3.2 [A]. Our results demonstrate that this method can be applied to complexes that are significantly smaller than those previously studied by conventional defocus-based approaches. Cryo-EM is now close to becoming a fast and cost-effective alternative to crystallography for high-resolution protein structure determination.

biophysics

Slow and steady wins the race: encounters of myosin-5 and myosin-6 on shared actin filaments

In the cellular environment multiple myosins use the same filamentous actin (F-actin) tracks, yet little is known about how this track sharing is achieved and maintained. To assess the influence that different myosin classes have on each other, we developed an assay that combines two dynamic elements: elongating actin filaments with identified barbed and pointed ends, and myosins moving along these filaments. We studied two different myosins, myosin-5 and myosin-6. These myosins have distinct functions in the cell and are known to travel in opposite directions along actin filaments. Myosin-5 walks towards the barbed end of F-actin and generally into dynamically rearranging actin at the cell periphery. Myosin-6 is a pointed-end directed myosin that generally walks towards the cell center. We successfully reconstituted simultaneous bidirectional motility of myosin-5 and myosin-6 on single polymerizing filaments of actin. We report and provide statistical analysis of encounters between myosin-5 and myosin-6 walking along the single filaments. When myosin-5 and myosin-6 collide, myosin-5 detaches more frequently than myosin-6. The experimental observations are consistent with a stochastic stepping model based upon known myosin kinetics, which suggests that faster motors are more likely to detach.

biophysics

In vivo imaging of coral tissue and skeleton with optical coherence tomography

Optical coherence tomography (OCT) is a non-invasive three-dimensional imaging technique with micrometer resolution allowing microstructural characterization of tissues in vivo and in real time. We present the first application of OCT for in vivo imaging of tissue and skeleton structure of intact living corals spanning a variety of morphologies and tissue thickness. OCT visualized different coral tissue layers (e.g. endoderm vs ectoderm), special structures such as mesenterial filaments and skeletal cavities, as well as mucus release from living corals. We also developed a new approach for non-invasive imaging and quantification of chromatophores containing green fluorescent protein (GFP)-like host pigment granules in coral tissue. The chromatophore system is hyper-reflective and can thus be imaged with good optical contrast in OCT, enabling quantification of chromatophore size, distribution and abundance. Because of its rapid imaging speed, OCT can also be used to quantify coral tissue movement showing that maximal linear contraction velocity was ~120 m per second upon high light stimulation. Based on OCT imaging of tissue expansion and contraction, we made first estimates of dynamic changes in the coral tissue surface area, which varied by a factor of 2 between the contracted and expanded state of the coral Pocillopora damicornis. We conclude that OCT is an excellent novel tool for in vivo tomographic imaging of corals that can reveal tissue and skeleton organization as well as quantify dynamic changes in tissue structure and coral surface area non-invasively and at high spatio-temporal resolution.

biophysics

How fast can fast-folding proteins autonomously fold in silico?

In reported microcanonical molecular dynamics simulations, fast-folding proteins CLN025 and Trp-cage autonomously folded to experimentally determined native conformations. However, the folding times of these proteins derived from the simulations were more than 4-10 times longer than their experimental values. This article reports autonomous folding of CLN025 and Trp-cage in isobaric-isothermal molecular dynamics simulations with agreements within factors of 0.69-1.75 between simulated and experimental folding times at different temperatures. These results show that CLN025 and Trp-cage can now autonomously fold in silico as fast as in experiments, and suggest that the accuracy of folding simulations for fast-folding proteins begins to overlap with the accuracy of folding experiments. This opens new prospects of developing computer algorithms that can predict both ensembles of conformations and their interconversion rates for a protein from its sequence for artificial intelligence on how and when a protein acts as a receiver, switch, and relay to facilitate various subcellular-to-tissue communications. Then the genetic information that encodes proteins can be better read in the context of intricate biological functions.

biophysics

Raoult’s law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, which often leads to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals on a beamline have led to this technique being increasingly adopted, as experiments become easier and more reproducible. Matching the relative humidity to the mother liquor is the first step to allow the stable mounting of a crystal. In previous work, we measured the equilibrium relative humidity for a range of concentrations of the most commonly used precipitants and showed how this related to Raoults law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between measured values and those predicted by theory could not be explained. Here, we have used a more precise humidity control device to determine equilibrium relative humidity points. The new results are in agreement with Raoults law. We also present a simple argument in statistical mechanics demonstrating that the saturated vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoults Law. The same argument can be extended to the case where solvent and solute molecules are of different size, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding samples.\n\nSynopsisThe equilibrium relative humidity values for a number of the most commonly used precipitants in biological macromolecule crystallisation have been measured using a new humidity control device. A simple argument in statistical mechanics demonstrates that the saturated vapour pressure of a solvent is proportional to its mole fraction in an ideal solution (Raoults Law). The same argument can be extended to the case where solvent and solute molecules are of different size.

biophysics