Prediction of water and metal binding sites and their affinities by using the Fold-X force field

The empirical force field Fold-X was developed previously to allow rapid free energy calculations in proteins. Here, we present an enhanced version of the force field allowing prediction of the position of structural water molecules and metal ions, together called single atom ligands. Fold-X picks up 76% of water molecules found to interact with two or more polar atoms of proteins in high-resolution crystal structures and predicts their position to within 0.8 A on average. The prediction of metal ion-binding sites have success rates between 90% and 97% depending on the metal, with an overall standard deviation on the position of binding of 0.3-0.6 A. The following metals were included in the force field: Mg2+, Ca2+, Zn2+, Mn2+, and Cu2+. As a result, the current version of Fold-X can accurately decorate a protein structure with biologically important ions and water molecules. Additionally, the free energy of binding of Ca2+ and Zn2+ (i.e., the natural logarithm of the dissociation constant) and its dependence on ionic strength correlate reasonably well with the experimental data available in the literature, allowing one to discriminate between high- and low-affinity binding sites. Importantly, the accuracy of the energy prediction presented here is sufficient to efficiently discriminate between Mg2+, Ca2+, and Zn2+ binding.

Combining experiments and simulations using the maximum entropy principle

A key component of computational biology is to compare the results of computer modelling with experimental measurements. Despite substantial progress in the models and algorithms used in many areas of computational biology, such comparisons sometimes reveal that the computations are not in quantitative agreement with experimental data. The principle of maximum entropy is a general procedure for constructing probability distributions in the light of new data, making it a natural tool in cases when an initial model provides results that are at odds with experiments. The number of maximum entropy applications in our field has grown steadily in recent years, in areas as diverse as sequence analysis, structural modelling, and neurobiology. In this Perspectives article, we give a broad introduction to the method, in an attempt to encourage its further adoption. The general procedure is explained in the context of a simple example, after which we proceed with a real-world application in the field of molecular simulations, where the maximum entropy procedure has recently provided new insight. Given the limited accuracy of force fields, macromolecular simulations sometimes produce results that are at not in complete and quantitative accordance with experiments. A common solution to this problem is to explicitly ensure agreement between the two by perturbing the potential energy function towards the experimental data. So far, a general consensus for how such perturbations should be implemented has been lacking. Three very recent papers have explored this problem using the maximum entropy approach, providing both new theoretical and practical insights to the problem. We highlight each of these contributions in turn and conclude with a discussion on remaining challenges.

Kinome-wide decoding of network-attacking mutations rewiring cancer signaling

Cancer cells acquire pathological phenotypes through accumulation of mutations that perturb signaling networks. However, global analysis of these events is currently limited. Here, we identify six types of network-attacking mutations (NAMs), including changes in kinase and SH2 modulation, network rewiring, and the genesis and extinction of phosphorylation sites. We developed a computational platform (ReKINect) to identify NAMs and systematically interpreted the exomes and quantitative (phospho-)proteomes of five ovarian cancer cell lines and the global cancer genome repository. We identified and experimentally validated several NAMs, including PKCγ M501I and PKD1 D665N, which encode specificity switches analogous to the appearance of kinases de novo within the kinome. We discover mutant molecular logic gates, a drift toward phospho-threonine signaling, weakening of phosphorylation motifs, and kinase-inactivating hotspots in cancer. Our method pinpoints functional NAMs, scales with the complexity of cancer genomes and cell signaling, and may enhance our capability to therapeutically target tumor-specific networks.

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Mutations perturbing signaling networks are systematically classified and interpreted

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Several such functional mutations are identified in cancer and experimentally validated

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The results suggest that a single point mutant can have profound signaling effects

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Systematic interpretation of genomic data may assist future precision-medicine efforts

SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks

SmartCell has been developed to be a general framework for modelling and simulation of diffusion-reaction networks in a whole-cell context. It supports localisation and diffusion by using a mesoscopic stochastic reaction model. The SmartCell package can handle any cell geometry, considers different cell compartments, allows localisation of species, supports DNA transcription and translation, membrane diffusion and multistep reactions, as well as cell growth. Moreover, different temporal and spatial constraints can be applied to the model. A GUI interface that facilitates model making is also available. In this work we discuss limitations and advantages arising from the approach used in SmartCell and determine the impact of localisation on the behaviour of simple well-defined networks, previously analysed with differential equations. Our results show that this factor might play an important role in the response of networks and cannot be neglected in cell simulations.

SNPeffect: a database mapping molecular phenotypic effects of human non-synonymous coding SNPs

Single nucleotide polymorphisms (SNPs) are an increasingly important tool for genetic and biomedical research. However, the accumulated sequence information on allelic variation is not matched by an understanding of the effect of SNPs on the functional attributes or ‘molecular phenotype’ of a protein. Towards this aim we developed SNPeffect, an online resource of human non-synonymous coding SNPs (nsSNPs) mapping phenotypic effects of allelic variation in human genes. SNPeffect contains 31 659 nsSNPs from 12 480 human proteins. The current release of SNPeffect incorporates data on protein stability, integrity of functional sites, protein phosphorylation and glycosylation, subcellular localization, protein turnover rates, protein aggregation, amyloidosis and chaperone interaction. The SNP entries are accessible through both a search and browse interface and are linked to most major biological databases. The data can be displayed as detailed descriptions of individual SNPs or as an overview of all SNPs for a given protein. SNPeffect will be regularly updated and can be accessed at http://snpeffect.vib.be/.

Recognizing and Defining True Ras Binding Domains II: In Silico Prediction Based on Homology Modelling and Energy Calculations

Considering the large number of putative Ras effector proteins, it is highly desirable to develop computational methods to be able to identify true Ras binding molecules. Based on a limited sequence homology among members of the Ras association (RA) and Ras binding (RB) sub-domain families of the ubiquitin super-family, we have built structural homology models of Ras proteins in complex with different RA and RB domains, using the FOLD-X software. A critical step in our approach is to use different templates of Ras complexes, in order to account for the structural variation among the RA and RB domains. The homology models are validated by predicting the effect of mutating hot spot residues in the interface, and residues important for the specificity of interaction with different Ras proteins. The FOLD-X calculated energies of the best-modelled complexes are in good agreement with previously published experimental data and with new data reported here. Based on these results, we can establish energy thresholds above, or below which, we can predict with 96% confidence that a RA/RB domain will or will not interact with Ras. This study shows the importance of in depth structural analysis, high quality force-fields and modelling for correct prediction. Our work opens the possibility of genome-wide prediction for this protein family and for others, where there is enough structural information.

A probabilistic model of RNA conformational space

The increasing importance of non-coding RNA in biology and medicine has led to a growing interest in the problem of RNA 3-D structure prediction. As is the case for proteins, RNA 3-D structure prediction methods require two key ingredients: an accurate energy function and a conformational sampling procedure. Both are only partly solved problems. Here, we focus on the problem of conformational sampling. The current state of the art solution is based on fragment assembly methods, which construct plausible conformations by stringing together short fragments obtained from experimental structures. However, the discrete nature of the fragments necessitates the use of carefully tuned, unphysical energy functions, and their non-probabilistic nature impairs unbiased sampling. We offer a solution to the sampling problem that removes these important limitations: a probabilistic model of RNA structure that allows efficient sampling of RNA conformations in continuous space, and with associated probabilities. We show that the model captures several key features of RNA structure, such as its rotameric nature and the distribution of the helix lengths. Furthermore, the model readily generates native-like 3-D conformations for 9 out of 10 test structures, solely using coarse-grained base-pairing information. In conclusion, the method provides a theoretical and practical solution for a major bottleneck on the way to routine prediction and simulation of RNA structure and dynamics in atomic detail.

Similarity measures for protein ensembles

Analyses of similarities and changes in protein conformation can provide important information regarding protein function and evolution. Many scores, including the commonly used root mean square deviation, have therefore been developed to quantify the similarities of different protein conformations. However, instead of examining individual conformations it is in many cases more relevant to analyse ensembles of conformations that have been obtained either through experiments or from methods such as molecular dynamics simulations. We here present three approaches that can be used to compare conformational ensembles in the same way as the root mean square deviation is used to compare individual pairs of structures. The methods are based on the estimation of the probability distributions underlying the ensembles and subsequent comparison of these distributions. We first validate the methods using a synthetic example from molecular dynamics simulations. We then apply the algorithms to revisit the problem of ensemble averaging during structure determination of proteins, and find that an ensemble refinement method is able to recover the correct distribution of conformations better than standard single-molecule refinement.

Potentials of mean force for protein structure prediction vindicated, formalized and generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances – so-called “potentials of mean force” (PMFs) – have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state – a necessary component of these potentials – is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities “reference ratio distributions” deriving from the application of the “reference ratio method.” This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

Experimental parameterization of an energy function for the simulation of unfolded proteins

The determination of conformational preferences in unfolded and disordered proteins is an important challenge in structural biology. We here describe an algorithm to optimize energy functions for the simulation of unfolded proteins. The procedure is based on the maximum likelihood principle and employs a fast and efficient gradient descent method to find the set of parameters of the energy function that best explain the experimental data. We first validate the method by using synthetic reference data, and subsequently apply the algorithms to data from nuclear magnetic resonance spin-labeling experiments on the Delta131Delta fragment of Staphylococcal nuclease. A significant strength of the procedure that we present is that it directly uses experimental data to optimize the energy parameters, without relying on the availability of high resolution structures. The procedure is fully general and can be applied to a range of experimental data and energy functions including the force fields used in molecular dynamics simulations.

Calculation of accurate small angle X-ray scattering curves from coarse-grained protein models

BACKGROUND

Genome sequencing projects have expanded the gap between the amount of known protein sequences and structures. The limitations of current high resolution structure determination methods make it unlikely that this gap will disappear in the near future. Small angle X-ray scattering (SAXS) is an established low resolution method for routinely determining the structure of proteins in solution. The purpose of this study is to develop a method for the efficient calculation of accurate SAXS curves from coarse-grained protein models. Such a method can for example be used to construct a likelihood function, which is paramount for structure determination based on statistical inference.

RESULTS

We present a method for the efficient calculation of accurate SAXS curves based on the Debye formula and a set of scattering form factors for dummy atom representations of amino acids. Such a method avoids the computationally costly iteration over all atoms. We estimated the form factors using generated data from a set of high quality protein structures. No ad hoc scaling or correction factors are applied in the calculation of the curves. Two coarse-grained representations of protein structure were investigated; two scattering bodies per amino acid led to significantly better results than a single scattering body.

CONCLUSION

We show that the obtained point estimates allow the calculation of accurate SAXS curves from coarse-grained protein models. The resulting curves are on par with the current state-of-the-art program CRYSOL, which requires full atomic detail. Our method was also comparable to CRYSOL in recognizing native structures among native-like decoys. As a proof-of-concept, we combined the coarse-grained Debye calculation with a previously described probabilistic model of protein structure, TorusDBN. This resulted in a significant improvement in the decoy recognition performance. In conclusion, the presented method shows great promise for use in statistical inference of protein structures from SAXS data.

Stop-and-go kinetics in amyloid fibrillation

Many human diseases are associated with protein aggregation and fibrillation. We present experiments on in vitro glucagon fibrillation using total internal reflection fluorescence microscopy, providing real-time measurements of single-fibril growth. We find that amyloid fibrils grow in an intermittent fashion, with periods of growth followed by long pauses. The observed exponential distributions of stop and growth times support a Markovian model, in which fibrils shift between the two states with specific rates. Even if the individual rates vary considerably, we observe that the probability of being in the growing (stopping) state is very close to 1/4 (3/4) in all experiments.

PHAISTOS: a framework for Markov chain Monte Carlo simulation and inference of protein structure

We present a new software framework for Markov chain Monte Carlo sampling for simulation, prediction, and inference of protein structure. The software package contains implementations of recent advances in Monte Carlo methodology, such as efficient local updates and sampling from probabilistic models of local protein structure. These models form a probabilistic alternative to the widely used fragment and rotamer libraries. Combined with an easily extendible software architecture, this makes PHAISTOS well suited for Bayesian inference of protein structure from sequence and/or experimental data. Currently, two force-fields are available within the framework: PROFASI and OPLS-AA/L, the latter including the generalized Born surface area solvent model. A flexible command-line and configuration-file interface allows users quickly to set up simulations with the desired configuration. PHAISTOS is released under the GNU General Public License v3.0. Source code and documentation are freely available from http://phaistos.sourceforge.net. The software is implemented in C++ and has been tested on Linux and OSX platforms.

Genome-wide prediction of SH2 domain targets using structural information and the FoldX algorithm

Current experiments likely cover only a fraction of all protein-protein interactions. Here, we developed a method to predict SH2-mediated protein-protein interactions using the structure of SH2-phosphopeptide complexes and the FoldX algorithm. We show that our approach performs similarly to experimentally derived consensus sequences and substitution matrices at predicting known in vitro and in vivo targets of SH2 domains. We use our method to provide a set of high-confidence interactions for human SH2 domains with known structure filtered on secondary structure and phosphorylation state. We validated the predictions using literature-derived SH2 interactions and a probabilistic score obtained from a naive Bayes integration of information on coexpression, conservation of the interaction in other species, shared interaction partners, and functions. We show how our predictions lead to a new hypothesis for the role of SH2 domains in signaling.

Understanding the functional role of every protein in the cell is a long-standing goal of cellular biology. An important step in this direction is to discover how and when proteins interact inside the cell to accomplish their tasks. Many of the cellular functions depend on reversible protein modifications like phosphorylation. To sense these modifications, cells have protein domains capable of binding phosphorylated proteins such as the SH2 domain. In this work, we show that it is possible to use the three-dimensional structure of protein domains to predict its binding preferences. Using a computational tool called FoldX, we have predicted the binding specificity of several human SH2 domains. These predictions, based on the computational analysis of the 3-D structure, were shown to be of similar accuracy as those obtained from experimental binding assays. We show here that it is also possible to understand how a mutation changes the binding preference of protein binding domains, opening the way for better understanding of some disease causing mutations. The combination of this novel computational approach with other sources of information allowed us to provide a set of high-confidence novel interactions for the proteins here studied.

Novel optical and statistical methods reveal colloid–wall interactions inconsistent with DLVO and Lifshitz theories

We present an experimental method based on video microscopy to perform nanometer scale position detection of a micrometer bead in the direction along the propagation of the detection light. Using the same bead for calibration and detection significantly improves the in depth resolution in comparison to video microscopy methods from literature. This method is used together with an optical trap to measure interaction potentials between a glass surface and colloids made of polystyrene or silica at different electrolyte concentrations. The results are confirmed by an independent method where the optical trap is used in connection with a quadrant photodiode. Also, we present a maximum likelihood analysis method which considerably improves the spatial resolution of interaction potentials by optimizing the underlying potential function to fit all observed position distributions. The measured interaction potentials agree well with DLVO theory for small electrolyte concentrations; however, for larger electrolyte concentrations the potentials differ qualitatively from both DLVO and Lifshitz theory.

Neural mechanism of activity spread in the cat motor cortex and its relation to the intrinsic connectivity

Motor cortical points are linked by intrinsic horizontal connections having a recurrent network topology. However, it is not known whether neural activity can propagate over the area covered by these intrinsic connections and whether there are spatial anisotropies of synaptic strength, as opposed to synaptic density. Moreover, the mechanisms by which activity spreads have yet to be determined. To address these issues, an 8 × 8 microelectrode array was inserted in the forelimb area of the cat motor cortex (MCx). The centre of the array had a laser etched hole ∼500 μm in diameter. A microiontophoretic pipette, with a tip diameter of 2-3 μm, containing bicuculline methiodide (BIC) was inserted in the hole and driven to a depth of 1200-1400 μm from the cortical surface. BIC was ejected for ∼2min from the tip of the micropipette with positive direct current ranging between 20 and 40 nA in different experiments. This produced spontaneous nearly periodic bursts (0.2-1.0 Hz) of multi-unit activity in a radius of about 400 μm from the tip of the micropipette. The bursts of neural activity spread at a velocity of 0.11-0.24 ms⁻¹ (mean=0.14 mm ms⁻¹, SD=0.05)with decreasing amplitude.The area activated was on average 7.22 mm² (SD=0.91 mm²), or ∼92% of the area covered by the recording array. The mode of propagation was determined to occur by progressive recruitment of cortical territory, driven by a central locus of activity of some 400 μm in radius. Thus, activity did not propagate as a wave. Transection of the connections between the thalamus and MCx did not significantly alter the propagation velocity or the size of the recruited area, demonstrating that the bursts spread along the routes of intrinsic cortical connectivity. These experiments demonstrate that neural activity initiated within a small motor cortical locus (≤ 400 μm in radius) can recruit a relatively large neighbourhood in which a variety of muscles acting at several forelimb joints are represented. These results support the hypothesis that the MCx controls the forelimb musculature in an integrated and anticipatory manner based on a recurrent network topology

Computational Redesign of Thioredoxin Is Hypersensitive toward Minor Conformational Changes in the Backbone Template

Despite the development of powerful computational tools, the full-sequence design of proteins still remains a challenging task. To investigate the limits and capabilities of computational tools, we conducted a study of the ability of the program Rosetta to predict sequences that recreate the authentic fold of thioredoxin. Focusing on the influence of conformational details in the template structures, we based our study on 8 experimentally determined template structures and generated 120 designs from each. For experimental evaluation, we chose six sequences from each of the eight templates by objective criteria. The 48 selected sequences were evaluated based on their progressive ability to (1) produce soluble protein in Escherichia coli and (2) yield stable monomeric protein, and (3) on the ability of the stable, soluble proteins to adopt the target fold. Of the 48 designs, we were able to synthesize 32, 20 of which resulted in soluble protein. Of these, only two were sufficiently stable to be purified. An X-ray crystal structure was solved for one of the designs, revealing a close resemblance to the target structure. We found a significant difference among the eight template structures to realize the above three criteria despite their high structural similarity. Thus, in order to improve the success rate of computational full-sequence design methods, we recommend that multiple template structures are used. Furthermore, this study shows that special care should be taken when optimizing the geometry of a structure prior to computational design when using a method that is based on rigid conformations.

Information theoretical quantification of cooperativity in signalling complexes

BACKGROUND

Intra-cellular information exchange, propelled by cascades of interacting signalling proteins, is essential for the proper functioning and survival of cells. Now that the interactome of several organisms is being mapped and several structural mechanisms of cooperativity at the molecular level in proteins have been elucidated, the formalization of this fundamental quantity, i.e. information, in these very diverse biological contexts becomes feasible.

RESULTS

We show here that Shannon's mutual information quantifies information in biological system and more specifically the cooperativity inherent to the assembly of macromolecular complexes. We show how protein complexes can be considered as particular instances of noisy communication channels. Further we show, using a portion of the p27 regulatory pathway, how classical equilibrium thermodynamic quantities such as binding affinities and chemical potentials can be used to quantify information exchange but also to determine engineering properties such as channel noise and channel capacity. As such, this information measure identifies and quantifies those protein concentrations that render the biochemical system most effective in switching between the active and inactive state of the intracellular process.

CONCLUSION

The proposed framework provides a new and original approach to analyse the effects of cooperativity in the assembly of macromolecular complexes. It shows the conditions, provided by the protein concentrations, for which a particular system acts most effectively, i.e. exchanges the most information. As such this framework opens the possibility of grasping biological qualities such as system sensitivity, robustness or plasticity directly in terms of their effect on information exchange. Although these parameters might also be derived using classical thermodynamic parameters, a recasting of biological signalling in terms of information exchange offers an alternative framework for visualising network cooperativity that might in some cases be more intuitive.

Size of quorum sensing communities

Ensembles of bacteria are able to coordinate their phenotypic behavior in accordance with the size, density, and growth state of the ensemble. This is achieved through production and exchange of diffusible signal molecules in a cell-cell regulatory system termed quorum sensing. In the generic quorum sensor a positive feedback in the production of signal molecules defines the conditions at which the collective behavior switches on. In spite of its conceptual simplicity, a proper measure of biofilm colony "size" appears to be lacking. We establish that the cell density multiplied by a geometric factor which incorporates the boundary conditions constitutes an appropriate size measure. The geometric factor is the square of the radius for a spherical colony or a hemisphere attached to a reflecting surface. If surrounded by a rapidly exchanged medium, the geometric factor is divided by three. For a disk-shaped biofilm the geometric factor is the horizontal dimension multiplied by the height, and the square of the height of the biofilm if there is significant flow above the biofilm. A remarkably simple factorized expression for the size is obtained, which separates the all-or-none ignition caused by the positive feedback from the smoother activation outside the switching region.

Generative probabilistic models extend the scope of inferential structure determination

Conventional methods for protein structure determination from NMR data rely on the ad hoc combination of physical forcefields and experimental data, along with heuristic determination of free parameters such as weight of experimental data relative to a physical forcefield. Recently, a theoretically rigorous approach was developed which treats structure determination as a problem of Bayesian inference. In this case, the forcefields are brought in as a prior distribution in the form of a Boltzmann factor. Due to high computational cost, the approach has been only sparsely applied in practice. Here, we demonstrate that the use of generative probabilistic models instead of physical forcefields in the Bayesian formalism is not only conceptually attractive, but also improves precision and efficiency. Our results open new vistas for the use of sophisticated probabilistic models of biomolecular structure in structure determination from experimental data.

Formulation of probabilistic models of protein structure in atomic detail using the reference ratio method

We propose a method to formulate probabilistic models of protein structure in atomic detail, for a given amino acid sequence, based on Bayesian principles, while retaining a close link to physics. We start from two previously developed probabilistic models of protein structure on a local length scale, which concern the dihedral angles in main chain and side chains, respectively. Conceptually, this constitutes a probabilistic and continuous alternative to the use of discrete fragment and rotamer libraries. The local model is combined with a nonlocal model that involves a small number of energy terms according to a physical force field, and some information on the overall secondary structure content. In this initial study we focus on the formulation of the joint model and the evaluation of the use of an energy vector as a descriptor of a protein's nonlocal structure; hence, we derive the parameters of the nonlocal model from the native structure without loss of generality. The local and nonlocal models are combined using the reference ratio method, which is a well-justified probabilistic construction. For evaluation, we use the resulting joint models to predict the structure of four proteins. The results indicate that the proposed method and the probabilistic models show considerable promise for probabilistic protein structure prediction and related applications.

Kinetic model for signal binding to the Quorum sensing regulator LasR

We propose a kinetic model for the activation of the las regulon in the opportunistic pathogen Pseudomonas aeruginosa. The model is based on in vitro data and accounts for the LasR dimerization and consecutive activation by binding of two OdDHL signal molecules. Experimentally, the production of the active LasR quorum-sensing regulator was studied in an Escherichia coli background as a function of signal molecule concentration. The functional activity of the regulator was monitored via a GFP reporter fusion to lasB expressed from the native lasB promoter. The new data shows that the active form of the LasR dimer binds two signal molecules cooperatively and that the timescale for reaching saturation is independent of the signal molecule concentration. This favors a picture where the dimerized regulator is protected against proteases and remains protected as it is activated through binding of two successive signal molecules. In absence of signal molecules, the dimerized regulator can dissociate and degrade through proteolytic turnover of the monomer. This resolves the apparent contradiction between our data and recent reports that the fully protected dimer is able to “degrade” when the induction of LasR ceases.