Coupling Protein Side-Chain and Backbone Flexibility Improves the Re-design of Protein-Ligand Specificity

Interactions between small molecules and proteins play critical roles in regulating and facilitating diverse biological functions, yet our ability to accurately re-engineer the specificity of these interactions using computational approaches has been limited. One main difficulty, in addition to inaccuracies in energy functions, is the exquisite sensitivity of protein–ligand interactions to subtle conformational changes, coupled with the computational problem of sampling the large conformational search space of degrees of freedom of ligands, amino acid side chains, and the protein backbone. Here, we describe two benchmarks for evaluating the accuracy of computational approaches for re-engineering protein-ligand interactions: (i) prediction of enzyme specificity altering mutations and (ii) prediction of sequence tolerance in ligand binding sites. After finding that current state-of-the-art “fixed backbone” design methods perform poorly on these tests, we develop a new “coupled moves” design method in the program Rosetta that couples changes to protein sequence with alterations in both protein side-chain and protein backbone conformations, and allows for changes in ligand rigid-body and torsion degrees of freedom. We show significantly increased accuracy in both predicting ligand specificity altering mutations and binding site sequences. These methodological improvements should be useful for many applications of protein – ligand design. The approach also provides insights into the role of subtle conformational adjustments that enable functional changes not only in engineering applications but also in natural protein evolution.     

How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility

To regulate shape changes, motility and chemotaxis in eukaryotic cells, signal transduction pathways channel extracellular stimuli to the reorganization of the actin cytoskeleton. The complexity of such networks makes it difficult to understand the roles of individual components, let alone their interactions and multiple feedbacks within a given layer and between layers of signalling. Even more challenging is the question of if and how the shape of the cell affects and is affected by this internal spatiotemporal reorganization. Here we build on our previous 2D cell motility model where signalling from the Rho family GTPases (Cdc42, Rac, and Rho) was shown to organize the cell polarization, actin reorganization, shape change, and motility in simple gradients. We extend this work in two ways: First, we investigate the effects of the feedback between the phosphoinositides (PIs) , and Rho family GTPases. We show how that feedback increases heights and breadths of zones of Cdc42 activity, facilitating global communication between competing cell “fronts”. This hastens the commitment to a single lamellipodium initiated in response to multiple, complex, or rapidly changing stimuli. Second, we show how cell shape feeds back on internal distribution of GTPases. Constraints on chemical isocline curvature imposed by boundary conditions results in the fact that dynamic cell shape leads to faster biochemical redistribution when the cell is repolarized. Cells with frozen cytoskeleton, and static shapes, consequently respond more slowly to reorienting stimuli than cells with dynamic shape changes, the degree of the shape-induced effects being proportional to the extent of cell deformation. We explain these concepts in the context of several in silico experiments using our 2D computational cell model.     

Challenges and dreams: physics of weak interactions essential to life

Biological systems display stunning capacities to self-organize. Moreover, their subcellular architectures are dynamic and responsive to changing needs and conditions. Key to these properties are manifold weak “quinary” interactions that have evolved to create specific spatial networks of macromolecules. These specific arrangements of molecules enable signals to be propagated over distances much greater than molecular dimensions, create phase separations that define functional regions in cells, and amplify cellular responses to changes in their environments. A major challenge is to develop biochemical tools and physical models to describe the panoply of weak interactions operating in cells. We also need better approaches to measure the biases in the spatial distributions of cellular macromolecules that result from the integrated action of multiple weak interactions. Partnerships between cell biologists, biochemists, and physicists are required to deploy these methods. Together these approaches will help us realize the dream of understanding the biological “glue” that sustains life at a molecular and cellular level.     

Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains

The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage savings over direct approaches.     

Pleomorphic Ensembles: Formation of Large Clusters Composed of Weakly Interacting Multivalent Molecules

Molecular interactions of importance to cell biology are subject to sol-gel transitions: large clusters of weakly interacting multivalent molecules (gel phase) are produced at a critical concentration of monomers. Examples include cell-cell and cell-matrix adhesions, nucleoprotein bodies, and cell signaling platforms. We use the term pleomorphic ensembles (PEs) to describe these clusters, because they have dynamic compositions and sizes and have rapid turnover of their molecular constituents; this plasticity can be highly responsive to cellular signals. The classical polymer physical chemistry theory developed by Flory and Stockmayer provides a brilliant framework for treating multivalent interactions for simple idealized systems. But the complexity and variability of PEs challenges existing modeling approaches. Here we describe and validate a computational algorithm that extends the Flory-Stockmayer formalism to overcome the limitations of analytic theories. We divide the problem by deterministically calculating the fraction of bound sites for each type of binding site, followed by the stochastic assignment of the bonds to a finite number of molecules. The method allows for high valency within many different kinds of interacting molecules and site types, permits simulation of steady-state distributions, as well as assembly kinetics, and can treat cooperative binding within one of the interacting molecules. We then apply our method to the analysis of interactions in the nephrin-Nck-N-Wasp signaling system, demonstrating how multivalent layered scaffolds produce PEs at low monomer concentrations despite weak binding interactions. We show how the experimental data for this system are most consistent with synergistic cooperative interactions between Nck and N-Wasp.     

Chapter 4: Protein Interactions and Disease

Proteins do not function in isolation; it is their interactions with one another and also with other molecules (e.g. DNA, RNA) that mediate metabolic and signaling pathways, cellular processes, and organismal systems. Due to their central role in biological function, protein interactions also control the mechanisms leading to healthy and diseased states in organisms. Diseases are often caused by mutations affecting the binding interface or leading to biochemically dysfunctional allosteric changes in proteins. Therefore, protein interaction networks can elucidate the molecular basis of disease, which in turn can inform methods for prevention, diagnosis, and treatment. In this chapter, we will describe the computational approaches to predict and map networks of protein interactions and briefly review the experimental methods to detect protein interactions. We will describe the application of protein interaction networks as a translational approach to the study of human disease and evaluate the challenges faced by these approaches.

What to Learn in This Chapter

• Experimental and computational methods to detect protein interactions
• Protein networks and disease
• Studying the genetic and molecular basis of disease
• Using protein interactions to understand disease

This article is part of the “Translational Bioinformatics” collection for PLOS Computational Biology.

     

Global Analysis of the Human Pathophenotypic Similarity Gene Network Merges Disease Module Components

The molecular complexity of genetic diseases requires novel approaches to break it down into coherent biological modules. For this purpose, many disease network models have been created and analyzed. We highlight two of them, “the human diseases networks” (HDN) and “the orphan disease networks” (ODN). However, in these models, each single node represents one disease or an ambiguous group of diseases. In these cases, the notion of diseases as unique entities reduces the usefulness of network-based methods. We hypothesize that using the clinical features (pathophenotypes) to define pathophenotypic connections between disease-causing genes improve our understanding of the molecular events originated by genetic disturbances. For this, we have built a pathophenotypic similarity gene network (PSGN) and compared it with the unipartite projections (based on gene-to-gene edges) similar to those used in previous network models (HDN and ODN). Unlike these disease network models, the PSGN uses semantic similarities. This pathophenotypic similarity has been calculated by comparing pathophenotypic annotations of genes (human abnormalities of HPO terms) in the “Human Phenotype Ontology”. The resulting network contains 1075 genes (nodes) and 26197 significant pathophenotypic similarities (edges). A global analysis of this network reveals: unnoticed pairs of genes showing significant pathophenotypic similarity, a biological meaningful re-arrangement of the pathological relationships between genes, correlations of biochemical interactions with higher similarity scores and functional biases in metabolic and essential genes toward the pathophenotypic specificity and the pleiotropy, respectively. Additionally, pathophenotypic similarities and metabolic interactions of genes associated with maple syrup urine disease (MSUD) have been used to merge into a coherent pathological module.Our results indicate that pathophenotypes contribute to identify underlying co-dependencies among disease-causing genes that are useful to describe disease modularity.     

Nutritional Systems Biology Modeling: From Molecular Mechanisms to Physiology

The use of computational modeling and simulation has increased in many biological fields, but despite their potential these techniques are only marginally applied in nutritional sciences. Nevertheless, recent applications of modeling have been instrumental in answering important nutritional questions from the cellular up to the physiological levels. Capturing the complexity of today''s important nutritional research questions poses a challenge for modeling to become truly integrative in the consideration and interpretation of experimental data at widely differing scales of space and time. In this review, we discuss a selection of available modeling approaches and applications relevant for nutrition. We then put these models into perspective by categorizing them according to their space and time domain. Through this categorization process, we identified a dearth of models that consider processes occurring between the microscopic and macroscopic scale. We propose a “middle-out” strategy to develop the required full-scale, multilevel computational models. Exhaustive and accurate phenotyping, the use of the virtual patient concept, and the development of biomarkers from “-omics” signatures are identified as key elements of a successful systems biology modeling approach in nutrition research—one that integrates physiological mechanisms and data at multiple space and time scales.     

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie''s algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.     

Bringing Statistics Up to Speed with Data in Analysis of Lymphocyte Motility

Two-photon (2P) microscopy provides immunologists with 3D video of the movement of lymphocytes in vivo. Motility parameters extracted from these videos allow detailed analysis of lymphocyte motility in lymph nodes and peripheral tissues. However, standard parametric statistical analyses such as the Student’s t-test are often used incorrectly, and fail to take into account confounds introduced by the experimental methods, potentially leading to erroneous conclusions about T cell motility. Here, we compare the motility of WT T cell versus PKCθ-/-, CARMA1-/-, CCR7-/-, and PTX-treated T cells. We show that the fluorescent dyes used to label T cells have significant effects on T cell motility, and we demonstrate the use of factorial ANOVA as a statistical tool that can control for these effects. In addition, researchers often choose between the use of “cell-based” parameters by averaging multiple steps of a single cell over time (e.g. cell mean speed), or “step-based” parameters, in which all steps of a cell population (e.g. instantaneous speed) are grouped without regard for the cell track. Using mixed model ANOVA, we show that we can maintain cell-based analyses without losing the statistical power of step-based data. We find that as we use additional levels of statistical control, we can more accurately estimate the speed of T cells as they move in lymph nodes as well as measure the impact of individual signaling molecules on T cell motility. As there is increasing interest in using computational modeling to understand T cell behavior in in vivo, these quantitative measures not only give us a better determination of actual T cell movement, they may prove crucial for models to generate accurate predictions about T cell behavior.     

The Oral Tolerance as a Complex Network Phenomenon

The phenomenon of oral tolerance refers to a local and systemic state of tolerance induced in the gut after its exposure to innocuous antigens. Recent findings have shown the interrelationship between cellular and molecular components of oral tolerance, but its representation through a network of interactions has not been investigated. Our work aims at identifying the causal relationship of each element in an oral tolerance network, and also to propose a phenomenological model that’s capable of predicting the stochastic behavior of this network when under manipulation. We compared the changes of a “healthy” network caused by “knock-outs” (KOs) in two approaches: an analytical approach by the Perron Frobenius theory; and a computational approach, which we describe within this work in order to find numerical results for the model. Both approaches have shown the most relevant immunological components for this phenomena, that happens to corroborate the empirical results from animal models. Besides explain in a intelligible fashion how the components interacts in a complex manner, we also managed to describe and quantify the importance of KOs that hasn’t been empirically tested.     

Process-driven inference of biological network structure: feasibility, minimality, and multiplicity

A common problem in molecular biology is to use experimental data, such as microarray data, to infer knowledge about the structure of interactions between important molecules in subsystems of the cell. By approximating the state of each molecule as “on” or “off”, it becomes possible to simplify the problem, and exploit the tools of Boolean analysis for such inference. Amongst Boolean techniques, the process-driven approach has shown promise in being able to identify putative network structures, as well as stability and modularity properties. This paper examines the process-driven approach more formally, and makes four contributions about the computational complexity of the inference problem, under the “dominant inhibition” assumption of molecular interactions. The first is a proof that the feasibility problem (does there exist a network that explains the data?) can be solved in polynomial-time. Second, the minimality problem (what is the smallest network that explains the data?) is shown to be NP-hard, and therefore unlikely to result in a polynomial-time algorithm. Third, a simple polynomial-time heuristic is shown to produce near-minimal solutions, as demonstrated by simulation. Fourth, the theoretical framework explains how multiplicity (the number of network solutions to realize a given biological process), which can take exponential-time to compute, can instead be accurately estimated by a fast, polynomial-time heuristic.     

Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation

Abstract

Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1?D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes.     

Pleomorphic Ensembles: Formation of Large Clusters Composed of Weakly Interacting Multivalent Molecules

Molecular interactions of importance to cell biology are subject to sol-gel transitions: large clusters of weakly interacting multivalent molecules (gel phase) are produced at a critical concentration of monomers. Examples include cell-cell and cell-matrix adhesions, nucleoprotein bodies, and cell signaling platforms. We use the term pleomorphic ensembles (PEs) to describe these clusters, because they have dynamic compositions and sizes and have rapid turnover of their molecular constituents; this plasticity can be highly responsive to cellular signals. The classical polymer physical chemistry theory developed by Flory and Stockmayer provides a brilliant framework for treating multivalent interactions for simple idealized systems. But the complexity and variability of PEs challenges existing modeling approaches. Here we describe and validate a computational algorithm that extends the Flory-Stockmayer formalism to overcome the limitations of analytic theories. We divide the problem by deterministically calculating the fraction of bound sites for each type of binding site, followed by the stochastic assignment of the bonds to a finite number of molecules. The method allows for high valency within many different kinds of interacting molecules and site types, permits simulation of steady-state distributions, as well as assembly kinetics, and can treat cooperative binding within one of the interacting molecules. We then apply our method to the analysis of interactions in the nephrin-Nck-N-Wasp signaling system, demonstrating how multivalent layered scaffolds produce PEs at low monomer concentrations despite weak binding interactions. We show how the experimental data for this system are most consistent with synergistic cooperative interactions between Nck and N-Wasp.     

Emotion Attribution to a Non-Humanoid Robot in Different Social Situations

In the last few years there was an increasing interest in building companion robots that interact in a socially acceptable way with humans. In order to interact in a meaningful way a robot has to convey intentionality and emotions of some sort in order to increase believability. We suggest that human-robot interaction should be considered as a specific form of inter-specific interaction and that human–animal interaction can provide a useful biological model for designing social robots. Dogs can provide a promising biological model since during the domestication process dogs were able to adapt to the human environment and to participate in complex social interactions. In this observational study we propose to design emotionally expressive behaviour of robots using the behaviour of dogs as inspiration and to test these dog-inspired robots with humans in inter-specific context. In two experiments (wizard-of-oz scenarios) we examined humans'' ability to recognize two basic and a secondary emotion expressed by a robot. In Experiment 1 we provided our companion robot with two kinds of emotional behaviour (“happiness” and “fear”), and studied whether people attribute the appropriate emotion to the robot, and interact with it accordingly. In Experiment 2 we investigated whether participants tend to attribute guilty behaviour to a robot in a relevant context by examining whether relying on the robot''s greeting behaviour human participants can detect if the robot transgressed a predetermined rule. Results of Experiment 1 showed that people readily attribute emotions to a social robot and interact with it in accordance with the expressed emotional behaviour. Results of Experiment 2 showed that people are able to recognize if the robot transgressed on the basis of its greeting behaviour. In summary, our findings showed that dog-inspired behaviour is a suitable medium for making people attribute emotional states to a non-humanoid robot.     

Where to Go: Breaking the Symmetry in Cell Motility

Cell migration in the “correct” direction is pivotal for many biological processes. Although most work is devoted to its molecular mechanisms, the cell’s preference for one direction over others, thus overcoming intrinsic random motility, epitomizes a profound principle that underlies all complex systems: the choice of one axis, in structure or motion, from a uniform or symmetric set of options. Explaining directional motility by an external chemo-attractant gradient does not solve but only shifts the problem of causation: whence the gradient? A new study in PLOS Biology shows cell migration in a self-generated gradient, offering an opportunity to take a broader look at the old dualism of extrinsic instruction versus intrinsic symmetry-breaking in cell biology.

When you come to a fork in the road, take it.–Yogi Berra 1925–2015

     

Multivalent protein–protein interactions are pivotal regulators of eukaryotic Hsp70 complexes

Heat shock protein 70 (Hsp70) is a molecular chaperone and central regulator of protein homeostasis (proteostasis). Paramount to this role is Hsp70’s binding to client proteins and co-chaperones to produce distinct complexes, such that understanding the protein–protein interactions (PPIs) of Hsp70 is foundational to describing its function and dysfunction in disease. Mounting evidence suggests that these PPIs include both “canonical” interactions, which are universally conserved, and “non-canonical” (or “secondary”) contacts that seem to have emerged in eukaryotes. These two categories of interactions involve discrete binding surfaces, such that some clients and co-chaperones engage Hsp70 with at least two points of contact. While the contributions of canonical interactions to chaperone function are becoming increasingly clear, it can be challenging to deconvolute the roles of secondary interactions. Here, we review what is known about non-canonical contacts and highlight examples where their contributions have been parsed, giving rise to a model in which Hsp70’s secondary contacts are not simply sites of additional avidity but are necessary and sufficient to impart unique functions. From this perspective, we propose that further exploration of non-canonical contacts will generate important insights into the evolution of Hsp70 systems and inspire new approaches for developing small molecules that tune Hsp70-mediated proteostasis.     

Protein coadaptation and the design of novel approaches to identify protein-protein interactions

Proteins rarely function in isolation but they form part of complex networks of interactions with other proteins within or among cells. The importance of a particular protein for cell viability is directly dependent upon the number of interactions where it participates and the function it performs: the larger the number of interactions of a protein the greater its functional importance is for the cell. With the advent of genome sequencing and "omics" technologies it became feasible conducting large-scale searches for protein interacting partners. Unfortunately, the accuracy of such analyses has been underwhelming owing to methodological limitations and to the inherent complexity of protein interactions. In addition to these experimental approaches, many computational methods have been developed to identify protein-protein interactions by assuming that interacting proteins coevolve resulting from the coadaptation dynamics between the amino acids of their interacting faces. We review the main technological advances made in the field of interactomics and discuss the feasibility of computational methods to identify protein-protein interactions based on the estimation of coevolution. As proof-of-concept, we present a classical case study: the interactions of cell surface proteins (receptors) and their ligands. Finally, we take this discussion one step forward to include interactions between organisms and species to understand the generation of biological complexity. Development of technologies for accurate detection of protein-protein interactions may shed light on processes that go from the fine-tuning of pathways and metabolic networks to the emergence of biological complexity.