Structure-Based Network Analysis of Activation Mechanisms in the ErbB Family of Receptor Tyrosine Kinases: The Regulatory Spine Residues Are Global Mediators of Structural Stability and Allosteric Interactions

The ErbB protein tyrosine kinases are among the most important cell signaling families and mutation-induced modulation of their activity is associated with diverse functions in biological networks and human disease. We have combined molecular dynamics simulations of the ErbB kinases with the protein structure network modeling to characterize the reorganization of the residue interaction networks during conformational equilibrium changes in the normal and oncogenic forms. Structural stability and network analyses have identified local communities integrated around high centrality sites that correspond to the regulatory spine residues. This analysis has provided a quantitative insight to the mechanism of mutation-induced “superacceptor” activity in oncogenic EGFR dimers. We have found that kinase activation may be determined by allosteric interactions between modules of structurally stable residues that synchronize the dynamics in the nucleotide binding site and the αC-helix with the collective motions of the integrating αF-helix and the substrate binding site. The results of this study have pointed to a central role of the conserved His-Arg-Asp (HRD) motif in the catalytic loop and the Asp-Phe-Gly (DFG) motif as key mediators of structural stability and allosteric communications in the ErbB kinases. We have determined that residues that are indispensable for kinase regulation and catalysis often corresponded to the high centrality nodes within the protein structure network and could be distinguished by their unique network signatures. The optimal communication pathways are also controlled by these nodes and may ensure efficient allosteric signaling in the functional kinase state. Structure-based network analysis has quantified subtle effects of ATP binding on conformational dynamics and stability of the EGFR structures. Consistent with the NMR studies, we have found that nucleotide-induced modulation of the residue interaction networks is not limited to the ATP site, and may enhance allosteric cooperativity with the substrate binding region by increasing communication capabilities of mediating residues.     

Probing molecular mechanisms of the Hsp90 chaperone: biophysical modeling identifies key regulators of functional dynamics

Deciphering functional mechanisms of the Hsp90 chaperone machinery is an important objective in cancer biology aiming to facilitate discovery of targeted anti-cancer therapies. Despite significant advances in understanding structure and function of molecular chaperones, organizing molecular principles that control the relationship between conformational diversity and functional mechanisms of the Hsp90 activity lack a sufficient quantitative characterization. We combined molecular dynamics simulations, principal component analysis, the energy landscape model and structure-functional analysis of Hsp90 regulatory interactions to systematically investigate functional dynamics of the molecular chaperone. This approach has identified a network of conserved regions common to the Hsp90 chaperones that could play a universal role in coordinating functional dynamics, principal collective motions and allosteric signaling of Hsp90. We have found that these functional motifs may be utilized by the molecular chaperone machinery to act collectively as central regulators of Hsp90 dynamics and activity, including the inter-domain communications, control of ATP hydrolysis, and protein client binding. These findings have provided support to a long-standing assertion that allosteric regulation and catalysis may have emerged via common evolutionary routes. The interaction networks regulating functional motions of Hsp90 may be determined by the inherent structural architecture of the molecular chaperone. At the same time, the thermodynamics-based "conformational selection" of functional states is likely to be activated based on the nature of the binding partner. This mechanistic model of Hsp90 dynamics and function is consistent with the notion that allosteric networks orchestrating cooperative protein motions can be formed by evolutionary conserved and sparsely connected residue clusters. Hence, allosteric signaling through a small network of distantly connected residue clusters may be a rather general functional requirement encoded across molecular chaperones. The obtained insights may be useful in guiding discovery of allosteric Hsp90 inhibitors targeting protein interfaces with co-chaperones and protein binding clients.     

A new approach for extracting information from protein dynamics

Increased ability to predict protein structures is moving research focus towards understanding protein dynamics. A promising approach is to represent protein dynamics through networks and take advantage of well-developed methods from network science. Most studies build protein dynamics networks from correlation measures, an approach that only works under very specific conditions, instead of the more robust inverse approach. Thus, we apply the inverse approach to the dynamics of protein dihedral angles, a system of internal coordinates, to avoid structural alignment. Using the well-characterized adhesion protein, FimH, we show that our method identifies networks that are physically interpretable, robust, and relevant to the allosteric pathway sites. We further use our approach to detect dynamical differences, despite structural similarity, for Siglec-8 in the immune system, and the SARS-CoV-2 spike protein. Our study demonstrates that using the inverse approach to extract a network from protein dynamics yields important biophysical insights.     

Transient dynamics of genetic regulatory networks

We present an approximation scheme for deriving reaction rate equations of genetic regulatory networks. This scheme predicts the timescales of transient dynamics of such networks more accurately than does standard quasi-steady state analysis by introducing prefactors to the ODEs that govern the dynamics of the protein concentrations. These prefactors render the ODE systems slower than their quasi-steady state approximation counterparts. We introduce the method by examining a positive feedback gene regulatory network, and show how the transient dynamics of this network are more accurately modeled when the prefactor is included. Next, we examine the repressilator, a genetic oscillator, and show that the period, amplitude, and bifurcation diagram defining the onset of the oscillations are better estimated by the prefactor method. Finally, we examine the consequences of the method to the dynamics of reduced models of the phage lambda switch, and show that the switching times between the two states is slowed by the presence of the prefactor that arises from protein multimerization and DNA binding.     

Exploring the Morphospace of Communication Efficiency in Complex Networks

Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system''s dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology.     

On the characterization of energy networks of proteins

The construction of a realistic theoretical model of proteins is determinant for improving the computational simulations of their structural and functional aspects. Modeling proteins as a network of non-covalent connections between the atoms of amino acid residues has shown valuable insights into these macromolecules. The energy-related properties of protein structures are known to be very important in molecular dynamics. However, these same properties have been neglected when the protein structures are modeled as networks of atoms and amino acid residues. A new approach for the construction of protein models based on a network of atoms is presented. This method, based on interatomic interaction, takes into account the energy and geometric aspects of the protein structures that were not employed before, such as atomic occlusion inside the protein, the use of solvation, protein modeling and analysis, and the use of energy potentials to estimate the energies of interatomic non-covalent contacts. As a result, we achieved a more realistic network model of proteins. This model has the virtue of being more robust in face of different unknown variables that usually are arbitrarily estimated. We were able to determine the most connected residues of all the proteins studied, so that we are now in a better condition to study their structural role.     

Cell behaviour as a dynamic attractor in the intracellular signalling system

We present a model of the cell signalling network based on the generic properties of interactions between protein kinases (PKs) and protein phosphatases (PPs) inside cells. The model is designed to examine the global properties and intrinsic dynamics of the phosphorylation system. A genetic algorithm (GA) is used to evolve populations of "cells". The GA selects cells and ranks them based on an analysis of the dynamics of the proteins within the networks from a series of different random starting conditions. The fittest cells are taken to be those which can generate a variety of different "behaviours" from a series of different initial conditions. During the GA, intracellular protein interactions evolve via mutation and an analogue of domain shuffling between protein types that is thought to occur during biological evolution. The dynamics of the simulated networks are presented and we discuss the hypothesis that changes in the behaviour of a cell may be interpretable as a switch between attractor basins in the intracellular signalling network.     

Tension and robustness in multitasking cellular networks

Cellular networks multitask by exhibiting distinct, context-dependent dynamics. However, network states (parameters) that generate a particular dynamic are often sub-optimal for others, defining a source of "tension" between them. Though multitasking is pervasive, it is not clear where tension arises, what consequences it has, and how it is resolved. We developed a generic computational framework to examine the source and consequences of tension between pairs of dynamics exhibited by the well-studied RB-E2F switch regulating cell cycle entry. We found that tension arose from task-dependent shifts in parameters associated with network modules. Although parameter sets common to distinct dynamics did exist, tension reduced both their accessibility and resilience to perturbation, indicating a trade-off between "one-size-fits-all" solutions and robustness. With high tension, robustness can be preserved by dynamic shifting of modules, enabling the network to toggle between tasks, and by increasing network complexity, in this case by gene duplication. We propose that tension is a general constraint on the architecture and operation of multitasking biological networks. To this end, our work provides a framework to quantify the extent of tension between any network dynamics and how it affects network robustness. Such analysis would suggest new ways to interfere with network elements to elucidate the design principles of cellular networks.     

An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks

We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.     

MDN: A Web Portal for Network Analysis of Molecular Dynamics Simulations

We introduce a web portal that employs network theory for the analysis of trajectories from molecular dynamics simulations. Users can create protein energy networks following methodology previously introduced by our group, and can identify residues that are important for signal propagation, as well as measure the efficiency of signal propagation by calculating the network coupling. This tool, called MDN, was used to characterize signal propagation in Escherichia coli heat-shock protein 70-kDa. Two variants of this protein experimentally shown to be allosterically active exhibit higher network coupling relative to that of two inactive variants. In addition, calculations of partial coupling suggest that this quantity could be used as part of the criteria to determine pocket druggability in drug discovery studies.     

Stochasticity,Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks

It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations, a power that is substantially enhanced when these cells form a population.     

Structure and Dynamics of ER: Minimal Networks and Biophysical Constraints

The endoplasmic reticulum (ER) in live cells is a highly mobile network whose structure dynamically changes on a number of timescales. The role of such drastic changes in any system is unclear, although there are correlations with ER function. A better understanding of the fundamental biophysical constraints on the system will allow biologists to determine the effects of molecular factors on ER dynamics. Previous studies have identified potential static elements that the ER may remodel around. Here, we use these structural elements to assess biophysical principles behind the network dynamics. By analyzing imaging data of tobacco leaf epidermal cells under two different conditions, i.e., native state (control) and latrunculin B (treated), we show that the geometric structure and dynamics of ER networks can be understood in terms of minimal networks. Our results show that the ER network is well modeled as a locally minimal-length network between the static elements that potentially anchor the ER to the cell cortex over longer timescales; this network is perturbed by a mixture of random and deterministic forces. The network need not have globally minimum length; we observe cases where the local topology may change dynamically between different Euclidean Steiner network topologies. The networks in the treated cells are easier to quantify, because they are less dynamic (the treatment suppresses actin dynamics), but the same general features are found in control cells. Using a Langevin approach, we model the dynamics of the nonpersistent nodes and use this to show that the images can be used to estimate both local viscoelastic behavior of the cytoplasm and filament tension in the ER network. This means we can explain several aspects of the ER geometry in terms of biophysical principles.     

Structure and Dynamics of ER: Minimal Networks and Biophysical Constraints

The endoplasmic reticulum (ER) in live cells is a highly mobile network whose structure dynamically changes on a number of timescales. The role of such drastic changes in any system is unclear, although there are correlations with ER function. A better understanding of the fundamental biophysical constraints on the system will allow biologists to determine the effects of molecular factors on ER dynamics. Previous studies have identified potential static elements that the ER may remodel around. Here, we use these structural elements to assess biophysical principles behind the network dynamics. By analyzing imaging data of tobacco leaf epidermal cells under two different conditions, i.e., native state (control) and latrunculin B (treated), we show that the geometric structure and dynamics of ER networks can be understood in terms of minimal networks. Our results show that the ER network is well modeled as a locally minimal-length network between the static elements that potentially anchor the ER to the cell cortex over longer timescales; this network is perturbed by a mixture of random and deterministic forces. The network need not have globally minimum length; we observe cases where the local topology may change dynamically between different Euclidean Steiner network topologies. The networks in the treated cells are easier to quantify, because they are less dynamic (the treatment suppresses actin dynamics), but the same general features are found in control cells. Using a Langevin approach, we model the dynamics of the nonpersistent nodes and use this to show that the images can be used to estimate both local viscoelastic behavior of the cytoplasm and filament tension in the ER network. This means we can explain several aspects of the ER geometry in terms of biophysical principles.     

Computer-based screening of functional conformers of proteins

A long-standing goal in biology is to establish the link between function, structure, and dynamics of proteins. Considering that protein function at the molecular level is understood by the ability of proteins to bind to other molecules, the limited structural data of proteins in association with other bio-molecules represents a major hurdle to understanding protein function at the structural level. Recent reports show that protein function can be linked to protein structure and dynamics through network centrality analysis, suggesting that the structures of proteins bound to natural ligands may be inferred computationally. In the present work, a new method is described to discriminate protein conformations relevant to the specific recognition of a ligand. The method relies on a scoring system that matches critical residues with central residues in different structures of a given protein. Central residues are the most traversed residues with the same frequency in networks derived from protein structures. We tested our method in a set of 24 different proteins and more than 260,000 structures of these in the absence of a ligand or bound to it. To illustrate the usefulness of our method in the study of the structure/dynamics/function relationship of proteins, we analyzed mutants of the yeast TATA-binding protein with impaired DNA binding. Our results indicate that critical residues for an interaction are preferentially found as central residues of protein structures in complex with a ligand. Thus, our scoring system effectively distinguishes protein conformations relevant to the function of interest.     

Recognition of a Key Anchor Residue by a Conserved Hydrophobic Pocket Ensures Subunit Interface Integrity in DNA Clamps

Sliding clamp proteins encircle duplex DNA and are involved in processive DNA replication and the DNA damage response. Clamp proteins are ring-shaped oligomers (dimers or trimers) and are loaded onto DNA by an ATP-dependent clamp loader complex that ruptures the interface between two adjacent subunits. Here we measured the solution dynamics of the human clamp protein, proliferating cell nuclear antigen, by monitoring the change in the fluorescence of a site-specifically labeled. To unravel the origins of clamp subunit interface stability, we carried out comprehensive comparative analysis of the interfaces of seven sliding clamps. We used computational modeling (molecular dynamic simulations and MM/GBSA binding energy decomposition analyses) to identify conserved networks of hydrophobic residues critical for clamp stability and ring-opening dynamics. The hydrophobic network is shared among clamp proteins and exhibits a “key in a keyhole” pattern where a bulky aromatic residue from one clamp subunit is anchored into a hydrophobic pocket of the opposing subunit. Bioinformatics and dynamic network analyses showed that this oligomeric latch is conserved across DNA sliding clamps from all domains of life and dictates the dynamics of clamp opening and closing.     

Chaperones as integrators of cellular networks: changes of cellular integrity in stress and diseases

The complex integrity of the cells and its sudden, but often predictable changes can be described and understood by the topology and dynamism of cellular networks. All these networks undergo both local and global rearrangements during stress and development of diseases. Here, we illustrate this by showing the stress-induced structural rearrangement of the yeast protein-protein interaction network (interactome). In an unstressed state, the yeast interactome is highly compact, and the centrally organized modules have a large overlap. During stress, several original modules became more separated, and a number of novel modules also appear. A few basic functions such as theproteasome preserve their central position; however, several functions with high energy demand, such the cell-cycle regulation loose their original centrality during stress. A number of key stress-dependent protein complexes, such as the disaggregation-specific chaperone, Hsp104 gain centrality in the stressed yeast interactome. Molecular chaperones, heat shock, or stress proteins became established as key elements in our molecular understanding of the cellular stress response. Chaperones form complex interaction networks (the chaperome) with each other and their partners. Here, we show that the human chaperome recovers the segregation of protein synthesis-coupled and stress-related chaperones observed in yeast recently. Examination of yeast and human interactomes shows that chaperones 1) are intermodular integrators of protein-protein interaction networks, which 2) often bridge hubs and 3) are favorite candidates for extensive phosphorylation. Moreover, chaperones 4) become more central in the organization of the isolated modules of the stressed yeast protein-protein interaction network, which highlights their importance in the decoupling and recoupling of network modules during and after stress. Chaperone-mediated evolvability of cellular networks may play a key role in cellular adaptation during stress and various polygenic and chronic diseases, such as cancer, diabetes or neurodegeneration.     

Architecture of basic building blocks in protein and domain structural interaction networks

MOTIVATION: The structural interaction of proteins and their domains in networks is one of the most basic molecular mechanisms for biological cells. Topological analysis of such networks can provide an understanding of and solutions for predicting properties of proteins and their evolution in terms of domains. A single paradigm for the analysis of interactions at different layers, such as domain and protein layers, is needed. RESULTS: Applying a colored vertex graph model, we integrated two basic interaction layers under a unified model: (1) structural domains and (2) their protein/complex networks. We identified four basic and distinct elements in the model that explains protein interactions at the domain level. We searched for motifs in the networks to detect their topological characteristics using a pruning strategy and a hash table for rapid detection. We obtained the following results: first, compared with a random distribution, a substantial part of the protein interactions could be explained by domain-level structural interaction information. Second, there were distinct kinds of protein interaction patterns classified by specific and distinguishable numbers of domains. The intermolecular domain interaction was the most dominant protein interaction pattern. Third, despite the coverage of the protein interaction information differing among species, the similarity of their networks indicated shared architectures of protein interaction network in living organisms. Remarkably, there were only a few basic architectures in the model (>10 for a 4-node network topology), and we propose that most biological combinations of domains into proteins and complexes can be explained by a small number of key topological motifs. CONTACT: doheon@kaist.ac.kr.     

Transitions between asynchronous and synchronous states: a theory of correlations in small neural circuits

The study of correlations in neural circuits of different size, from the small size of cortical microcolumns to the large-scale organization of distributed networks studied with functional imaging, is a topic of central importance to systems neuroscience. However, a theory that explains how the parameters of mesoscopic networks composed of a few tens of neurons affect the underlying correlation structure is still missing. Here we consider a theory that can be applied to networks of arbitrary size with multiple populations of homogeneous fully-connected neurons, and we focus its analysis to a case of two populations of small size. We combine the analysis of local bifurcations of the dynamics of these networks with the analytical calculation of their cross-correlations. We study the correlation structure in different regimes, showing that a variation of the external stimuli causes the network to switch from asynchronous states, characterized by weak correlation and low variability, to synchronous states characterized by strong correlations and wide temporal fluctuations. We show that asynchronous states are generated by strong stimuli, while synchronous states occur through critical slowing down when the stimulus moves the network close to a local bifurcation. In particular, strongly positive correlations occur at the saddle-node and Andronov-Hopf bifurcations of the network, while strongly negative correlations occur when the network undergoes a spontaneous symmetry-breaking at the branching-point bifurcations. These results show how the correlation structure of firing-rate network models is strongly modulated by the external stimuli, even keeping the anatomical connections fixed. These results also suggest an effective mechanism through which biological networks may dynamically modulate the encoding and integration of sensory information.     

Accurate measurements of dynamics and reproducibility in small genetic networks

Quantification of gene expression has become a central tool for understanding genetic networks. In many systems, the only viable way to measure protein levels is by immunofluorescence, which is notorious for its limited accuracy. Using the early Drosophila embryo as an example, we show that careful identification and control of experimental error allows for highly accurate gene expression measurements. We generated antibodies in different host species, allowing for simultaneous staining of four Drosophila gap genes in individual embryos. Careful error analysis of hundreds of expression profiles reveals that less than ～20% of the observed embryo‐to‐embryo fluctuations stem from experimental error. These measurements make it possible to extract not only very accurate mean gene expression profiles but also their naturally occurring fluctuations of biological origin and corresponding cross‐correlations. We use this analysis to extract gap gene profile dynamics with ～1 min accuracy. The combination of these new measurements and analysis techniques reveals a twofold increase in profile reproducibility owing to a collective network dynamics that relays positional accuracy from the maternal gradients to the pair‐rule genes.