An allosteric mechanism inferred from molecular dynamics simulations on phospholamban pentamer in lipid membranes

Phospholamban functions as a regulator of Ca(2+) concentration of cardiac muscle cells by triggering the bioactivity of sarcoplasmic reticulum Ca(2+)-ATPase. In order to understand its dynamic mechanism in the environment of bilayer surroundings, we performed long time-scale molecular dynamic simulations based on the high-resolution NMR structure of phospholamban pentamer. It was observed from the molecular dynamics trajectory analyses that the conformational transitions between the "bellflower" and "pinwheel" modes were detected for phospholamban. Particularly, the two modes became quite similar to each other after phospholamban was phosphorylated at Ser16. Based on these findings, an allosteric mechanism was proposed to elucidate the dynamic process of phospholamban interacting with Ca(2+)-ATPase.     

Substrate-Modulated Thermal Fluctuations Affect Long-Range Allosteric Signaling in Protein Homodimers: Exemplified in CAP

The role of conformational dynamics in allosteric signaling of proteins is increasingly recognized as an important and subtle aspect of this ubiquitous phenomenon. Cooperative binding is commonly observed in proteins with twofold symmetry that bind two identical ligands. We construct a coarse-grained model of an allosteric coupled dimer and show how the signal can be propagated between the distant binding sites via change in slow global vibrational modes alone. We demonstrate that modulation on substrate binding of as few as 5-10 slow modes can give rise to cooperativity observed in biological systems and that the type of cooperativity is given by change of interaction between the two monomers upon ligand binding. To illustrate the application of the model, we apply it to a challenging test case: the catabolite activator protein (CAP). CAP displays negative cooperativity upon association with two identical ligands. The conformation of CAP is not affected by the binding, but its vibrational spectrum undergoes a strong modification. Intriguingly, the first binding enhances thermal fluctuations, yet the second quenches them. We show that this counterintuitive behavior is, in fact, necessary for an optimal anticooperative system, and captured within a well-defined region of the model's parameter space. From analyzing the experimental results, we conclude that fast local modes take an active part in the allostery of CAP, coupled to the more-global slow modes. By including them into the model, we elucidate the role of the modes on different timescales. We conclude that such dynamic control of allostery in homodimers may be a general phenomenon and that our model framework can be used for extended interpretation of thermodynamic parameters in other systems.     

Coupling between Normal Modes Drives Protein Conformational Dynamics: Illustrations Using Allosteric Transitions in Myosin II

Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.     

Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter ones are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together.     

Subsets of Slow Dynamic Modes Reveal Global Information Sources as Allosteric Sites

Allostery is a key biological control mechanism, and dynamic information flow provides a perspective to describe allosteric interactions in causal relationships. Here, as a novel implementation of the Gaussian Network Model (GNM) based Transfer Entropy (TE) calculations, we show that the dissection of dynamic information into subsets of slow dynamic modes discloses different layers of multi-directional allosteric pathways inherent in a given protein structure. In these subsets of slow modes, the degree of collectivity (Col) in the information transfer of residues with their TE values (TECol score) identifies distinct residues as powerful effectors, global information sources; showing themselves with a high dynamic capacity to collectively disseminate information to others. As exemplified on aspartate transcarbamoylase (ATCase), Na⁺/K⁺-adenosine triphosphatase (Na⁺/K⁺-ATPase), and human transient receptor potential melastatin 2 (TRPM2) along with a dataset of 20 proteins, these specific residues are associated with known active and allosteric sites. These information source residues, which collectively control others and lead allosteric communication pathways, hint at plausible binding sites for structure-based rational drug design.     

Dynamic versus instantaneous models of diet choice

We investigate the dynamics of a series of two-prey-one-predator models in which the predator exhibits adaptive diet choice based on the different energy contents and/or handling times of the two prey species. The predator is efficient at exploiting its prey and has a saturating functional response; these two features combine to produce sustained population cycles over a wide range of parameter values. Two types of models of behavioral change are compared. In one class of models ("instantaneous choice"), the probability of acceptance of the poorer prey by the predator instantaneously approximates the optimal choice, given current prey densities. In the second class of models ("dynamic choice"), the probability of acceptance of the poorer prey is a dynamic variable, which begins to change in an adaptive direction when prey densities change but which requires a finite amount of time to approach the new optimal behavior. The two types of models frequently predict qualitatively different population dynamics of the three-species system, with chaotic dynamics and complex cycles being a common outcome only in the dynamic choice models. In dynamic choice models, factors that reduce the rate of behavioral change when the probability of accepting the poorer prey approaches extreme values often produce complex population dynamics. Instantaneous and dynamic models often predict different average population densities and different indirect interactions between prey species. Alternative dynamic models of behavior are analyzed and suggest, first, that instantaneous choice models may be good approximations in some circumstances and, second, that different types of dynamic choice models often lead to significantly different population dynamics. The results suggest possible behavioral mechanisms leading to complex population dynamics and highlight the need for more empirical study of the dynamics of behavioral change.     

Allosteric Dynamic Control of Binding

Proteins have a highly dynamic nature and there is a complex interrelation between their structural dynamics and binding behavior. By assuming various conformational ensembles, they perform both local and global fluctuations to interact with other proteins in a dynamic infrastructure adapted to functional motion. Here, we show that there is a significant association between allosteric mutations, which lead to high-binding-affinity changes, and the hinge positions of global modes, as revealed by a large-scale statistical analysis of data in the Structural Kinetic and Energetic Database of Mutant Protein Interactions (SKEMPI). We further examined the mechanism of allosteric dynamics by conducting studies on human growth hormone (hGH) and pyrin domain (PYD), and the results show how mutations at the hinge regions could allosterically affect the binding-site dynamics or induce alternative binding modes by modifying the ensemble of accessible conformations. The long-range dissemination of perturbations in local chemistry or physical interactions through an impact on global dynamics can restore the allosteric dynamics. Our findings suggest a mechanism for the coupling of structural dynamics to the modulation of protein interactions, which remains a critical phenomenon in understanding the effect of mutations that lead to functional changes in proteins.     

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.     

Filtering molecular dynamics trajectories to reveal low-frequency collective motions: phospholipase A2

A novel method for analysing molecular dynamics trajectories has been developed, which filters out high frequencies using digital signal processing techniques and facilitates focusing on the low-frequency collective motions of proteins. These motions involve low energy slow motions, which lead to important biological phenomena such as domain closure and allosteric effects in enzymes. The filtering method treats each of the atomic trajectories obtained from the molecular dynamics simulation as a "signal". The trajectories of each of the atoms in the system (or any subset of interest) are Fourier transformed to the frequency domain, a filtering function is applied and then an inverse transformation back to the time domain yields the filtered trajectory. The filtering method has been used to study the dynamics of the enzyme phospholipase A2. In the filtered trajectory, all the high frequency bond and valence angle vibrations were eliminated, leaving only low-frequency motion, mainly fluctuations in torsions and conformational transitions. Analysis of this trajectory revealed interesting motions of the protein, including concerted movements of helices, and changes in shape of the active site cavity. Unlike normal mode analysis, which has been used to study the motion of proteins, this method does not require converged minimizations or diagonalization of a matrix of second derivatives. In addition, anharmonicity, multiple minima and conformational transitions are treated explicitly. Thus, the filtering method avoids most of the approximations implicit in other investigations of the dynamic behaviour of large systems.     

Critical slowing down as an indicator of transitions in two-species models

Transitions in ecological systems often occur without apparent warning, and may represent shifts between alternative persistent states. Decreasing ecological resilience (the size of the basin of attraction around a stable state) can signal an impending transition, but this effect is difficult to measure in practice. Recent research has suggested that a decreasing rate of recovery from small perturbations (critical slowing down) is a good indicator of ecological resilience. Here we use analytical techniques to draw general conclusions about the conditions under which critical slowing down provides an early indicator of transitions in two-species predator-prey and competition models. The models exhibit three types of transition: the predator-prey model has a Hopf bifurcation and a transcritical bifurcation, and the competition model has two saddle-node bifurcations (in which case the system exhibits hysteresis) or two transcritical bifurcations, depending on the parameterisation. We find that critical slowing down is an earlier indicator of the Hopf bifurcation in predator-prey models in which prey are regulated by predation rather than by intrinsic density-dependent effects and an earlier indicator of transitions in competition models in which the dynamics of the rare species operate on slower timescales than the dynamics of the common species. These results lead directly to predictions for more complex multi-species systems, which can be tested using simulation models or real ecosystems.     

Parallel Allostery by cAMP and PDE Coordinates Activation and Termination Phases in cAMP Signaling

The second messenger molecule cAMP regulates the activation phase of the cAMP signaling pathway through high-affinity interactions with the cytosolic cAMP receptor, the protein kinase A regulatory subunit (PKAR). Phosphodiesterases (PDEs) are enzymes responsible for catalyzing hydrolysis of cAMP to 5′ AMP. It was recently shown that PDEs interact with PKAR to initiate the termination phase of the cAMP signaling pathway. While the steps in the activation phase are well understood, steps in the termination pathway are unknown. Specifically, the binding and allosteric networks that regulate the dynamic interplay between PKAR, PDE, and cAMP are unclear. In this study, PKAR and PDE from Dictyostelium discoideum (R_D and RegA, respectively) were used as a model system to monitor complex formation in the presence and absence of cAMP. Amide hydrogen/deuterium exchange mass spectrometry was used to monitor slow conformational transitions in R_D, using disordered regions as conformational probes. Our results reveal that R_D regulates its interactions with cAMP and RegA at distinct loci by undergoing slow conformational transitions between two metastable states. In the presence of cAMP, R_D and RegA form a stable ternary complex, while in the absence of cAMP they maintain transient interactions. RegA and cAMP each bind at orthogonal sites on R_D with resultant contrasting effects on its dynamics through parallel allosteric relays at multiple important loci. R_D thus serves as an integrative node in cAMP termination by coordinating multiple allosteric relays and governing the output signal response.     

Emergence of donor control in patchy predator—prey systems

We study a general predator—prey system in a spatially heterogeneous environment. The predation process, which occurs on a behavioural time-scale, is much faster than the other processes (reproduction, natural mortality and migrations) occurring on the population dynamics time-scale. We show that, taking account of this difference in time-scales, and assuming that the prey have a refuge, the dynamics of the system on a slow time-scale become donor-controlled. Even though predators may control the prey density locally and on a behavioural fast time-scale, nevertheless, both globally and on a slow time-scale, the prey dynamics are independent of predator density: the presence of predators generates a constant prey mortality. In other words, in heterogeneous environments, the prey population dynamics depend in a switch-like manner on the presence or absence of predators, not on their actual density.     

Noise-induced transitions in slow wave neuronal dynamics

Many neuronal systems exhibit slow random alternations and sudden switches in activity states. Models with noisy relaxation dynamics (oscillatory, excitable or bistable) account for these temporal, slow wave, patterns and the fluctuations within states. The noise-induced transitions in a relaxation dynamics are analogous to escape by a particle in a slowly changing double-well potential. In this formalism, we obtain semi-analytically the first and second order statistical properties: the distributions of the slow process at the transitions and the temporal correlations of successive switching events. We find that the temporal correlations can be used to help distinguish among biophysical mechanisms for the slow negative feedback, such as divisive or subtractive. We develop our results in the context of models for cellular pacemaker neurons; they also apply to mean-field models for spontaneously active networks with slow wave dynamics.     

Transient sensitivities of non-indigenous shrub species indicate complicated invasion dynamics

As biological invasions increasingly affect natural systems, the need for methods that can quantify the processes responsible for invasion success has increased. Further, methods should be geared to the formulation of management strategies. Demographic analyses are designed to explore the causes and properties of population change. Matrix population models, a commonly used technique for demographic analysis, have been applied to the analysis of stage-structured populations. However, most commonly, analyses have focused on long-term outcomes dynamics (ergodic dynamics). The methods available for analysis of matrix population models have recently been extended to facilitate analysis of the transient dynamics most important to invasion analysis. In this paper we analyze the transient population dynamics of three invasive shrubs and compare them to ergodic dynamics. Cytisus scoparius, Clidemia hirta, and Ardisia elliptica come from different parts of the world and are all now found in the United States of America. They also have published transition matrices that measure the probabilities that any one life-history stage will transition to another over an annual time step. These matrices have been estimated from multi-year data collected from plots in various environments. Our comparative study of transient and ergodic dynamics of invasive shrubs shows that, for all the considered shrub species, there was a clear difference between the sensitivities drawn from these two approaches. The transient sensitivities of earlier life-history transitions showed magnified importance relative to ergodic sensitivities. This was especially true of A. elliptica for which the stable population structure was most different from the starting structure analyzed in detail here. For other species, as stable population structures were heavily weighted towards early stages, the differences in the importance of early transitions transiently and ergodically were less dramatic. Late life transitions showed magnified importance in areas towards the center of the invasion or in older invasion areas. Finally, populations with shorter estimated generation times show greater transient sensitivity to early life-history stages; but the pattern was complex and varied according to species, and was also observed across other life-history transitions. Overall, the ambiguity and complexity of the results highlight the power of considering transient population dynamics for invading species, as well as the importance of specific biological and ecological knowledge of the invading species. Although there may be commonalities across invasions, important decisions on control or inference on population dynamics should treat invasions as individual, unique events.     

Mobility unevenness in rock–paper–scissors models

We investigate a tritrophic system whose cyclic dominance is modelled by the rock–paper–scissors game. We consider that organisms of one or two species are affected by movement limitations, which unbalances the cyclic spatial game. Performing stochastic simulations, we show that mobility unevenness controls the population dynamics. In the case of one slow species, the predominant species depends on the level of mobility restriction, with the slow species being preponderant if the mobility limitations are substantial. If two species face mobility limitations, our outcomes show that being higher dispersive does not constitute an advantage in terms of population growth. On the contrary, if organisms move with higher mobility, they expose themselves to enemies more frequently, being more vulnerable to being eliminated. Finally, our findings show that biodiversity benefits in regions where species are slowed. Biodiversity loss for high mobility organisms, common to cyclic systems, may be avoided with coexistence probability being higher for robust mobility limitations. Our results may help biologists understand the dynamics of unbalanced spatial systems where organisms’ dispersal is fundamental to biodiversity conservation.     

Linking dynamics of the inhibitory network to the input structure

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network’s response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.     

Transients and attractors in epidemics

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.     

Change in allosteric network affects binding affinities of PDZ domains: analysis through perturbation response scanning

The allosteric mechanism plays a key role in cellular functions of several PDZ domain proteins (PDZs) and is directly linked to pharmaceutical applications; however, it is a challenge to elaborate the nature and extent of these allosteric interactions. One solution to this problem is to explore the dynamics of PDZs, which may provide insights about how intramolecular communication occurs within a single domain. Here, we develop an advancement of perturbation response scanning (PRS) that couples elastic network models with linear response theory (LRT) to predict key residues in allosteric transitions of the two most studied PDZs (PSD-95 PDZ3 domain and hPTP1E PDZ2 domain). With PRS, we first identify the residues that give the highest mean square fluctuation response upon perturbing the binding sites. Strikingly, we observe that the residues with the highest mean square fluctuation response agree with experimentally determined residues involved in allosteric transitions. Second, we construct the allosteric pathways by linking the residues giving the same directional response upon perturbation of the binding sites. The predicted intramolecular communication pathways reveal that PSD-95 and hPTP1E have different pathways through the dynamic coupling of different residue pairs. Moreover, our analysis provides a molecular understanding of experimentally observed hidden allostery of PSD-95. We show that removing the distal third alpha helix from the binding site alters the allosteric pathway and decreases the binding affinity. Overall, these results indicate that (i) dynamics plays a key role in allosteric regulations of PDZs, (ii) the local changes in the residue interactions can lead to significant changes in the dynamics of allosteric regulations, and (iii) this might be the mechanism that each PDZ uses to tailor their binding specificities regulation.