Essential dynamics of proteins

Analysis of extended molecular dynamics (MD) simulations of lysozyme in vacuo and in aqueous solution reveals that it is possible to separate the configurational space into two subspaces: (1) an “essential” subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as “physically constrained.” If overall translation and rotation are eliminated, the two spaces can be constructed by a simple linear transformation in Cartesian coordinate space, which remains valid over several hundred picoseconds. The transformation follows from the covariance matrix of the positional deviations. The essential degrees of freedom seem to describe motions which are relevant for the function of the protein, while the physically constrained subspace merely describes irrelevant local fluctuations. The near-constraint behavior of the latter subspace allows the separation of equations of motion and promises the possibility of investigating independently the essential space and performing dynamic simulations only in this reduced space. © 1993 Wiley-Liss, Inc.     

Eco-evolutionary dynamics

Evolutionary ecologists and population biologists have recently considered that ecological and evolutionary changes are intimately linked and can occur on the same time-scale. Recent theoretical developments have shown how the feedback between ecological and evolutionary dynamics can be linked, and there are now empirical demonstrations showing that ecological change can lead to rapid evolutionary change. We also have evidence that microevolutionary change can leave an ecological signature. We are at a stage where the integration of ecology and evolution is a necessary step towards major advances in our understanding of the processes that shape and maintain biodiversity. This special feature about ‘eco-evolutionary dynamics’ brings together biologists from empirical and theoretical backgrounds to bridge the gap between ecology and evolution and provide a series of contributions aimed at quantifying the interactions between these fundamental processes.     

Spatial dynamics in fluctuating vole populations

Summary Patterns and consistency of distribution, spatial and temporal components, and the extent of spatial density-dependence were compared between semi-cyclic and cyclic populations of the vole species Clethrionomys glareolus and Microtus agrestis in south-central and north Sweden. Cyclic populations were less clumped and only C. glareolus showed a consistency in distribution between years. Spatial variation contributed little to the distributions in cyclic populations while the spatial and temporal variations were of the same magnitude in the semi-cyclic populations. The latter populations could be subdivided into areas with different spatial and temporal components. The spatial density-dependence increased from increase to decline years in C. glareolus but not in M. agrestis, which differed conspicuously between reregions in population development. The data imply that spatial dynamics should be considered as much as temporal ones for non-cyclic populations, that the same regulating or limiting factors may be at work in both spatial and temporal components and that, in addition, social behaviour may be important in explaining spatial dynamics. However, the latter effects may be fairly species-specific.     

Multiple time step diffusive Langevin dynamics for proteins

We present an algorithm for simulating the long time scale dynamics of proteins and other macromolecules. Our method applies the concept of multiple time step integration to the diffusive Langevin equation, in which short time scale dynamics are replaced by friction and noise. The macromolecular force field is represented at atomic resolution. Slow motions are modeled by constrained Langevin dynamics with very large time steps, while faster degrees of freedom are kept in local thermal equilibrium. In the limit of a sufficiently large molecule, our algorithm is shown to reduce the CPU time required by two orders of magnitude. We test the algorithm on two systems, alanine dipeptide and bovine pancreatic trypsin inhibitor (BPTI), and find that it accurately calculates a variety of equilibrium and dynamical properties. In the case of BPTI, the CPU time required is reduced by nearly a factor of 60 compared to a conventional, unconstrained Langevin simulation using the same force field. Proteins 30:215–227, 1998. © 1998 Wiley-Liss, Inc.     

Spatial and temporal dynamics of the cardiac mitochondrial proteome

Mitochondrial proteins alter in their composition and quantity drastically through time and space in correspondence to changing energy demands and cellular signaling events. The integrity and permutations of this dynamism are increasingly recognized to impact the functions of the cardiac proteome in health and disease. This article provides an overview on recent advances in defining the spatial and temporal dynamics of mitochondrial proteins in the heart. Proteomics techniques to characterize dynamics on a proteome scale are reviewed and the physiological consequences of altered mitochondrial protein dynamics are discussed. Lastly, we offer our perspectives on the unmet challenges in translating mitochondrial dynamics markers into the clinic.     

Population dynamics: Limits of predictability

Problems related to the complex pattern of ecosystem dynamics are discussed. Examples of studies on the complex population dynamics are considered, including those of plankton populations in a spatially heterogeneous environment and of an agroecosystem invaded by pests resistant to Bt toxins produced by genetically modified insecticidal crops.     

Role of methyl groups in dynamics and evolution of biomolecules

Recent studies have discovered strong differences between the dynamics of nucleic acids (RNA and DNA) and proteins, especially at low hydration and low temperatures. This difference is caused primarily by dynamics of methyl groups that are abundant in proteins, but are absent or very rare in RNA and DNA. In this paper, we present a hypothesis regarding the role of methyl groups as intrinsic plasticizers in proteins and their evolutionary selection to facilitate protein dynamics and activity. We demonstrate the profound effect methyl groups have on protein dynamics relative to nucleic acid dynamics, and note the apparent correlation of methyl group content in protein classes and their need for molecular flexibility. Moreover, we note the fastest methyl groups of some enzymes appear around dynamical centers such as hinges or active sites. Methyl groups are also of tremendous importance from a hydrophobicity/folding/entropy perspective. These significant roles, however, complement our hypothesis rather than preclude the recognition of methyl groups in the dynamics and evolution of biomolecules.     

Local segmental dynamics of cis-1,4-polybutadiene,polypropylene and polyethylene terephthalate via molecular dynamics simulations

The local segmental dynamics of cis-1,4-polybutadiene, polypropylene and polyethylene terephthalate have been investigated via isothermal-isobaric molecular dynamics simulations. The simulation pressure was 1 atm for all systems, with all simulation temperatures being at least 150 K above the polymer's glass transition temperature. The trajectories have been analysed via autocorrelation functions (ACFs) of chord vectors spanning different number of chain backbone bonds. Inverse Laplace transformations of these ACFs using the CONTIN algorithm afforded the corresponding distribution of relaxation times (DRTs) for the simulated dynamics. All DRTs illustrated a peak on fast timescales corresponding to short length scale segmental motion and a peak at longer timescales corresponding to longer length scale relaxations. A third peak, intermediate between the fast and slow processes, appears as the relaxation of chord vectors spanning increasing number of backbone bonds is considered. The temperature dependence of the relaxation dynamics is also investigated.     

Resident-invader dynamics and the coexistence of similar strategies

We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of -limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies are similar to one another.This work was supported by the Academy of Finland     

Nutrient enrichment alters dynamics in experimental plant populations

Controlling weed populations requires an understanding of their underlying population dynamics which can be achieved through a combination of model development and long-term studies. In this paper, we develop models based on long-term data from experimental populations of the weedy annual plant Cardamine pensylvanica. Four replicate populations of C. pensylvanica were grown in growth chambers under three different nutrient levels but with all other environmental conditions held constant. We analyze the resulting time series using generalized additive models and perform stability analyses using Lyapunov exponents. Further, we test whether the proposed mechanism, delayed density dependence caused by maternal effects, is operating in our system by experimentally manipulating maternal density and assessing the resulting offspring quality. Our results show that that increasing the frequency of nutrients causes plant population dynamics to shift from stable to damped 2-point oscillations to longer cycles. This shift in population dynamics is due to a shift at high nutrients from populations being regulated by first order density feedbacks to being regulated by both first order and second order density feedbacks. A consequence of these first order and second order feedbacks was an increase in cycle lengths as demonstrated by the presence of complex eigenvalues. A short-term experiment confirmed that when grown under high nutrients, the density of maternal plants strongly affected offspring size, providing a mechanism whereby these second order density feedbacks could operate. Our results demonstrate that increasing nutrient frequency results in a qualitative shift in dynamics from stable to longer cycles.     

Originator dynamics

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose "prelife" and "prevolution" as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting "prevolutionary dynamics" have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this "originator equation" gives the classical selection equation. In the other limit, we obtain "prelife." There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to "reversals" in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.     

OmpA: Gating and dynamics via molecular dynamics simulations

Outer membrane proteins (OMPs) of Gram-negative bacteria have a variety of functions including passive transport, active transport, catalysis, pathogenesis and signal transduction. Whilst the structures of ∼ 25 OMPs are currently known, there is relatively little known about their dynamics in different environments. The outer membrane protein, OmpA from Escherichia coli has been studied extensively in different environments both experimentally and computationally, and thus provides an ideal test case for the study of the dynamics and environmental interactions of outer membrane proteins. We review molecular dynamics simulations of OmpA and its homologues in a variety of different environments and discuss possible mechanisms of pore gating. The transmembrane domain of E. coli OmpA shows subtle differences in dynamics and interactions between a detergent micelle and a lipid bilayer environment. Simulations of the crystallographic unit cell reveal a micelle-like network of detergent molecules interacting with the protein monomers. Simulation and modelling studies emphasise the role of an electrostatic-switch mechanism in the pore-gating mechanism. Simulation studies have been extended to comparative models of OmpA homologues from Pseudomonas aeruginosa (OprF) and Pasteurella multocida (PmOmpA), the latter model including the periplasmic C-terminal domain.     

Molecular dynamics simulations of ribonuclease T1

Molecular dynamics simulations in vacuum and with a water sphere around the active site were performed on the 2GMP-RNase T1 complex. The presence of water led to the maintenance of the 2-GMP-RNase T1 interactions as compared to the X-ray structure, including the hydrogen bonds implicated in the enzyme-inhibitor recognition process. The sidechain of His92 in the molecular dynamics water simulation, however, hydrogen bonds directly to the phosphate of 2GMP in contrast to the X-ray structure but in support of the role of that residue in the enzyme's catalytic mechanism. Fluctuations of activesite residues are not strongly influenced by water, possibly owing to the exclusion of water by the bound 2GMP, which did show an increase in mobility. Analysis of the 2GMP-RNase T1 interactions versus time reveal an equilibrium fluctuation in the presence of water, leading to a less favorable 2GMP-RNase T1 interaction energy, suggesting a possible relationship between picosecond fluctuations and inhibitor dissociation occurring in the millisecond time domain.Abbreviations RNase T1 Ribonuclease T1 (EC.3.1.27.3) - 2GMP Guanosine-2-monophosphate - SBS Stochastic Bondary Simulation - VS Vacuum Simulation - MD Molecular Dynamics     

Successional state dynamics: A novel approach to modeling nonequilibrium foodweb dynamics

Communities and ecosystems are often far from equilibrium, but our understanding of nonequilibrium dynamics has been hampered by a paucity of analytical tools. Here I describe a novel approach to modeling seasonally forced food webs, called “successional state dynamics” (SSD). It is applicable to communities where species dynamics are fast relative to the external forcing, such as plankton and other microbes, diseases, and some insect communities. The approach treats succession as a series of state transitions driven by both the internal dynamics of species interactions and external forcing. First, I motivate the approach with numerical solutions of a seasonally forced predator-prey model. Second, I describe how to set up and analyze an SSD model. Finally, I apply the techniques to three additional models of two-species interactions: resource competition (r-K selection), facilitation, and flip-flop competition (where the competitive hierarchy alternates over time). This approach allows easy and thorough exploration of how dynamics depend on the environmental forcing regime, and uncovers unexpected phenomena such as multiple stable annual trajectories and year-to-year irregularity in successional trajectories (chaos).     

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.     

Spatial models of virus-immune dynamics

To date, the majority of theoretical models describing the dynamics of infectious diseases in vivo are based on the assumption of well-mixed virus and cell populations. Because many infections take place in solid tissues, spatially structured models represent an important step forward in understanding what happens when the assumption of well-mixed populations is relaxed. Here, we explore models of virus and virus-immune dynamics where dispersal of virus and immune effector cells was constrained to occur locally. The stability properties of our spatial virus-immune dynamics models remained robust under almost all biologically plausible dispersal schemes, regardless of their complexity. The various spatial dynamics were compared to the basic non-spatial dynamics and important differences were identified: When space was assumed to be homogeneous, the dynamics generated by non-spatial and spatially structured models differed substantially at the peak of the infection. Thus, non-spatial models may lead to systematic errors in the estimates of parameters underlying acute infection dynamics. When space was assumed to be heterogeneous, spatial coupling not only changed the equilibrium properties of the uncoupled populations but also equalized the dynamics and thereby reduced the likelihood of dynamic elimination of the infection. In line with experimental and clinical observations, long-lasting oscillation periods were virtually absent. When source-sink dynamics were considered, the long-term outcome of the infection depended critically on the degree of spatial coupling. The infection collapsed when emigration from source sites became too large. Finally, we discuss the implications of spatially structured models on medical treatment of infectious diseases, and note that a huge gap exists in data accurately describing infection dynamics in solid tissues.