Exploration of the correlation between solvation dynamics and internal dynamics of a protein

Protein function is intimately related to the dynamics of the protein as well as to the dynamics of the solvent shell around the protein. Although it has been argued extensively that protein dynamics is slaved to solvent dynamics, experimental support for this hypothesis is scanty. In this study, measurements of fluorescence anisotropy decay kinetics have been used to determine the motional dynamics of the fluorophore acrylodan linked to several locations in a small protein barstar in its various structural forms, including the native and unfolded states as well as the acid and protofibril forms. Fluorescence upconversion and streak camera measurements have been used to determine the solvation dynamics around the fluorophore. Both the motional dynamics and solvent dynamics were found to be dependent upon the location of the probe as well as on the structural form of the protein. While the (internal) motional dynamics of the fluorophore occur in the 0.1-3 ns time domain, the observed mean solvent relaxation times are in the range of 20-300 ps. A strong positive correlation between these two dynamical modes was found in spite of the significant difference in their time scales. This observed correlation is a strong indicator of the coupling between solvent dynamics and the dynamics in the protein.     

On the mechanistic underpinning of discrete-time population models with complex dynamics

We present a mechanistic underpinning for various discrete-time population models that can produce limit cycles and chaotic dynamics. Specific examples include the discrete-time logistic model and the Hassell model, which for a long time eluded convincing mechanistic interpretations, and also the Ricker- and Beverton-Holt models. We first formulate a continuous-time resource consumption model for the dynamics within a year, and from that we derive a discrete-time model for the between-year dynamics. Without influx of resources from the outside into the system, the resulting between-year dynamics is always overcompensating and hence may produce complex dynamics as well as extinction in finite time. We recover a connection between various standard types of continuous-time models for the resource dynamics within a year on the one hand and various standard types of discrete-time models for the population dynamics between years on the other. The model readily generalizes to several resource and consumer species as well as to more than two trophic levels for the within-year dynamics.     

Evolution of taxis responses in virtual bacteria: non-adaptive dynamics

Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances.     

Modulation of microtubule dynamics by drugs: a paradigm for the actions of cellular regulators

Microtubules are intrinsically dynamic polymers. Two kinds of dynamic behaviors, dynamic instability and treadmilling, are important for microtubule function in cells. Both dynamic behaviors appear to be tightly regulated, but the cellular molecules and the mechanisms responsible for the regulation remain largely unexplored. While microtubule dynamics can be modulated transiently by the interaction of regulatory molecules with soluble tubulin, the microtubule itself is likely to be the primary target of cellular molecules that regulate microtubule dynamics. The antimitotic drugs that modulate microtubule dynamics serve as excellent models for such cellular molecules. Our laboratory has been investigating the interactions of small drug molecules and stabilizing microtubule-associated proteins (MAPs) with microtubule surfaces and ends. We find that drugs such as colchicine, vinblastine, and taxol, and stabilizing MAPs such as tau, strongly modulate microtubule dynamics at extremely low concentrations under conditions in which the microtubule polymer mass is minimally affected. The powerful modulation of the dynamics is brought about by the binding of only a few drug or MAP molecules to distinct binding sites at the microtubule surface or end. Based upon our understanding of the well-studied drugs and stabilizing MAPs, it is clear that molecules that regulate dynamics such as Kin 1 and stathmin could bind to a large number of distinct tubulin sites on microtubules and employ an array of mechanisms to selectively and powerfully regulate microtubule dynamics and dynamics-dependent cellular functions.     

A simulating cognitive system with adaptive capability.

Dedicated to the memory of Michael Conrad, this paper builds on his seminal ideas expressed in his famous book Adaptability, as well as in his later works. We investigate a recently published adaptive system for the instantaneous recognition of dynamics with respect to its adaptability to the Lorenz system. The system consists of a pool of internal dynamical elements. These elements are defined through a set of parameter values that encode for a specific dynamics behavior. If the system is now faced with an unknown external dynamics-unknown with respect to the parameter-it is capable not only to recognize the dynamics but also to adapt to the correct dynamics, which in turn leads to a simulation capability. The system impressively quickly follows the sudden qualitative changes of the external dynamics. The adaptation works even quicker when the correct dynamics are already represented within the internal pool. This leads to the idea of memorizing the represented dynamics within the pool, whereby the elements that correspond to rarely externally presented dynamics can be given free for the adaptation and memorization of more frequently presented dynamics.     

Categorization of environmental sounds

Sounds in the natural environment are non-stationary, in that their spectral dynamics is time-dependent. We develop measures to analyze the spectral dynamics of environmental sound signals and find that they fall into two categories—simple sounds with slowly varying spectral dynamics and complex sounds with rapidly varying spectral dynamics. Based on our results and those from auditory processing we suggest rate of spectral dynamics as a possible scheme to categorize sound signals in the environment.     

Continuum modeling of forces in growing viscoelastic cytoskeletal networks

Mechanical properties of the living cell are important in cell movement, cell division, cancer development and cell signaling. There is considerable interest in measuring local mechanical properties of living materials and the living cytoskeleton using micromechanical techniques. However, living materials are constantly undergoing internal dynamics such as growth and remodeling. A modeling framework that combines mechanical deformations with cytoskeletal growth dynamics is necessary to describe cellular shape changes. The present paper develops a general finite deformation modeling approach that can treat the viscoelastic cytoskeleton. Given the growth dynamics in the cytoskeletal network and the relationship between deformation and stress, the shape of the network is computed in an incremental fashion. The growth dynamics of the cytoskeleton can be modeled as stress dependent. The result is a consistent treatment of overall cell deformation. The framework is applied to a growing 1-d bundle of actin filaments against an elastic cantilever, and a 2-d cell undergoing wave-like protrusion dynamics. In the latter example, mechanical forces on the cell adhesion are examined as a function of the protrusion dynamics.     

Co‐adaptation impacts the robustness of predator–prey dynamics against perturbations

Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co‐adaptation in a predator–prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre‐ and post‐perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre‐perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.     

Relation between stability, dynamics and enzyme activity in 3-phosphoglycerate kinases from yeast and Thermus thermophilus.

3-Phosphoglycerate kinases from yeast and the extreme thermophilic bacterium Thermus thermophilus HB8 have been used as models for investigating the relationship between stability, dynamics and activity. It was found that while at a given temperature the thermophilic protein is more stable, its conformational dynamics as measured by the ability of acrylamide to quench the fluorescence of a buried tryptophan as well as its specific activity, are both lower than for the mesophilic protein. As the temperature is increased, the thermodynamic stability of the thermophilic protein approaches that of the mesophilic protein at its working temperature. Its conformational dynamics and specific activity however were both shown to increase, until at the physiologically operational temperature, they become similar to those of the mesophilic enzyme at its operational temperature. These results confirm the proposal that a direct relationship and balance holds between thermodynamic stability, dynamics and specific activity in globular proteins. They demonstrate also the constraining effect of increased stability upon conformational dynamics and enzyme activity.     

Classical metapopulation dynamics and eco‐evolutionary feedbacks in dendritic networks

Eco‐evolutionary dynamics are now recognized to be highly relevant for population and community dynamics. However, the impact of evolutionary dynamics on spatial patterns, such as the occurrence of classical metapopulation dynamics, is less well appreciated. Here, we analyse the evolutionary consequences of spatial network connectivity and topology for dispersal strategies and quantify the eco‐evolutionary feedback in terms of altered classical metapopulation dynamics. We find that network properties, such as topology and connectivity, lead to predictable spatio‐temporal correlations in fitness expectations. These spatio‐temporally stable fitness patterns heavily impact evolutionarily stable dispersal strategies and lead to eco‐evolutionary feedbacks on landscape level metrics, such as the number of occupied patches, the number of extinctions and recolonizations as well as metapopulation extinction risk and genetic structure. Our model predicts that classical metapopulation dynamics are more likely to occur in dendritic networks, and especially in riverine systems, compared to other types of landscape configurations. As it remains debated whether classical metapopulation dynamics are likely to occur in nature at all, our work provides an important conceptual advance for understanding the occurrence of classical metapopulation dynamics which has implications for conservation and management of spatially structured populations.     

Nonlinear transient computation as a potential "kernel trick" in cortical processing

Evidence has been found for the presence of chaotic dynamics at all levels of the mammalian brain. This has led to some searching questions about the potential role that nonlinear dynamics may have in neural information processing. We propose that chaos equips the brain with the equivalent of a kernel trick for solving hard nonlinear problems. The approach presented, which is described as nonlinear transient computation, uses the dynamics of a well known chaotic attractor. The paper provides experimental results to show that this approach can be used to solve some challenging pattern recognition tasks. The paper also offers evidence to suggest that the efficacy of nonlinear transient computation for nonlinear pattern classification is dependent only on the generic properties of chaotic attractors and is not sensitive to the particular dynamics of specific sub-regions of chaotic phase space. If, as this work suggests, nonlinear transient computation is independent of the particulars of any given chaotic attractor, then it could be offered as a possible explanation of how the chaotic dynamics that have been observed in brain structures contribute to neural information processing tasks.     

Failure of Arm Movement Control in Stroke Patients,Characterized by Loss of Complexity

We study the mechanism of human arm-posture control by means of nonlinear dynamics and quantitative time series analysis methods. Utilizing linear and nonlinear measures in combination, we find that pathological tremors emerge in patient dynamics and serve as a main feature discriminating between normal and patient groups. The deterministic structure accompanied with loss of complexity inherent in the tremor dynamics is also revealed. To probe the underlying mechanism of the arm-posture dynamics, we further analyze the coupling patterns between joints and components, and discuss their roles in breaking of the organization structure. As a result, we elucidate the mechanisms in the arm-posture dynamics of normal subjects responding to the gravitational force and for the reduction of the dynamic degrees of freedom in the patient dynamics. This study provides an integrated framework for the origin of the loss of complexity in the dynamics of patients as well as the coupling structure in the arm-posture dynamics.     

Geographical variation in the population dynamics of <Emphasis Type="Italic">Thecodiplosis japonensis</Emphasis>: causes and effects on spatial synchrony

Geographical variation in population dynamics of a species offers an opportunity to understand the factors determining observed patterns of spatial dynamics. We evaluated the spatial variation in the population dynamics of the pine needle gall midge (PNGM), Thecodiplosis japonensis, which is a severe insect pest in pine forests in Korea, and studied the influences of weather factors that could affect its population dynamics. Results revealed that PNGM population dynamics were classified into five clusters based on the analysis of autocorrelation function and self-organizing map, which is an artificial neural network. We also quantified spatial synchrony in the population dynamics of PNGM using the nonparametric covariance function. Variation in spatial synchrony was strongly related to differences in maximum temperature and precipitation in Random Forest analysis, suggesting that the synchrony in PNGM population dynamics is largely the result of the Moran effect. In addition, spatial differences in population dynamics could be influenced by transient process of synchronization following invasion. Finally, the present results indicate that differences in population dynamics can be induced by interactions among several factors such as maximum temperature, precipitation, and invasion history of species.     

Propagation of dynamic changes in barnase upon binding of barstar: an NMR and computational study

NMR spectroscopy and computer simulations were used to examine changes in chemical shifts and in dynamics of the ribonuclease barnase that result upon binding to its natural inhibitor barstar. Although the spatial structures of free and bound barnase are very similar, binding results in changes of the dynamics of both fast side-chains, as revealed by (2)H relaxation measurements, and NMR chemical shifts in an extended beta-sheet that is located far from the binding interface. Both side-chain dynamics and chemical shifts are sensitive to variations in the ensemble populations of the inter-converting molecular states, which can escape direct structural observation. Molecular dynamics simulations of free barnase and barnase in complex with barstar, as well as a normal mode analysis of barnase using a Gaussian network model, reveal relatively rigid domains that are separated by the extended beta-sheet mentioned above. The observed changes in NMR parameters upon ligation can thus be rationalized in terms of changes in inter-domain dynamics and in populations of exchanging states, without measurable structural changes. This provides an alternative model for the propagation of a molecular response to ligand binding across a protein that is based exclusively on changes in dynamics.     

The effects of alterations in temperature and flow regime on organic carbon dynamics in Mediterranean river networks

It is only recently that freshwaters have been identified as important quantitative components of the carbon (C) cycle at global and regional scales. To date there are no studies that quantitatively predict the effects of alterations in temperature and flow regimes, individually, or in concert, on organic C dynamics in streams. To address this need, we applied a mechanistic model to simulate organic C dynamics in Mediterranean river networks under 27 different scenarios of altered temperature and flow regimes. We predict that the organic C dynamics in freshwaters in the Mediterranean, as well as in other semiarid regions, will be highly sensitive to global climate change owing to major increases in the degree of intermittency as well as in flood frequency and magnitude. Results indicate that flow regime alterations increase C export rates, whereas temperature alterations increase instream metabolism of organic C. However, flow regime alterations exhibit a much greater influence on C dynamics than do changes in the temperature regime. Reservoirs partly counteract the effects of flow extremes on C export rates, and their role in the C dynamics increases with increasing flow variability. The present study is one of the first studies to quantify the complex interactions between the flow and the temperature regime on C dynamics, emphasizing the key role of extreme events such as dry periods and floods, compared with overall trend effects. This information is pivotal in understanding the impact of future climate change on global C dynamics.     

Two- and Higher Point Correlation Functions in Proteins

Abstract

A method is presented for a more efficient sampling of the configurational space of proteins as compared to conventional sampling techniques such as molecular dynamics. The method is based on the large conformational changes in proteins revealed by the “essential dynamics” analysis. A form of constrained dynamics is performed, forcing the system to move along some of the essential coordinates. This results in a broader sampling of the essential subspace than in a comparable conventional molecular dynamics simulation without constraints. The new sampling method (essential dynamics sampling) was applied to the histidine-containing phosphocarrier protein HPr. The results indicate that the essential dynamics sampling method produces physically allowed structures, as estimated by the evaluation of many geometrical properties. In addition, a study of the motions in the essential subspace reveals a diffusion-like behavior.     

Environmental colour affects aspects of single-species population dynamics

Single-species populations of ciliates (Colpidium and Paramecium) experienced constant temperature or white or reddened temperature fluctuations in aquatic microcosms in order to test three hypotheses about how environmental colour influences population dynamics. (i) Models predict that the colour of population dynamics is tinged by the colour of the environmental variability. However, environmental colour had no effect on the colour of population dynamics. All population dynamics in this experiment were reddened, regardless of environmental colour. (ii) Models predict that populations will track reddened environmental variability more closely than white environmental variability and that populations with a higher intrinsic growth rate (r) will track environmental variability more closely than populations with a low r. The experimental populations behaved as predicted. (iii) Models predict that population variability is determined by interaction between r and the environmental variability. The experimental populations behaved as predicted. These results show that (i) reddened population dynamics may need no special explanation, such as reddened environments, spatial subdivision or interspecific interactions, and (ii) and (iii) that population dynamics are sensitive to environmental colour, in agreement with population models. Correct specification of the colour of the environmental variability in models is required for accurate predictions. Further work is needed to study the effects of environmental colour on communities and ecosystems.     

Abstract heterarchy: time/state-scale re-entrant form

A heterarchy is a dynamical hierarchical system inheriting logical inconsistencies between levels. Because of these inconsistencies, it is very difficult to formalize a heterarchy as a dynamical system. Here, the essence of a heterarchy is proposed as a pair of the property of self-reference and the property of a frame problem interacting with each other. The coupling of them embodies a one-ity inheriting logical inconsistency. The property of self-reference and a frame problem are defined in terms of logical operations, and are replaced by two kinds of dynamical system, temporal dynamics and state-scale dynamics derived from the same "liar statement". A modified tent map serving as the temporal dynamics is twisted and coupled with a tent map serving as the state-scale dynamics, and this results in a discontinuous self-similar map as a dynamical system. This reveals that the state-scale and temporal dynamics attribute to the system, and shows both robust and emergent behaviors.     

Time delay as a key factor of model plankton dynamics

Studies of the mechanisms underlying complex dynamics of ecological systems at various spatial and time scales bring increasing awareness that complexity is an intrinsic feature of ecological functioning. This paper is to investigate the role of such an ecologically significant parameter as the time delay due to maturation processes in the complex plankton dynamics. We show that the time lag T1, associated with the zooplankton maturation period can lead to essential changes in the plankton dynamics. Particularly, we show that the coexistence of limit cycle and chaotic attractor we have recently found to be typical of the system at T1 = 0 [A.B. Medvinsky, I.A. Tikhonova, R.R. Aliev, B.-L. Li, Z.-S. Lin, H. Malchow, Patchy environment as a factor of complex plankton dynamics, Phys. Rev. E 64 (2001) 021915] is replaced by pure chaotic plankton dynamics as T1 becomes more than a critical value. The results obtained imply that chaos is a rather common phenomenon in the plankton functioning.