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.     

Protein dynamics and enzyme catalysis: insights from simulations

The role of protein dynamics in enzyme catalysis is one of the most active and controversial areas in enzymology today. Some researchers claim that protein dynamics are at the heart of enzyme catalytic efficiency, while others state that dynamics make no significant contribution to catalysis. What is the biochemist - or student - to make of the ferocious arguments in this area? Protein dynamics are complex and fascinating, as molecular dynamics simulations and experiments have shown. The essential question is: do these complex motions have functional significance? In particular, how do they affect or relate to chemical reactions within enzymes, and how are chemical and conformational changes coupled together? Biomolecular simulations can analyse enzyme reactions and dynamics in atomic detail, beyond that achievable in experiments: accurate atomistic modelling has an essential part to play in clarifying these issues. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.     

Flexible representations of dynamics are used in object manipulation

To manipulate an object skillfully, the brain must learn its dynamics, specifying the mapping between applied force and motion. A fundamental issue in sensorimotor control is whether such dynamics are represented in an extrinsic frame of reference tied to the object or an intrinsic frame of reference linked to the arm. Although previous studies have suggested that objects are represented in arm-centered coordinates [1-6], all of these studies have used objects with unusual and complex dynamics. Thus, it is not known how objects with natural dynamics are represented. Here we show that objects with simple (or familiar) dynamics and those with complex (or unfamiliar) dynamics are represented in object- and arm-centered coordinates, respectively. We also show that objects with simple dynamics are represented with an intermediate coordinate frame when vision of the object is removed. These results indicate that object dynamics can be flexibly represented in different coordinate frames by the brain. We suggest that with experience, the representation of the dynamics of a manipulated object may shift from a coordinate frame tied to the arm toward one that is linked to the object. The additional complexity required to represent dynamics in object-centered coordinates would be economical for familiar objects because such a representation allows object use regardless of the orientation of the object in hand.     

Oscillations in peroxidase-catalyzed reactions and their potential function in vivo

The peroxidase-oxidase reaction has become a model system for the study of oscillations and complex dynamics in biochemical systems. In the present paper we give an overview of previous experimental and theoretical studies of the peroxidase-oxidase reaction. Recent in vitro experiments have raised the question whether the reaction also exhibits oscillations and complex dynamics in vivo. To investigate this possibility further we have undertaken new experimental studies of the reaction, using horseradish extracts and phenols which are widely distributed in plants. The results are discussed in light of the occurrence and a possible functional role of oscillations and complex dynamics of the peroxidase-oxidase reaction in vivo.     

Interplay between local dynamics and dispersal in discrete-time metapopulation models

The effects of synchronous dispersal on discrete-time metapopulation dynamics with local (patch) dynamics of the same (compensatory or overcompensatory) or mixed (compensatory and overcompensatory) types are explored. Single-species metapopulation models behave as single-species single-patch models, whenever all local patches are governed by compensatory dynamics. Dispersal gives rise to multiple attractors with complex basin structures, whenever some local patches are under overcompensatory dynamics. In mixed systems, dispersal is capable of altering the local dynamics from compensatory to overcompensatory dynamics and vice versa. Examples are provided of metapopulation models supporting multiple attractors with intermingled basins of attraction.     

The promise of cryo-EM to explore RNA structural dynamics

Conformational dynamics are essential to macromolecular function. This is certainly true of RNA, whose ability to undergo programmed conformational dynamics is essential to create and regulate complex biological processes. However, methods to easily and simultaneously interrogate both the structure and conformational dynamics of fully functional RNAs in isolation and in complex with proteins have not historically been available. Due to its ability to image and classify single particles, cryogenic electron microscopy (cryo-EM) has the potential to address this gap and may be particularly amenable to exploring structural dynamics within the three-dimensional folds of biologically active RNAs. We discuss the possibilities and current limitations of applying cryo-EM to simultaneously study RNA structure and conformational dynamics, and present one example that illustrates this (as of yet) not fully realized potential.     

Neurodynamics: nonlinear dynamics and neurobiology

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.     

Numerically evaluated functional equivalence between chaotic dynamics in neural networks and cellular automata under totalistic rules

Chaotic dynamics in a recurrent neural network model and in two-dimensional cellular automata, where both have finite but large degrees of freedom, are investigated from the viewpoint of harnessing chaos and are applied to motion control to indicate that both have potential capabilities for complex function control by simple rule(s). An important point is that chaotic dynamics generated in these two systems give us autonomous complex pattern dynamics itinerating through intermediate state points between embedded patterns (attractors) in high-dimensional state space. An application of these chaotic dynamics to complex controlling is proposed based on an idea that with the use of simple adaptive switching between a weakly chaotic regime and a strongly chaotic regime, complex problems can be solved. As an actual example, a two-dimensional maze, where it should be noted that the spatial structure of the maze is one of typical ill-posed problems, is solved with the use of chaos in both systems. Our computer simulations show that the success rate over 300 trials is much better, at least, than that of a random number generator. Our functional simulations indicate that both systems are almost equivalent from the viewpoint of functional aspects based on our idea, harnessing of chaos.     

Computational Models of Consumer Confidence from Large-Scale Online Attention Data: Crowd-Sourcing Econometrics

Economies are instances of complex socio-technical systems that are shaped by the interactions of large numbers of individuals. The individual behavior and decision-making of consumer agents is determined by complex psychological dynamics that include their own assessment of present and future economic conditions as well as those of others, potentially leading to feedback loops that affect the macroscopic state of the economic system. We propose that the large-scale interactions of a nation''s citizens with its online resources can reveal the complex dynamics of their collective psychology, including their assessment of future system states. Here we introduce a behavioral index of Chinese Consumer Confidence (C3I) that computationally relates large-scale online search behavior recorded by Google Trends data to the macroscopic variable of consumer confidence. Our results indicate that such computational indices may reveal the components and complex dynamics of consumer psychology as a collective socio-economic phenomenon, potentially leading to improved and more refined economic forecasting.     

Changes in actin structural transitions associated with oxidative inhibition of muscle contraction

We have used transient phosphorescence anisotropy (TPA) to detect changes in actin structural dynamics associated with oxidative inhibition of muscle contraction. Contractility of skinned rabbit psoas muscle fibers was inhibited by treatment with 50 mM H 2O 2, which induced oxidative modifications in the myosin head and in actin, as previously reported. Using proteins purified from oxidized and unoxidized muscle, we used TPA to measure the effects of weakly (+ATP) and strongly (no ATP) bound myosin heads (S1) on the microsecond dynamics of actin labeled at Cys374 with erythrosine iodoacetamide. Oxidative modification of S1 had no effect on actin dynamics in the absence of ATP (strong binding complex), but restricted the dynamics in the presence of ATP (weakly bound complex). In contrast, oxidative modification of actin did not have a significant effect on the weak-to-strong transitions. Thus, we concluded that (1) the effects of oxidation on the dynamics of actin in the actomyosin complex are predominantly determined by oxidation-induced changes in S1, and (2) changes in weak-to-strong structural transitions in actin and myosin are coupled to each other and are associated with oxidative inhibition of muscle contractility.     

Effects of fluorine substitution on the structure and dynamics of complexes of dihydrofolate reductase (Escherichia coli).

Fluorine NMR experiments with a protein containing fluorinated amino acid analogs can often be used to probe structure and dynamics of the protein as well as conformational changes produced by binding of small molecules. The relevance of NMR experiments with fluorine-containing materials to characteristics of the corresponding native (nonfluorinated) proteins depends upon the extent to which these characteristics are altered by the presence of fluorine. The present work uses molecular dynamics simulations to explore the effects of replacement of tryptophan by 6-fluorotryptophan in folate and methotrexate complexes of the enzyme dihydrofolate reductase (DHFR) (Escherichia coli). Simulations of the folate-native enzyme complex produce local correlation times and order parameters that are generally in good agreement with experimental values. Simulations of the corresponding fluorotryptophan-containing system indicate that the structure and dynamics of this complex are scarcely changed by the presence of fluorinated amino acids. Calculations with the pharmacologically important methotrexate-enzyme complex predict dynamical behavior of the protein similar to that of the folate complex for both the fluorinated and native enzyme. It thus appears that, on the time scale sampled by these computer simulations, substitution of 6-fluorotryptophan for tryptophan has little effect on either the structures or dynamics of DHFR in these complexes.     

Phylodynamic Inference for Structured Epidemiological Models

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.     

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.     

Cyclic dynamics in simulated plant populations

Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual-based model of a hypothetical, non-clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field-of-neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide-ranging implications for the understanding of plant community dynamics and coexistence.     

Simulated complex dynamics of glycolysis in the protozoan parasite Trypanosoma brucei

Glycolysis in Trypanosoma brucei was modeled using a reaction transport simulator and tested for possible complex dynamics. The glycolytic model is multi-compartmentalized and accounts for the exchange of metabolites between the glycosomes, cytosol, mitochondrion and the host medium. The model is used to examine the effects of a range of culture medium concentrations of oxygen on the glycolysis of T. brucei. Our results are in good agreement with steady-state experiments. We also find that under aerobic conditions, increasing the activity of glycerol-3-phosphate dehydrogenase induces complex dynamics in the system. We report the presence of three distinct types of these dynamics. Varying the oxygen concentration in the medium can induce the transition between these dynamics.     

Interactions matter—complexity in landscapes and ecosystems

In this review we argue that theories and methodology arising from the field of complex systems form a new paradigm for ecology. Patterns and processes resulting from interactions between individuals, populations, species and communities in landscapes are the core topic of ecology. These interactions form complex networks, which are the subject of intense research in complexity theory, informatics and statistical mechanics. This research has shown that complex natural networks often share common structures such as loops, trees and clusters. The observed structures contribute to widespread processes including feedback, non-linear dynamics, criticality and self-organisation. Simulation modelling is a key tool in studying complex networks and has become popular in ecology, especially in adaptive management. Important techniques include cellular automata and individual-based models. The complex systems paradigm has led to advances in landscape ecology, including a deeper understanding of the dynamics of spatial pattern formation, habitat fragmentation, epidemic processes, and genetic variation. Network analysis reveals that underlying patterns of interactions, such as small worlds and clusters, in food webs and ecosystems have strong implications for their stability and dynamics. These investigations illustrate how complexity theory and associated methodologies are transforming ecological research, providing new perspectives on old questions as well as raising many new ones.     

Gamma-tubulin complexes and microtubule organization

Microtubule nucleation requires gamma-tubulin, which exists in two main protein complexes: the gamma-tubulin small complex, and the gamma-tubulin ring complex. During mitosis, these complexes accumulate at the centrosome to support spindle formation. Gamma-tubulin complexes are also present at non-centrosomal microtubule nucleation sites, both in interphase and in mitosis. In interphase, non-centrosomal nucleation enables the formation of microtubule bundles or networks of branched microtubules. Gamma-tubulin complexes may be involved not only in microtubule nucleation, but also in regulating microtubule dynamics. Recent findings indicate that the dynamics of microtubule plus-ends are altered, depending on the expression of gamma-tubulin complex proteins.     

The Effect of Different Force Applications on the Protein-Protein Complex Barnase-Barstar

Steered molecular dynamics simulations are a tool to examine the energy landscape of protein-protein complexes by applying external forces. Here, we analyze the influence of the velocity and geometry of the probing forces on a protein complex using this tool. With steered molecular dynamics, we probe the stability of the protein-protein complex Barnase-Barstar. The individual proteins are mechanically labile. The Barnase-Barstar binding site is more stable than the folds of the individual proteins. By using different force protocols, we observe a variety of responses of the system to the applied tension.