Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the “within” versus “between” connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed “winnerless competition”, which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.     

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.     

Networks of Causal Linkage Between Eigenmodes Characterize Behavioral Dynamics of Caenorhabditis elegans

Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans, where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called “eigenworms”). We find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create “interaction profiles” to represent an individual’s behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.     

Insights into diterpene cyclization from structure of bifunctional abietadiene synthase from Abies grandis

Abietadiene synthase from Abies grandis (AgAS) is a model system for diterpene synthase activity, catalyzing class I (ionization-initiated) and class II (protonation-initiated) cyclization reactions. Reported here is the crystal structure of AgAS at 2.3 Å resolution and molecular dynamics simulations of that structure with and without active site ligands. AgAS has three domains (α, β, and γ). The class I active site is within the C-terminal α domain, and the class II active site is between the N-terminal γ and β domains. The domain organization resembles that of monofunctional diterpene synthases and is consistent with proposed evolutionary origins of terpene synthases. Molecular dynamics simulations were carried out to determine the effect of substrate binding on enzymatic structure. Although such studies of the class I active site do lead to an enclosed substrate-Mg²⁺ complex similar to that observed in crystal structures of related plant enzymes, it does not enforce a single substrate conformation consistent with the known product stereochemistry. Simulations of the class II active site were more informative, with observation of a well ordered external loop migration. This “loop-in” conformation not only limits solvent access but also greatly increases the number of conformational states accessible to the substrate while destabilizing the nonproductive substrate conformation present in the “loop-out” conformation. Moreover, these conformational changes at the class II active site drive the substrate toward the proposed transition state. Docked substrate complexes were further assessed with regard to the effects of site-directed mutations on class I and II activities.     

本科遗传学教学中的遗传漂变概念探讨

遗传漂变是遗传学教学的难点之一,因其涉及随机性和概率,特别容易引起误解。定义中的“抽样误差”常被误解为遗传漂变是由于“抽样”这一研究方法干扰才导致基因频率的随机变化。本文首先对国内外《遗传学》教材中的遗传漂变定义进行了分析比较,发现“抽样误差”的定义为各教材普遍采用,但只有少数教材对“抽样误差”概念进行了正确的解释,多数未作进一步的说明。文章介绍了遗传漂变的研究历史,亦即Wright、 Fisher和Kimura等学者对遗传漂变研究的贡献。进而,特别介绍了近年来国外关于本科生遗传漂变教学的两篇代表性教学研究论文,指出本科生在学习过程中容易出现错误理解是难以避免的现象,对此也提供了初步的解决办法。作者最后结合自己的教学实践,提出本科生教学中遗传漂变仍然采用含有“抽样误差”概念的定义,只是需要对“抽样误差”做进一步的解释,指出“抽样误差”是等位基因世代传递过程中存在的、配子间的随机结合,“相当于”对整个参与交配的配子库中的配子进行的一次“随机抽样”,而与一般遗传学研究中的人为抽样行为无关。本文旨在为本科遗传学教学中关于遗传源变概念的讲解提供借鉴和参考。     

Cortical oscillations support sampling-based computations in spiking neural networks

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these “valid” states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering.     

A density-dependent switch drives stochastic clustering and polarization of signaling molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.     

Memory for Expectation-Violating Concepts: The Effects of Agents and Cultural Familiarity

Previous research has shown that ideas which violate our expectations, such as schema-inconsistent concepts, enjoy privileged status in terms of memorability. In our study, memory for concepts that violate cultural (cultural schema-level) expectations (e.g., “illiterate teacher”, “wooden bottle”, or “thorny grass”) versus domain-level (ontological) expectations (e.g., “speaking cat”, “jumping maple”, or “melting teacher”) was examined. Concepts that violate cultural expectations, or counter-schematic, were remembered to a greater extent compared with concepts that violate ontological expectations and with intuitive concepts (e.g., “galloping pony”, “drying orchid”, or “convertible car”), in both immediate recall, and delayed recognition tests. Importantly, concepts related to agents showed a memory advantage over concepts not pertaining to agents, but this was true only for expectation-violating concepts. Our results imply that intuitive, everyday concepts are equally attractive and memorable regardless of the presence or absence of agents. However, concepts that violate our expectations (cultural-schema or domain-level) are more memorable when pertaining to agents (humans and animals) than to non-agents (plants or objects/artifacts). We conclude that due to their evolutionary salience, cultural ideas which combine expectancy violations and the involvement of an agent are especially memorable and thus have an enhanced probability of being successfully propagated.     

Population shuffling between ground and high energy excited states

Stochastic processes powered by thermal energy lead to protein motions traversing time-scales from picoseconds to seconds. Fundamental to protein functionality is the utilization of these dynamics for tasks such as catalysis, folding, and allostery. A hierarchy of motion is hypothesized to connect and synergize fast and slow dynamics toward performing these essential activities. Population shuffling predicts a “top-down” temporal hierarchy, where slow time-scale conformational interconversion leads to a shuffling of the free energy landscape for fast time-scale events. Until now, population shuffling was only applied to interconverting ground states. Here, we extend the framework of population shuffling to be applicable for a system interconverting between low energy ground and high energy excited states, such as the SH3 domain mutants G48M and A39V/N53P/V55L from the Fyn tyrosine kinase, providing another tool for accessing the structural dynamics of high energy excited states. Our results indicate that the higher energy gauche− rotameric state for the leucine χ₂ dihedral angle contributes significantly to the distribution of rotameric states in both the major and minor forms of the SH3 domain. These findings are corroborated with unrestrained molecular dynamics (MD) simulations on both the major and minor states of the SH3 domain demonstrating high correlations between experimental and back-calculated leucine χ₂ rotameric populations. Taken together, we demonstrate how fast time-scale rotameric side-chain population distributions can be extracted from slow time-scale conformational exchange data further extending the scope and the applicability of the population shuffling model.     

Microbial Communication,Cooperation and Cheating: Quorum Sensing Drives the Evolution of Cooperation in Bacteria

An increasing body of empirical evidence suggests that cooperation among clone-mates is common in bacteria. Bacterial cooperation may take the form of the excretion of “public goods”: exoproducts such as virulence factors, exoenzymes or components of the matrix in biofilms, to yield significant benefit for individuals joining in the common effort of producing them. Supposedly in order to spare unnecessary costs when the population is too sparse to supply the sufficient exoproduct level, many bacteria have evolved a simple chemical communication system called quorum sensing (QS), to “measure” the population density of clone-mates in their close neighborhood. Cooperation genes are expressed only above a threshold rate of QS signal molecule re-capture, i.e., above the local quorum of cooperators. The cooperative population is exposed to exploitation by cheaters, i.e., mutants who contribute less or nil to the effort but fully enjoy the benefits of cooperation. The communication system is also vulnerable to a different type of cheaters (“Liars”) who may produce the QS signal but not the exoproduct, thus ruining the reliability of the signal. Since there is no reason to assume that such cheaters cannot evolve and invade the populations of honestly signaling cooperators, the empirical fact of the existence of both bacterial cooperation and the associated QS communication system seems puzzling. Using a stochastic cellular automaton approach and allowing mutations in an initially non-cooperating, non-communicating strain we show that both cooperation and the associated communication system can evolve, spread and remain persistent. The QS genes help cooperative behavior to invade the population, and vice versa; cooperation and communication might have evolved synergistically in bacteria. Moreover, in good agreement with the empirical data recently available, this synergism opens up a remarkably rich repertoire of social interactions in which cheating and exploitation are commonplace.     

Evolution of Proliferation and the Angiogenic Switch in Tumors with High Clonal Diversity

Natural selection among tumor cell clones is thought to produce hallmark properties of malignancy. Efforts to understand evolution of one such hallmark—the angiogenic switch—has suggested that selection for angiogenesis can “run away” and generate a hypertumor, a form of evolutionary suicide by extreme vascular hypo- or hyperplasia. This phenomenon is predicted by models of tumor angiogenesis studied with the techniques of adaptive dynamics. These techniques also predict that selection drives tumor proliferative potential towards an evolutionarily stable strategy (ESS) that is also convergence-stable. However, adaptive dynamics are predicated on two key assumptions: (i) no more than two distinct clones or evolutionary strategies can exist in the tumor at any given time; and (ii) mutations cause small phenotypic changes. Here we show, using a stochastic simulation, that relaxation of these assumptions has no effect on the predictions of adaptive dynamics in this case. In particular, selection drives proliferative potential towards, and angiogenic potential away from, their respective ESSs. However, these simulations also show that tumor behavior is highly contingent on mutational history, particularly for angiogenesis. Individual tumors frequently grow to lethal size before the evolutionary endpoint is approached. In fact, most tumor dynamics are predicted to be in the evolutionarily transient regime throughout their natural history, so that clinically, the ESS is often largely irrelevant. In addition, we show that clonal diversity as measured by the Shannon Information Index correlates with the speed of approach to the evolutionary endpoint. This observation dovetails with results showing that clonal diversity in Barrett''s esophagus predicts progression to malignancy.     

Growth and asymmetry of soil microfungal colonies from "Evolution Canyon," Lower Nahal Oren, Mount Carmel, Israel

Background

Fluctuating asymmetry is a contentious indicator of stress in populations of animals and plants. Nevertheless, it is a measure of developmental noise, typically obtained by measuring asymmetry across an individual organism''s left-right axis of symmetry. These individual, signed asymmetries are symmetrically distributed around a mean of zero. Fluctuating asymmetry, however, has rarely been studied in microorganisms, and never in fungi.

Objective and Methods

We examined colony growth and random phenotypic variation of five soil microfungal species isolated from the opposing slopes of “Evolution Canyon,” Mount Carmel, Israel. This canyon provides an opportunity to study diverse taxa inhabiting a single microsite, under different kinds and intensities of abiotic and biotic stress. The south-facing “African” slope of “Evolution Canyon” is xeric, warm, and tropical. It is only 200 m, on average, from the north-facing “European” slope, which is mesic, cool, and temperate. Five fungal species inhabiting both the south-facing “African” slope, and the north-facing “European” slope of the canyon were grown under controlled laboratory conditions, where we measured the fluctuating radial asymmetry and sizes of their colonies.

Results

Different species displayed different amounts of radial asymmetry (and colony size). Moreover, there were highly significant slope by species interactions for size, and marginally significant ones for fluctuating asymmetry. There were no universal differences (i.e., across all species) in radial asymmetry and colony size between strains from “African” and “European” slopes, but colonies of Clonostachys rosea from the “African” slope were more asymmetric than those from the “European” slope.

Conclusions and Significance

Our study suggests that fluctuating radial asymmetry has potential as an indicator of random phenotypic variation and stress in soil microfungi. Interaction of slope and species for both growth rate and asymmetry of microfungi in a common environment is evidence of genetic differences between the “African” and “European” slopes of “Evolution Canyon.”     

Twin Town in South Brazil: A Nazi's Experiment or a Genetic Founder Effect?

Cândido Godói (CG) is a small municipality in South Brazil with approximately 6,000 inhabitants. It is known as the “Twins'' Town” due to its high rate of twin births. Recently it was claimed that such high frequency of twinning would be connected to experiments performed by the German Nazi doctor Joseph Mengele. It is known, however, that this town was founded by a small number of families and therefore a genetic founder effect may represent an alternatively explanation for the high twinning prevalence in CG. In this study, we tested specific predictions of the “Nazi''s experiment” and of the “founder effect” hypotheses. We surveyed a total of 6,262 baptism records from 1959–2008 in CG catholic churches, and identified 91 twin pairs and one triplet. Contrary to the “Nazi''s experiment hypothesis”, there is no spurt in twinning between the years (1964–1968) when Mengele allegedly was in CG (P = 0.482). Moreover, there is no temporal trend for a declining rate of twinning since the 1960s (P = 0.351), and no difference in twinning among CG districts considering two different periods: 1927–1958 and 1959–2008 (P = 0.638). On the other hand, the “founder effect hypothesis” is supported by an isonymy analysis that shows that women who gave birth to twins have a higher inbreeding coefficient when compared to women who never had twins (0.0148, 0.0081, respectively, P = 0.019). In summary, our results show no evidence for the “Nazi''s experiment hypothesis” and strongly suggest that the “founder effect hypothesis” is a much more likely alternative for explaining the high prevalence of twinning in CG. If this hypothesis is correct, then this community represents a valuable population where genetic factors linked to twinning may be identified.     

Classification and analysis of regulatory pathways using graph property, biochemical and physicochemical property, and functional property

Given a regulatory pathway system consisting of a set of proteins, can we predict which pathway class it belongs to? Such a problem is closely related to the biological function of the pathway in cells and hence is quite fundamental and essential in systems biology and proteomics. This is also an extremely difficult and challenging problem due to its complexity. To address this problem, a novel approach was developed that can be used to predict query pathways among the following six functional categories: (i) “Metabolism”, (ii) “Genetic Information Processing”, (iii) “Environmental Information Processing”, (iv) “Cellular Processes”, (v) “Organismal Systems”, and (vi) “Human Diseases”. The prediction method was established trough the following procedures: (i) according to the general form of pseudo amino acid composition (PseAAC), each of the pathways concerned is formulated as a 5570-D (dimensional) vector; (ii) each of components in the 5570-D vector was derived by a series of feature extractions from the pathway system according to its graphic property, biochemical and physicochemical property, as well as functional property; (iii) the minimum redundancy maximum relevance (mRMR) method was adopted to operate the prediction. A cross-validation by the jackknife test on a benchmark dataset consisting of 146 regulatory pathways indicated that an overall success rate of 78.8% was achieved by our method in identifying query pathways among the above six classes, indicating the outcome is quite promising and encouraging. To the best of our knowledge, the current study represents the first effort in attempting to identity the type of a pathway system or its biological function. It is anticipated that our report may stimulate a series of follow-up investigations in this new and challenging area.     

Crystal structure of a trimeric form of the KV7.1 (KCNQ1) A‐domain tail coiled‐coil reveals structural plasticity and context dependent changes in a putative coiled‐coil trimerization motif

Coiled-coils are widespread protein–protein interaction motifs typified by the heptad repeat (abcdefg)_n in which “a” and “d” positions are hydrophobic residues. Although identification of likely coiled-coil sequences is robust, prediction of strand order remains elusive. We present the X-ray crystal structure of a short form (residues 583–611), “Q1-short,” of the coiled-coil assembly specificity domain from the voltage-gated potassium channel Kv7.1 (KCNQ1) determined at 1.7 Å resolution. Q1-short lacks one and half heptads present in a previously studied tetrameric coiled-coil construct, Kv7.1 585–621, “Q1-long.” Surprisingly, Q1-short crystallizes as a trimer. In solution, Q1-short self-assembles more poorly than Q1-long and depends on an R-h-x-x-h-E motif common to trimeric coiled-coils. Addition of native sequences that include “a” and “d” positions C-terminal to Q1-short overrides the R-h-x-x-h-E motif influence and changes assembly state from a weakly associated trimer to a strongly associated tetramer. These data provide a striking example of a naturally occurring amino sequence that exhibits context-dependent folding into different oligomerization states, a three-stranded versus a four-stranded coiled-coil. The results emphasize the degenerate nature of coiled-coil energy landscapes in which small changes can have drastic effects on oligomerization. Discovery of these properties in an ion channel assembly domain and prevalence of the R-h-x-x-h-E motif in coiled-coil assembly domains of a number of different channels that are thought to function as tetrameric assemblies raises the possibility that such sequence features may be important for facilitating the assembly of intermediates en route to the final native state.     

Mesoscopic biochemical basis of isogenetic inheritance and canalization: stochasticity, nonlinearity, and emergent landscape

Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: (a) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and (b) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors it represents, are all themselves emergent properties of complex, mesoscopic dynamics. In terms of the landscape, we show a generalization of Kramers' approach is possible to provide a rate theory. The emergence of attractors is a form of self-organization in the mesoscopic system; stochastic attractors in biochemical systems such as gene regulation and cellular signaling are naturally inheritable via cell division. Delbrück-Gillespie's mesoscopic reaction system theory, therefore, provides a biochemical basis for spontaneous isogenetic switching and canalization.     

Patterns of mesenchymal condensation in a multiscale, discrete stochastic model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development.     

Susceptibility of Anopheles stephensi to Plasmodium gallinaceum: a trait of the mosquito, the parasite, and the environment

Background

Vector susceptibility to Plasmodium infection is treated primarily as a vector trait, although it is a composite trait expressing the joint occurrence of the parasite and the vector with genetic contributions of both. A comprehensive approach to assess the specific contribution of genetic and environmental variation on “vector susceptibility” is lacking. Here we developed and implemented a simple scheme to assess the specific contributions of the vector, the parasite, and the environment to “vector susceptibility.” To the best of our knowledge this is the first study that employs such an approach.

Methodology/Principal Findings

We conducted selection experiments on the vector (while holding the parasite “constant”) and on the parasite (while holding the vector “constant”) to estimate the genetic contributions of the mosquito and the parasite to the susceptibility of Anopheles stephensi to Plasmodium gallinaceum. We separately estimated the realized heritability of (i) susceptibility to parasite infection by the mosquito vector and (ii) parasite compatibility (transmissibility) with the vector while controlling the other. The heritabilities of vector and the parasite were higher for the prevalence, i.e., fraction of infected mosquitoes, than the corresponding heritabilities of parasite load, i.e., the number of oocysts per mosquito.

Conclusions

The vector''s genetics (heritability) comprised 67% of “vector susceptibility” measured by the prevalence of mosquitoes infected with P. gallinaceum oocysts, whereas the specific contribution of parasite genetics (heritability) to this trait was only 5%. Our parasite source might possess minimal genetic diversity, which could explain its low heritability (and the high value of the vector). Notably, the environment contributed 28%. These estimates are relevant only to the particular system under study, but this experimental design could be useful for other parasite-host systems. The prospects and limitations of the genetic manipulation of vector populations to render the vector resistant to the parasite are better considered on the basis of this framework.     

Ergodic Sets as Cell Phenotype of Budding Yeast Cell Cycle

It has been suggested that irreducible sets of states in Probabilistic Boolean Networks correspond to cellular phenotype. In this study, we identify such sets of states for each phase of the budding yeast cell cycle. We find that these “ergodic sets” underly the cyclin activity levels during each phase of the cell cycle. Our results compare to the observations made in several laboratory experiments as well as the results of differential equation models. Dynamical studies of this model: (i) indicate that under stochastic external signals the continuous oscillating waves of cyclin activity and the opposing waves of CKIs emerge from the logic of a Boolean-based regulatory network without the need for specific biochemical/kinetic parameters; (ii) suggest that the yeast cell cycle network is robust to the varying behavior of cell size (e.g., cell division under nitrogen deprived conditions); (iii) suggest the irreversibility of the Start signal is a function of logic of the G1 regulon, and changing the structure of the regulatory network can render start reversible.