The effect of dispersal and neighbourhood in games of cooperation

The prisoner's dilemma (PD) and the snowdrift (SD) games are paradigmatic tools to investigate the origin of cooperation. Whereas spatial structure (e.g. nonrandom spatial distribution of strategies) present in the spatially explicit models facilitates the emergence of cooperation in the PD game, recent investigations have suggested that spatial structure can be unfavourable for cooperation in the SD game. The frequency of cooperators in a spatially explicit SD game can be lower than it would be in an infinitely large well-mixed population. However, the source of this effect cannot be identified with certainty as spatially explicit games differ from well-mixed games in two aspects: (i) they introduce spatial correlations, (ii) and limited neighbourhood. Here we extend earlier investigations to identify the source of this effect, and thus accordingly we study a spatially explicit version of the PD and SD games with varying degrees of dispersal and neighbourhood size. It was found that dispersal favours selfish individuals in both games. We calculated the frequency of cooperators at strong dispersal limit, which in concordance with the numerical results shows that it is the short range of interactions (i.e. limited neighbourhood) and not spatial correlations that decreases the frequency of cooperators in spatially explicit models of populations. Our results demonstrate that spatial correlations are always beneficial to cooperators in both the PD and SD games. We explain the opposite effect of dispersal and neighbourhood structure, and discuss the relevance of distinguishing the two effects in general.     

NADPH inhibits [2Fe-2S] cluster protein transfer from diabetes drug target MitoNEET to an apo-acceptor protein

MitoNEET (mNT) is the founding member of the recently discovered CDGSH family of [2Fe-2S] proteins capable of [2Fe-2S] cluster transfer to apo-acceptor proteins. It is a target of the thiazolidinedione (TZD) class of anti-diabetes drugs whose binding modulate both electron transfer and cluster transfer properties. The [2Fe-2S] cluster in mNT is destabilized upon binding of NADPH, which leads to loss of the [2Fe-2S] cluster to the solution environment. Because mNT is capable of transferring [2Fe-2S] clusters to apo-acceptor proteins, we sought to determine whether NADPH binding also affects cluster transfer. We show that NADPH inhibits transfer of the [2Fe-2S] cluster to an apo-acceptor protein with an inhibition constant (K(i)) of 200 μm, which reflects that of NADPH concentrations expected under physiological conditions. In addition, we determined that the strictly conserved cluster interacting residue Asp-84 in the CDGSH domain is necessary for the NADPH-dependent inhibition of [2Fe-2S] cluster transfer. The most critical cellular function of NADPH is in the maintenance of a pool of reducing equivalents, which is essential to counteract oxidative damage. Taken together, our findings suggest that NADPH can regulate both mNT [2Fe-2S] cluster levels in the cell as well as the ability of the protein to transfer [2Fe-2S] clusters to cytosolic or mitochondrial acceptors.     

Effect of Initial Fraction of Cooperators on Cooperative Behavior in Evolutionary Prisoner's Dilemma Game

We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner''s dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.     

Evolutionary game dynamics in finite populations with strong selection and weak mutation

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.     

Selection of the Maximum Spatial Cluster Size of the Spatial Scan Statistic by Using the Maximum Clustering Set-Proportion Statistic

Spatial scan statistics are widely used in various fields. The performance of these statistics is influenced by parameters, such as maximum spatial cluster size, and can be improved by parameter selection using performance measures. Current performance measures are based on the presence of clusters and are thus inapplicable to data sets without known clusters. In this work, we propose a novel overall performance measure called maximum clustering set–proportion (MCS-P), which is based on the likelihood of the union of detected clusters and the applied dataset. MCS-P was compared with existing performance measures in a simulation study to select the maximum spatial cluster size. Results of other performance measures, such as sensitivity and misclassification, suggest that the spatial scan statistic achieves accurate results in most scenarios with the maximum spatial cluster sizes selected using MCS-P. Given that previously known clusters are not required in the proposed strategy, selection of the optimal maximum cluster size with MCS-P can improve the performance of the scan statistic in applications without identified clusters.     

Probabilistic Clustering of the Human Connectome Identifies Communities and Hubs

A fundamental assumption in neuroscience is that brain function is constrained by its structural properties. This motivates the idea that the brain can be parcellated into functionally coherent regions based on anatomical connectivity patterns that capture how different areas are interconnected. Several studies have successfully implemented this idea in humans using diffusion weighted MRI, allowing parcellation to be conducted in vivo. Two distinct approaches to connectivity-based parcellation can be identified. The first uses the connection profiles of brain regions as a feature vector, and groups brain regions with similar connection profiles together. Alternatively, one may adopt a network perspective that aims to identify clusters of brain regions that show dense within-cluster and sparse between-cluster connectivity. In this paper, we introduce a probabilistic model for connectivity-based parcellation that unifies both approaches. Using the model we are able to obtain a parcellation of the human brain whose clusters may adhere to either interpretation. We find that parts of the connectome consistently cluster as densely connected components, while other parts consistently result in clusters with similar connections. Interestingly, the densely connected components consist predominantly of major cortical areas, while the clusters with similar connection profiles consist of regions that have previously been identified as the ‘rich club’; regions known for their integrative role in connectivity. Furthermore, the probabilistic model allows quantification of the uncertainty in cluster assignments. We show that, while most clusters are clearly delineated, some regions are more difficult to assign. These results indicate that care should be taken when interpreting connectivity-based parcellations obtained using alternative deterministic procedures.     

Metal centers in the anaerobic microbial metabolism of CO and CO2

Carbon dioxide and carbon monoxide are important components of the carbon cycle. Major research efforts are underway to develop better technologies to utilize the abundant greenhouse gas, CO(2), for harnessing 'green' energy and producing biofuels. One strategy is to convert CO(2) into CO, which has been valued for many years as a synthetic feedstock for major industrial processes. Living organisms are masters of CO(2) and CO chemistry and, here, we review the elegant ways that metalloenzymes catalyze reactions involving these simple compounds. After describing the chemical and physical properties of CO and CO(2), we shift focus to the enzymes and the metal clusters in their active sites that catalyze transformations of these two molecules. We cover how the metal centers on CO dehydrogenase catalyze the interconversion of CO and CO(2) and how pyruvate oxidoreductase, which contains thiamin pyrophosphate and multiple Fe(4)S(4) clusters, catalyzes the addition and elimination of CO(2) during intermediary metabolism. We also describe how the nickel center at the active site of acetyl-CoA synthase utilizes CO to generate the central metabolite, acetyl-CoA, as part of the Wood-Ljungdahl pathway, and how CO is channelled from the CO dehydrogenase to the acetyl-CoA synthase active site. We cover how the corrinoid iron-sulfur protein interacts with acetyl-CoA synthase. This protein uses vitamin B(12) and a Fe(4)S(4) cluster to catalyze a key methyltransferase reaction involving an organometallic methyl-Co(3+) intermediate. Studies of CO and CO(2) enzymology are of practical significance, and offer fundamental insights into important biochemical reactions involving metallocenters that act as nucleophiles to form organometallic intermediates and catalyze C-C and C-S bond formations.     

A Spatial Model for Integrin Clustering as a Result of Feedback between Integrin Activation and Integrin Binding

Integrins are transmembrane adhesion receptors that bind extracellular matrix (ECM) proteins and signal bidirectionally to regulate cell adhesion and migration. In many cell types, integrins cluster at cell-ECM contacts to create the foundation for adhesion complexes that transfer force between the cell and the ECM. Even though the temporal and spatial regulation of these integrin clusters is essential for cell migration, how cells regulate their formation is currently unknown. It has been shown that integrin cluster formation is independent of actin stress fiber formation, but requires active (high-affinity) integrins, phosphoinositol-4,5-bisphosphate (PIP2), talin, and immobile ECM ligand. Based on these observations, we propose a minimal model for initial formation of integrin clusters, facilitated by localized activation and binding of integrins to ECM ligands as a result of biochemical feedback between integrin binding and integrin activation. By employing a diffusion-reaction framework for modeling these reactions, we show how spatial organization of bound integrins into clusters may be achieved by a local source of active integrins, namely protein complexes formed on the cytoplasmic tails of bound integrins. Further, we show how such a mechanism can turn small local increases in the concentration of active talin or active integrin into integrin clusters via positive feedback. Our results suggest that the formation of integrin clusters by the proposed mechanism depends on the relationships between production and diffusion of integrin-activating species, and that changes to the relative rates of these processes may affect the resulting properties of integrin clusters.     

Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. snowdrift games

The evolution of cooperation is an enduring conundrum in biology and the social sciences. Two social dilemmas, the prisoner's dilemma and the snowdrift game have emerged as the most promising mathematical metaphors to study cooperation. Spatial structure with limited local interactions has long been identified as a potent promoter of cooperation in the prisoner's dilemma but in the spatial snowdrift game, space may actually enhance or inhibit cooperation. Here we investigate and link the microscopic interaction between individuals to the characteristics of the emerging macroscopic patterns generated by the spatial invasion process of cooperators in a world of defectors. In our simulations, individuals are located on a square lattice with Moore neighborhood and update their strategies by probabilistically imitating the strategies of better performing neighbors. Under sufficiently benign conditions, cooperators can survive in both games. After rapid local equilibration, cooperators expand quadratically until global saturation is reached. Under favorable conditions, cooperators expand as a large contiguous cluster in both games with minor differences concerning the shape of embedded defectors. Under less favorable conditions, however, distinct differences arise. In the prisoner's dilemma, cooperators break up into isolated, compact clusters. The compact clustering reduces exploitation and leads to positive assortment, such that cooperators interact more frequently with other cooperators than with defectors. In contrast, in the snowdrift game, cooperators form small, dendritic clusters, which results in negative assortment and cooperators interact more frequently with defectors than with other cooperators. In order to characterize and quantify the emerging spatial patterns, we introduce a measure for the cluster shape and demonstrate that the macroscopic patterns can be used to determine the characteristics of the underlying microscopic interactions.     

Cancer-Related NEET Proteins Transfer 2Fe-2S Clusters to Anamorsin,a Protein Required for Cytosolic Iron-Sulfur Cluster Biogenesis

Iron-sulfur cluster biogenesis is executed by distinct protein assembly systems. Mammals have two systems, the mitochondrial Fe-S cluster assembly system (ISC) and the cytosolic assembly system (CIA), that are connected by an unknown mechanism. The human members of the NEET family of 2Fe-2S proteins, nutrient-deprivation autophagy factor-1 (NAF-1) and mitoNEET (mNT), are located at the interface between the mitochondria and the cytosol. These proteins have been implicated in cancer cell proliferation, and they can transfer their 2Fe-2S clusters to a standard apo-acceptor protein. Here we report the first physiological 2Fe-2S cluster acceptor for both NEET proteins as human Anamorsin (also known as cytokine induced apoptosis inhibitor-1; CIAPIN-1). Anamorsin is an electron transfer protein containing two iron-sulfur cluster-binding sites that is required for cytosolic Fe-S cluster assembly. We show, using UV-Vis spectroscopy, that both NAF-1 and mNT can transfer their 2Fe-2S clusters to apo-Anamorsin with second order rate constants similar to those of other known human 2Fe-2S transfer proteins. A direct protein-protein interaction of the NEET proteins with apo-Anamorsin was detected using biolayer interferometry. Furthermore, electrospray mass spectrometry of holo-Anamorsin prepared by cluster transfer shows that it receives both of its 2Fe-2S clusters from the NEETs. We propose that mNT and NAF-1 can provide parallel routes connecting the mitochondrial ISC system and the CIA. 2Fe-2S clusters assembled in the mitochondria are received by NEET proteins and when needed transferred to Anamorsin, activating the CIA.     

Cluster detection based on spatial associations and iterated residuals in generalized linear mixed models

Summary .  Spatial clustering is commonly modeled by a Bayesian method under the framework of generalized linear mixed effect models (GLMMs). Spatial clusters are commonly detected by a frequentist method through hypothesis testing. In this article, we provide a frequentist method for assessing spatial properties of GLMMs. We propose a strategy that detects spatial clusters through parameter estimates of spatial associations, and assesses spatial aspects of model improvement through iterated residuals. Simulations and a case study show that the proposed method is able to consistently and efficiently detect the locations and magnitudes of spatial clusters.     

Basketball Teams as Strategic Networks

We asked how team dynamics can be captured in relation to function by considering games in the first round of the NBA 2010 play-offs as networks. Defining players as nodes and ball movements as links, we analyzed the network properties of degree centrality, clustering, entropy and flow centrality across teams and positions, to characterize the game from a network perspective and to determine whether we can assess differences in team offensive strategy by their network properties. The compiled network structure across teams reflected a fundamental attribute of basketball strategy. They primarily showed a centralized ball distribution pattern with the point guard in a leadership role. However, individual play-off teams showed variation in their relative involvement of other players/positions in ball distribution, reflected quantitatively by differences in clustering and degree centrality. We also characterized two potential alternate offensive strategies by associated variation in network structure: (1) whether teams consistently moved the ball towards their shooting specialists, measured as “uphill/downhill” flux, and (2) whether they distributed the ball in a way that reduced predictability, measured as team entropy. These network metrics quantified different aspects of team strategy, with no single metric wholly predictive of success. However, in the context of the 2010 play-offs, the values of clustering (connectedness across players) and network entropy (unpredictability of ball movement) had the most consistent association with team advancement. Our analyses demonstrate the utility of network approaches in quantifying team strategy and show that testable hypotheses can be evaluated using this approach. These analyses also highlight the richness of basketball networks as a dataset for exploring the relationships between network structure and dynamics with team organization and effectiveness.     

Markov chain methods in enzyme kinetics

An enzyme cluster is a system of enzymes attached to a membrane, whose spatial organization makes it possible for the product of one enzymatic reaction tobe directly available as a substrate of another reaction within the cluster. We show how to model enzyme clusters by Markov chains, and how to compute their overall reaction rate. As a by-product we prove a formula for the number of completed cycles per unit time in a Markov chain.     

Does a tag system effectively support emerging cooperation?

This paper investigates whether the so-called Tag Systems support emerging cooperation with respect to 2x2 games. The Tag System, initially proposed by Riolo et al. [2001. Evolution of cooperation without reciprocity. Nature 414, 441-443], gives each agent both a Tag and Tol defined by [0,1] real numbers. Tol is a tolerance for recognizing an opponent as a company. Both Tag and Tol are assumed to be evolving. Results show that the tag's effectiveness depends on whether the AllD strategy is allowed in the system. Allowing AllD implies that green beard effect does not work in the system. Thus, (1) the tag's effectiveness is more meager than that reported by Riolo et al., (2) the Tag System can use alternating reciprocity more effectively than the analytic solution in a Hero game; (3) a system using a 2D tag space supports cooperation more effectively than the usual Tag System.     

GDI-Mediated Cell Polarization in Yeast Provides Precise Spatial and Temporal Control of Cdc42 Signaling

Cell polarization is a prerequisite for essential processes such as cell migration, proliferation or differentiation. The yeast Saccharomyces cerevisiae under control of the GTPase Cdc42 is able to polarize without the help of cytoskeletal structures and spatial cues through a pathway depending on its guanine nucleotide dissociation inhibitor (GDI) Rdi1. To develop a fundamental understanding of yeast polarization we establish a detailed mechanistic model of GDI-mediated polarization. We show that GDI-mediated polarization provides precise spatial and temporal control of Cdc42 signaling and give experimental evidence for our findings. Cell cycle induced changes of Cdc42 regulation enhance positive feedback loops of active Cdc42 production, and thereby allow simultaneous switch-like regulation of focused polarity and Cdc42 activation. This regulation drives the direct formation of a unique polarity cluster with characteristic narrowing dynamics, as opposed to the previously proposed competition between transient clusters. As the key components of the studied system are conserved among eukaryotes, we expect our findings also to apply to cell polarization in other organisms.     

Hyperproduction of recombinant ferredoxins in escherichia coli by coexpression of the ORF1-ORF2-iscS-iscU-iscA-hscB-hs cA-fdx-ORF3 gene cluster.

Fe-S proteins acquire Fe-S clusters by an unknown post-translational mechanism. To study the in vivo synthesis of the Fe-S clusters, we constructed an experimental system to monitor the expressed ferredoxin (Fd) as a reporter of protein-bound Fe-S clusters assembled in Escherichia coli. Overexpression of five Fds in a T7 polymerase-based system led to the formation of soluble apoFds and mature holoFds, indicating that assembly of the Fe-S cluster into apoFd polypeptides is a rate-limiting step. We examined the coexpression of the E. coli ORF1-ORF2-iscS-iscU-iscA-hscB-hsc A-fdx-ORF3 gene cluster, which has recently been suggested to be involved in the formation or repair of Fe-S protein [Zheng, L., Cash, V.L., Flint, D.H., and Dean, D.R. (1998) J. Biol. Chem. 273, 13264-13272], with reporter Fds using compatible plasmids. The production of all five reporter holoFds examined was dramatically increased by the coexpression of the gene cluster, and apparent specificity to the polypeptides or to the type of Fe-S clusters was not observed. The increase in holoFd production was observed under the coexpression conditions in all culture media examined, with either 2 x YT medium or Terrific broth, and with or without supplemental cysteine or iron. These results indicate that the proteins encoded by the gene cluster are involved in the assembly of the Fe-S clusters in a wide variety of Fe-S proteins.     

Ecological symmetry breaking can favour the evolution of altruism in an action-response game

The evolution of altruistic behaviour is studied in a simple action-response game with a tunable degree of conflict of interest. It is shown that for the continuous, mixed-medium approach no stable polymorphism favours altruism. Ecological dynamics are explored with the addition of a spatial dimension and a local energy variable. A continuous spatial model with finite local range does not introduce any substantial difference in the results with respect to the level of altruism. However, the model illustrates how ecological coupling may lead to the formation of stable spatial patterns in the form of discrete and isolated clusters of players as a consequence of inverse density dependence. A discrete, individual-based model is built in which local interactions are also modelled as occurring within a finite neighbourhood of each individual and spatial positions are not restricted as in lattice models. This model shows substantially different results. A high level of altruism is observed for low (but positive) degrees of conflict and this level decreases linearly for higher degrees of conflict. The evolution of altruism is explained by studying the broken symmetries introduced by the spatial clusters themselves, mainly between their central and peripheral regions which, in combination with the discrete and the stochastic nature of the model, result in the stabilization of strategies in which players behave altruistically towards the same type. As a consequence of the activity of the players, energy resources at the centre of an altruistic cluster are very depleted; so much so that, for low conflict, fitter non-altruistic mutants may initially invade only to become locally extinct due to their less efficient use of energy as their numbers increase. In peripheral regions invader may subsist; however, for geometrical reasons long-lasting genealogies tend to originate only at the centre of a cluster.     

Three-dimensional cluster analysis identifies interfaces and functional residue clusters in proteins

Three-dimensional cluster analysis offers a method for the prediction of functional residue clusters in proteins. This method requires a representative structure and a multiple sequence alignment as input data. Individual residues are represented in terms of regional alignments that reflect both their structural environment and their evolutionary variation, as defined by the alignment of homologous sequences. From the overall (global) and the residue-specific (regional) alignments, we calculate the global and regional similarity matrices, containing scores for all pairwise sequence comparisons in the respective alignments. Comparing the matrices yields two scores for each residue. The regional conservation score (C(R)(x)) defines the conservation of each residue x and its neighbors in 3D space relative to the protein as a whole. The similarity deviation score (S(x)) detects residue clusters with sequence similarities that deviate from the similarities suggested by the full-length sequences. We evaluated 3D cluster analysis on a set of 35 families of proteins with available cocrystal structures, showing small ligand interfaces, nucleic acid interfaces and two types of protein-protein interfaces (transient and stable). We present two examples in detail: fructose-1,6-bisphosphate aldolase and the mitogen-activated protein kinase ERK2. We found that the regional conservation score (C(R)(x)) identifies functional residue clusters better than a scoring scheme that does not take 3D information into account. C(R)(x) is particularly useful for the prediction of poorly conserved, transient protein-protein interfaces. Many of the proteins studied contained residue clusters with elevated similarity deviation scores. These residue clusters correlate with specificity-conferring regions: 3D cluster analysis therefore represents an easily applied method for the prediction of functionally relevant spatial clusters of residues in proteins.     

Geometrical properties of gel and fluid clusters in DMPC/DSPC bilayers: Monte Carlo simulation approach using a two-state model

In this paper the geometrical properties of gel and fluid clusters of equimolar dimyristoylphosphatidylcholine/distearoylphosphatidylcholine (DMPC/DSPC) lipid bilayers are calculated by using an Ising-type model (Sugar, I. P., T. E. Thompson, and R. L. Biltonen. 1999. Biophys. J. 76:2099-2110). The model is able to predict the following properties in agreement with the respective experimental data: the excess heat capacity curves, fluorescence recovery after photobleaching (FRAP) threshold temperatures at different mixing ratios, the most frequent center-to-center distance between DSPC clusters, and the fractal dimension of gel clusters. In agreement with the neutron diffraction and fluorescence microscopy data, the simulations show that below the percolation threshold temperature of gel clusters many nanometer-size gel clusters co-exist with one large gel cluster of size comparable with the membrane surface area. With increasing temperature the calculated effective fractal dimension and capacity dimension of gel and fluid clusters decrease and increase, respectively, within the (0, 2) interval. In the region of the gel-to-fluid transition the following geometrical properties are independent from the temperature and the state of the cluster: 1) the cluster perimeter linearly increases with the number of cluster arms at a rate of 8.2 nm/arm; 2) the average number of inner islands in a cluster increases with increasing cluster size, S, according to a power function of 0.00427 x S(1.3); 3) the following exponential function describes the average size of an inner island versus the size of the host cluster, S: 1 + 1.09(1 - e(-0.0072xS)). By means of the equations describing the average geometry of the clusters the process of the association of clusters is investigated.     

Comparative functional features of plant potassium HvHAK1 and HvHAK2 transporters

Plant K(+) transporters of the HAK family belong to four rather divergent phylogenetic clusters, although most of the transporters belong to clusters I or II. A simple phylogenetic analysis of fungal and plant HAK transporters suggests that an original HAK gene duplicated even before fungi and plants diverged, generating transporters that at present fulfill different functions in the plant. The HvHAK1 transporter belongs to cluster I and mediates high-affinity K(+) uptake in barley roots, but no function is known for the cluster II transporter, HvHAK2, which is not functional in yeast. The function of HvHAK2 was investigated by constructing HvHAK1-HAK2 chimeric transporters, which were not functional even when they included only short fragments of HvHAK2. Then, amino acids characteristic of cluster II in the N terminus and in the first transmembrane domain were introduced into HvHAK1. All of these changes increased the Rb(+) K(m), introducing minimal changes in the Na(+) K(m), which suggested that HvHAK2 is a low-affinity, Na(+)-sensitive K(+) transporter. Using a K(+)-defective Escherichia coli mutant, we functionally expressed HvHAK2 and found that the predicted characteristics were correct, as well as discovering that the bacterial expression of HvHAK2 is functional at pH 5.5 but not at 7.5. We discuss whether HvHAK2 may be a tonoplast transporter effective for vacuolar K(+) depletion in K(+) starved plants.