Stochastic Heterogeneous Interaction Promotes Cooperation in Spatial Prisoner's Dilemma Game

Previous studies mostly investigate player''s cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.     

Time series modeling of neuromuscular system

The dynamic response of the human ankle joint to a bandlimited random torque perturbation superimposed on a constant bias torque is observed in normal human subjects. The applied torque input, the joint angular rotation output, and the electromyographic activity using surface electrodes from the extensor and the flexor muscles of the ankle joint were recorded. Transfer function models using time series techniques were developed for the torque — angular rotation input-output pair and for the angular rotation — electromyographic activity input-output pair. A parameter constraining technique was applied to develop more reliable models. It is shown that the asymptotic behavior of the system must be taken into account during parameter optimization to develop better predictive models.This work was supported in part by National Science Foundation grant ENG-7608754 and grants from the National Institutes of Health NS-12877 and NS-00196     

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.     

An autonomous system for identifying and governing a cell's state in yeast

We present an approach for an autonomous system that detects a particular state of interest in a living cell and can govern cell fate accordingly. Cell states could be better identified by the expression pattern of several genes than of a single one. Therefore, autonomous identification can be achieved by a system that measures the expression of these several genes and integrates their activities into a single output. We have constructed a system that diagnoses a unique state in yeast, in which two independent pathways, methionine anabolism and galactose catabolism, are active. Our design is based on modifications of the yeast two-hybrid system. We show that cells could autonomously report on their state, identify the state of interest, and inhibit their growth accordingly. The system's sensitivity is adjustable to detect states with limited dynamic range of inputs. The system's output depends only on the activity of input pathways, not on their identity; hence it is straightforward to diagnose any pair of inputs. A simple model is presented that accounts for the data and provides predictive power. We propose that such systems could handle real-life states-of-interest such as identification of aberrant versus normal growth.     

Using Uncertainty and Sensitivity Analyses in Socioecological Agent-Based Models to Improve Their Analytical Performance and Policy Relevance

Agent-based models (ABMs) have been widely used to study socioecological systems. They are useful for studying such systems because of their ability to incorporate micro-level behaviors among interacting agents, and to understand emergent phenomena due to these interactions. However, ABMs are inherently stochastic and require proper handling of uncertainty. We propose a simulation framework based on quantitative uncertainty and sensitivity analyses to build parsimonious ABMs that serve two purposes: exploration of the outcome space to simulate low-probability but high-consequence events that may have significant policy implications, and explanation of model behavior to describe the system with higher accuracy. The proposed framework is applied to the problem of modeling farmland conservation resulting in land use change. We employ output variance decomposition based on quasi-random sampling of the input space and perform three computational experiments. First, we perform uncertainty analysis to improve model legitimacy, where the distribution of results informs us about the expected value that can be validated against independent data, and provides information on the variance around this mean as well as the extreme results. In our last two computational experiments, we employ sensitivity analysis to produce two simpler versions of the ABM. First, input space is reduced only to inputs that produced the variance of the initial ABM, resulting in a model with output distribution similar to the initial model. Second, we refine the value of the most influential input, producing a model that maintains the mean of the output of initial ABM but with less spread. These simplifications can be used to 1) efficiently explore model outcomes, including outliers that may be important considerations in the design of robust policies, and 2) conduct explanatory analysis that exposes the smallest number of inputs influencing the steady state of the modeled system.     

Activation of command fibres to the stomatogastric ganglion by input from a gastric mill proprioceptor in the crab,Cancer pagurus †

In semi‐intact preparations of the crab Cancer pagurus the normal output from the stomatogastric ganglion (StG) was a regular pyloric cycle (Figure 4). Repeated stimulation of the posterior stomach nerve (psn) of the posterior gastric mill proprioceptor (PSR) often induced series of spontaneous gastric cycles. We were therefore able to describe the normal gastric cycle as recorded in the output nerves from StG and to identify most of the relevant motor neurones by reference to the muscles that they innervate (Figure 10). The gastric cycle output was variable (Figures 5, 6), although in many preparations one complex type of output predominated (Figure 7). The basic feature of the gastric cycle was an alternation of activity between the single cardio‐pyloric neurone (CP) and a complex variable burst in the lateral cardiac (LC), the gastro‐pyloric (GP), the gastric (GM), and other associated neurones. During this normally occurring complex gastric burst significant changes occurred in the pyloric cycle, notably an increase in activity of the pacemaker pyloric dilator (PD) group and an inhibition of the lateral pyloric (LP), inferior cardiac (IC) and ventricular dilator (VD) neurones (Figures 6, 7, 8, 9). These changes are probably associated with an opening of the cardio‐pyloric valve and food passage into the pyloric filter. The gastric output was related to the normally observed movements of the dorsal ossicles of the gastric mill and thus to the operation of the teeth of the mill (Figure 11). Increased input from the PSR is associated with the grinding action of the teeth which is caused by the complex gastric burst (Figure 12).

Stimulation of the psn during an ongoing regular pyloric output caused changes in the cycle which mimicked those occurring during the spontaneous gastric cycle (Figure 13; Table 1). Stimulation of the psn during ongoing gastric activity also affected the gastric units (Figure 14). The input pathway from the PSR is shown to be through the stomatogastric nerve (sgn), the connection between the commissural ganglia and the stomatogastric ganglion (Figure 15). The commissural ganglia are known to receive most of the sensory input from the foregut and PSR input is probably processed there. Recordings from the sgn show that psn stimulation activates a small number of centrally originating units, and that the activity of these units coincides with the pyloric output changes (Figures 15, 16). We therefore label the units command interneurones. Their effects could be mediated by direct connections to only the PD pacemaker neurones of the pyloric cycle. Control experiments showed that PSR input is not necessary for the pyloric output changes to occur during gastric output but that similar output changes can be evoked by input resulting from induced gastric movements (Figure 15(E)). We think that the pyloric cycle output changes are normally controlled by a number of mechanisms at different levels (Figure 17). We cannot easily explain the effects of PSR input on the gastric cycle neurones.

These findings are important because they allow us to study a specific input to the StG without disrupting its normal input‐output pathways to the central nervous system. Further experiments on the system designed to test the assumption that the sgn units are in fact responsible for the pyloric output changes, and to investigate the processing of the PSR input are outlined.     

A stochastic model of input effectiveness during irregular gamma rhythms

Gamma-band synchronization has been linked to attention and communication between brain regions, yet the underlying dynamical mechanisms are still unclear. How does the timing and amplitude of inputs to cells that generate an endogenously noisy gamma rhythm affect the network activity and rhythm? How does such ”communication through coherence” (CTC) survive in the face of rhythm and input variability? We present a stochastic modelling approach to this question that yields a very fast computation of the effectiveness of inputs to cells involved in gamma rhythms. Our work is partly motivated by recent optogenetic experiments (Cardin et al. Nature, 459(7247), 663–667 2009) that tested the gamma phase-dependence of network responses by first stabilizing the rhythm with periodic light pulses to the interneurons (I). Our computationally efficient model E-I network of stochastic two-state neurons exhibits finite-size fluctuations. Using the Hilbert transform and Kuramoto index, we study how the stochastic phase of its gamma rhythm is entrained by external pulses. We then compute how this rhythmic inhibition controls the effectiveness of external input onto pyramidal (E) cells, and how variability shapes the window of firing opportunity. For transferring the time variations of an external input to the E cells, we find a tradeoff between the phase selectivity and depth of rate modulation. We also show that the CTC is sensitive to the jitter in the arrival times of spikes to the E cells, and to the degree of I-cell entrainment. We further find that CTC can occur even if the underlying deterministic system does not oscillate; quasicycle-type rhythms induced by the finite-size noise retain the basic CTC properties. Finally a resonance analysis confirms the relative importance of the I cell pacing for rhythm generation. Analysis of whole network behaviour, including computations of synchrony, phase and shifts in excitatory-inhibitory balance, can be further sped up by orders of magnitude using two coupled stochastic differential equations, one for each population. Our work thus yields a fast tool to numerically and analytically investigate CTC in a noisy context. It shows that CTC can be quite vulnerable to rhythm and input variability, which both decrease phase preference.     

Signal transduction across alamethicin ion channels in the presence of noise.

We have studied voltage-dependent ion channels of alamethicin reconstituted into an artificial planar lipid bilayer membrane from the point of view of electric signal transduction. Signal transduction properties of these channels are highly sensitive to the external electric noise. Specifically, addition of bandwidth-restricted "white" noise of 10-20 mV (r.m.s.) to a small sine wave input signal increases the output signal by approximately 20-40 dB conserving, and even slightly increasing, the signal-to-noise ratio at the system output. We have developed a small-signal adiabatic theory of stochastic resonance for a threshold-free system of voltage-dependent ion channels. This theory describes our main experimental findings giving good qualitative understanding of the underlying mechanism. It predicts the right value of the output signal-to-noise ratio and provides a reliable estimate for the noise intensity corresponding to its maximum. Our results suggest that the alamethicin channel in a lipid bilayer is a good model system for studies of mechanisms of primary electrical signal processing in biology showing an important feature of signal transduction improvement by a fluctuating environment.     

Adaptive rescaling maximizes information transmission

Adaptation is a widespread phenomenon in nervous systems, providing flexibility to function under varying external conditions. Here, we relate an adaptive property of a sensory system directly to its function as a carrier of information about input signals. We show that the input/output relation of a sensory system in a dynamic environment changes with the statistical properties of the environment. Specifically, when the dynamic range of inputs changes, the input/output relation rescales so as to match the dynamic range of responses to that of the inputs. We give direct evidence that the scaling of the input/output relation is set to maximize information transmission for each distribution of signals. This adaptive behavior should be particularly useful in dealing with the intermittent statistics of natural signals.     

Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson''s disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson''s disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson''s disease.     

Probabilistic secretion of quanta in the central nervous system: granule cell synaptic control of pattern separation and activity regulation.

The implications of probabilistic secretion of quanta for the functioning of neural networks in the central nervous system have been explored. A model of stochastic secretion at synapses in simple networks, consisting of large numbers of granule cells and a relatively small number of inhibitory interneurons, has been analysed. Such networks occur in the input to the cerebellum Purkinje cells as well as to hippocampal CA3 pyramidal cells and to pyramidal cells in the visual cortex. In this model the input axons terminate on granule cells as well as on an inhibitory interneuron that projects to the granule cells. Stochastic secretion at these synapses involves both temporal variability in secretion at single synapses in the network as well as spatial variability in the secretion at different synapses. The role of this stochastic variability in controlling the size of the granule cell output to a level independent of the size of the input and in separating overlapping inputs has been determined analytically as well as by simulation. The regulation of granule-cell output activity to a reasonably constant value for different size inputs does not occur in the absence of an inhibitory interneuron when both spatial and temporal stochastic variability occurs at the remaining synapses; it is still very poor in the presence of such an interneuron but in the absence of stochastic variability. However, quite good regulation is achieved when the inhibitory interneuron is present with spatial and temporal stochastic variability of secretion at synapses in the network. Excellent regulation is achieved if, in addition, allowance is made for the nonlinear behaviour of the input-output characteristics of inhibitory interneurons. The capacity of granule-cell networks to separate overlapping patterns of activity on their inputs is adequate, with spatial variability in the secretion at synapses, but is improved if there is also temporal variability in the stochastic secretion at individual synapses, although this is at the expense of reliability in the network. Other factors which improve pattern separation are control of the output to very low activity levels, and a restriction on the cumulative size of the excitatory input terminals of each granule cell. Application of the theory to the input neural networks of the cerebellum and the hippocampus shows the role of stochastic variability in quantal transmission in determining the capacity of these networks for pattern separation and activity regulation.     

Screening stochastic Life Cycle assessment inventory models

A screening methodology is presented that utilizes the linear structure within the deterministic life cycle inventory (LCI) model. The methodology ranks each input data element based upon the amount it contributes toward the final output. The identified data elements along with their position in the deterministic model are then sorted into descending order based upon their individual contributions. This enables practitioners and model users to identify those input data elements that contribute the most in the inventory stage. Percentages of the top ranked data elements are then selected, and their corresponding data quality index (DQI) value is upgraded in the stochastic LCI model. Monte Carlo computer simulations are obtained and used to compare the output variance of the original stochastic model with modified stochastic model. The methodology is applied to four real-world beverage delivery system LCA inventory models for verification. This research assists LCA practitioners by streamlining the conversion process when converting a deterministic LCI model to a stochastic model form. Model users and decision-makers can benefit from the reduction in output variance and the increase in ability to discriminate between product system alternatives.     

Trends, stasis, and drift in the evolution of nematode vulva development

BACKGROUND: A surprising amount of developmental variation has been observed for otherwise highly conserved features, a phenomenon known as developmental system drift. Either stochastic processes (e.g., drift and absence of selection-independent constraints) or deterministic processes (e.g., selection or constraints) could be the predominate mechanism for the evolution of such variation. We tested whether evolutionary patterns of change were unbiased or biased, as predicted by the stochastic or deterministic hypotheses, respectively. As a model, we used the nematode vulva, a highly conserved, essential organ, the development of which has been intensively studied in the model systems Caenorhabditis elegans and Pristionchus pacificus. RESULTS: For 51 rhabditid species, we analyzed more than 40 characteristics of vulva development, including cell fates, fate induction, cell competence, division patterns, morphogenesis, and related aspects of gonad development. We then defined individual characters and plotted their evolution on a phylogeny inferred for 65 species from three nuclear gene sequences. This taxon-dense phylogeny provides for the first time a highly resolved picture of rhabditid evolution and allows the reconstruction of the number and directionality of changes in the vulva development characters. We found an astonishing amount of variation and an even larger number of evolutionary changes, suggesting a high degree of homoplasy (convergences and reversals). Surprisingly, only two characters showed unbiased evolution. Evolution of all other characters was biased. CONCLUSIONS: We propose that developmental evolution is primarily governed by selection and/or selection-independent constraints, not stochastic processes such as drift in unconstrained phenotypic space.     

Intrinsic fluctuations, robustness, and tunability in signaling cycles

Covalent modification cycles (e.g., phosphorylation-dephosphorylation) underlie most cellular signaling and control processes. Low molecular copy number, arising from compartmental segregation and slow diffusion between compartments, potentially renders these cycles vulnerable to intrinsic chemical fluctuations. How can a cell operate reliably in the presence of this inherent stochasticity? How do changes in extrinsic parameters lead to variability of response? Can cells exploit these parameters to tune cycles to different ranges of stimuli? We study the dynamics of an isolated phosphorylation cycle. Our model shows that the cycle transmits information reliably if it is tuned to an optimal parameter range, despite intrinsic fluctuations and even for small input signal amplitudes. At the same time, the cycle is sensitive to changes in the concentration and activity of kinases and phosphatases. This sensitivity can lead to significant cell-to-cell response variability. It also provides a mechanism to tune the cycle to transmit signals in various amplitude ranges. Our results show that signaling cycles possess a surprising combination of robustness and tunability. This combination makes them ubiquitous in eukaryotic signaling, optimizing signaling in the presence of fluctuations using their inherent flexibility. On the other hand, cycles tuned to suppress intrinsic fluctuations can be vulnerable to changes in the number and activity of kinases and phosphatases. Such trade-offs in robustness to intrinsic and extrinsic fluctuations can influence the evolution of signaling cascades, making them the weakest links in cellular circuits.     

Pair hidden Markov models on tree structures

MOTIVATION: Computationally identifying non-coding RNA regions on the genome has much scope for investigation and is essentially harder than gene-finding problems for protein-coding regions. Since comparative sequence analysis is effective for non-coding RNA detection, efficient computational methods are expected for structural alignments of RNA sequences. On the other hand, Hidden Markov Models (HMMs) have played important roles for modeling and analysing biological sequences. Especially, the concept of Pair HMMs (PHMMs) have been examined extensively as mathematical models for alignments and gene finding. RESULTS: We propose the pair HMMs on tree structures (PHMMTSs), which is an extension of PHMMs defined on alignments of trees and provides a unifying framework and an automata-theoretic model for alignments of trees, structural alignments and pair stochastic context-free grammars. By structural alignment, we mean a pairwise alignment to align an unfolded RNA sequence into an RNA sequence of known secondary structure. First, we extend the notion of PHMMs defined on alignments of 'linear' sequences to pair stochastic tree automata, called PHMMTSs, defined on alignments of 'trees'. The PHMMTSs provide various types of alignments of trees such as affine-gap alignments of trees and an automata-theoretic model for alignment of trees. Second, based on the observation that a secondary structure of RNA can be represented by a tree, we apply PHMMTSs to the problem of structural alignments of RNAs. We modify PHMMTSs so that it takes as input a pair of a 'linear' sequence and a 'tree' representing a secondary structure of RNA to produce a structural alignment. Further, the PHMMTSs with input of a pair of two linear sequences is mathematically equal to the pair stochastic context-free grammars. We demonstrate some computational experiments to show the effectiveness of our method for structural alignments, and discuss a complexity issue of PHMMTSs.     

Amplification of Asynchronous Inhibition-Mediated Synchronization by Feedback in Recurrent Networks

Synchronization of 30–80 Hz oscillatory activity of the principle neurons in the olfactory bulb (mitral cells) is believed to be important for odor discrimination. Previous theoretical studies of these fast rhythms in other brain areas have proposed that principle neuron synchrony can be mediated by short-latency, rapidly decaying inhibition. This phasic inhibition provides a narrow time window for the principle neurons to fire, thus promoting synchrony. However, in the olfactory bulb, the inhibitory granule cells produce long lasting, small amplitude, asynchronous and aperiodic inhibitory input and thus the narrow time window that is required to synchronize spiking does not exist. Instead, it has been suggested that correlated output of the granule cells could serve to synchronize uncoupled mitral cells through a mechanism called “stochastic synchronization”, wherein the synchronization arises through correlation of inputs to two neural oscillators. Almost all work on synchrony due to correlations presumes that the correlation is imposed and fixed. Building on theory and experiments that we and others have developed, we show that increased synchrony in the mitral cells could produce an increase in granule cell activity for those granule cells that share a synchronous group of mitral cells. Common granule cell input increases the input correlation to the mitral cells and hence their synchrony by providing a positive feedback loop in correlation. Thus we demonstrate the emergence and temporal evolution of input correlation in recurrent networks with feedback. We explore several theoretical models of this idea, ranging from spiking models to an analytically tractable model.     

Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.     

Electronic transduction in model enzyme sensors assisted by a photoisomerizable azo-polymer

We develop a stochastic model of electronic transduction by means of a rod-like azo-polymer (single peptide molecule doped with a given amount of azo-benzene structural units) in polymer-redox enzyme biosensor. We propose a configuration where the azo-polymer is anchored next to the enzyme reaction center and functions as a light-driven micromechanical actuator shuttling electrons toward the electrode. We show that the output catalytic current is exponentially sensitive to variations in geometrical size of the polymer (a 'switch off' effect) and suggest a scheme where the switching effect is triggered by polymer photoisomerization, resulting in its overall length change.