What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing “noise benefits”, and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.     

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of “dynamical relaying” – a mechanism that relies on a specific network motif – has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair – a “resonance pair” – plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.     

Information processing in the adaptation of Saccharomyces cerevisiae to osmotic stress: an analysis of the phosphorelay system

Cellular signaling is key for organisms to survive immediate stresses from fluctuating environments as well as relaying important information about external stimuli. Effective mechanisms have evolved to ensure appropriate responses for an optimal adaptation process. For them to be functional despite the noise that occurs in biochemical transmission, the cell needs to be able to infer reliably what was sensed in the first place. For example Saccharomyces cerevisiae are able to adjust their response to osmotic shock depending on the severity of the shock and initiate responses that lead to near perfect adaptation of the cell. We investigate the Sln1–Ypd1–Ssk1-phosphorelay as a module in the high-osmolarity glycerol pathway by incorporating a stochastic model. Within this framework, we can imitate the noisy perception of the cell and interpret the phosphorelay as an information transmitting channel in the sense of C.E. Shannon’s “Information Theory”. We refer to the channel capacity as a measure to quantify and investigate the transmission properties of this system, enabling us to draw conclusions on viable parameter sets for modeling the system.     

Noise Management by Molecular Networks

Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise.     

Transition to quorum sensing in an Agrobacterium population: A stochastic model

Understanding of the intracellular molecular machinery that is responsible for the complex collective behavior of multicellular populations is an exigent problem of modern biology. Quorum sensing, which allows bacteria to activate genetic programs cooperatively, provides an instructive and tractable example illuminating the causal relationships between the molecular organization of gene networks and the complex phenotypes they control. In this work we—to our knowledge for the first time—present a detailed model of the population-wide transition to quorum sensing using the example of Agrobacterium tumefaciens. We construct a model describing the Ti plasmid quorum-sensing gene network and demonstrate that it behaves as an “on–off” gene expression switch that is robust to molecular noise and that activates the plasmid conjugation program in response to the increase in autoinducer concentration. This intracellular model is then incorporated into an agent-based stochastic population model that also describes bacterial motion, cell division, and chemical communication. Simulating the transition to quorum sensing in a liquid medium and biofilm, we explain the experimentally observed gradual manifestation of the quorum-sensing phenotype by showing that the transition of individual model cells into the “on” state is spread stochastically over a broad range of autoinducer concentrations. At the same time, the population-averaged values of critical autoinducer concentration and the threshold population density are shown to be robust to variability between individual cells, predictable and specific to particular growth conditions. Our modeling approach connects intracellular and population scales of the quorum-sensing phenomenon and provides plausible answers to the long-standing questions regarding the ecological and evolutionary significance of the phenomenon. Thus, we demonstrate that the transition to quorum sensing requires a much higher threshold cell density in liquid medium than in biofilm, and on this basis we hypothesize that in Agrobacterium quorum sensing serves as the detector of biofilm formation.     

An Automated,Adaptive Framework for Optimizing Preprocessing Pipelines in Task-Based Functional MRI

BOLD fMRI is sensitive to blood-oxygenation changes correlated with brain function; however, it is limited by relatively weak signal and significant noise confounds. Many preprocessing algorithms have been developed to control noise and improve signal detection in fMRI. Although the chosen set of preprocessing and analysis steps (the “pipeline”) significantly affects signal detection, pipelines are rarely quantitatively validated in the neuroimaging literature, due to complex preprocessing interactions. This paper outlines and validates an adaptive resampling framework for evaluating and optimizing preprocessing choices by optimizing data-driven metrics of task prediction and spatial reproducibility. Compared to standard “fixed” preprocessing pipelines, this optimization approach significantly improves independent validation measures of within-subject test-retest, and between-subject activation overlap, and behavioural prediction accuracy. We demonstrate that preprocessing choices function as implicit model regularizers, and that improvements due to pipeline optimization generalize across a range of simple to complex experimental tasks and analysis models. Results are shown for brief scanning sessions (<3 minutes each), demonstrating that with pipeline optimization, it is possible to obtain reliable results and brain-behaviour correlations in relatively small datasets.     

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.     

Transfer Functions for Protein Signal Transduction: Application to a Model of Striatal Neural Plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.     

Injection of Fully-Defined Signal Mixtures: A Novel High-Throughput Tool to Study Neuronal Encoding and Computations

Understanding of how neurons transform fluctuations of membrane potential, reflecting input activity, into spike responses, which communicate the ultimate results of single-neuron computation, is one of the central challenges for cellular and computational neuroscience. To study this transformation under controlled conditions, previous work has used a signal immersed in noise paradigm where neurons are injected with a current consisting of fluctuating noise that mimics on-going synaptic activity and a systematic signal whose transmission is studied. One limitation of this established paradigm is that it is designed to examine the encoding of only one signal under a specific, repeated condition. As a result, characterizing how encoding depends on neuronal properties, signal parameters, and the interaction of multiple inputs is cumbersome. Here we introduce a novel fully-defined signal mixture paradigm, which allows us to overcome these problems. In this paradigm, current for injection is synthetized as a sum of artificial postsynaptic currents (PSCs) resulting from the activity of a large population of model presynaptic neurons. PSCs from any presynaptic neuron(s) can be now considered as “signal”, while the sum of all other inputs is considered as “noise”. This allows us to study the encoding of a large number of different signals in a single experiment, thus dramatically increasing the throughput of data acquisition. Using this novel paradigm, we characterize the detection of excitatory and inhibitory PSCs from neuronal spike responses over a wide range of amplitudes and firing-rates. We show, that for moderately-sized neuronal populations the detectability of individual inputs is higher for excitatory than for inhibitory inputs during the 2–5 ms following PSC onset, but becomes comparable after 7–8 ms. This transient imbalance of sensitivity in favor of excitation may enhance propagation of balanced signals through neuronal networks. Finally, we discuss several open questions that this novel high-throughput paradigm may address.     

Experimental and Computational Analysis of a Large Protein Network That Controls Fat Storage Reveals the Design Principles of a Signaling Network

An approach combining genetic, proteomic, computational, and physiological analysis was used to define a protein network that regulates fat storage in budding yeast (Saccharomyces cerevisiae). A computational analysis of this network shows that it is not scale-free, and is best approximated by the Watts-Strogatz model, which generates “small-world” networks with high clustering and short path lengths. The network is also modular, containing energy level sensing proteins that connect to four output processes: autophagy, fatty acid synthesis, mRNA processing, and MAP kinase signaling. The importance of each protein to network function is dependent on its Katz centrality score, which is related both to the protein’s position within a module and to the module’s relationship to the network as a whole. The network is also divisible into subnetworks that span modular boundaries and regulate different aspects of fat metabolism. We used a combination of genetics and pharmacology to simultaneously block output from multiple network nodes. The phenotypic results of this blockage define patterns of communication among distant network nodes, and these patterns are consistent with the Watts-Strogatz model.     

Network Bursting Dynamics in Excitatory Cortical Neuron Cultures Results from the Combination of Different Adaptive Mechanism

In the brain, synchronization among cells of an assembly is a common phenomenon, and thought to be functionally relevant. Here we used an in vitro experimental model of cell assemblies, cortical cultures, combined with numerical simulations of a spiking neural network (SNN) to investigate how and why spontaneous synchronization occurs. In order to deal with excitation only, we pharmacologically blocked GABA_Aergic transmission using bicuculline. Synchronous events in cortical cultures tend to involve almost every cell and to display relatively constant durations. We have thus named these “network spikes” (NS). The inter-NS-intervals (INSIs) proved to be a more interesting phenomenon. In most cortical cultures NSs typically come in series or bursts (“bursts of NSs”, BNS), with short (∼1 s) INSIs and separated by long silent intervals (tens of s), which leads to bimodal INSI distributions. This suggests that a facilitating mechanism is at work, presumably short-term synaptic facilitation, as well as two fatigue mechanisms: one with a short timescale, presumably short-term synaptic depression, and another one with a longer timescale, presumably cellular adaptation. We thus incorporated these three mechanisms into the SNN, which, indeed, produced realistic BNSs. Next, we systematically varied the recurrent excitation for various adaptation timescales. Strong excitability led to frequent, quasi-periodic BNSs (CV∼0), and weak excitability led to rare BNSs, approaching a Poisson process (CV∼1). Experimental cultures appear to operate within an intermediate weakly-synchronized regime (CV∼0.5), with an adaptation timescale in the 2–8 s range, and well described by a Poisson-with-refractory-period model. Taken together, our results demonstrate that the INSI statistics are indeed informative: they allowed us to infer the mechanisms at work, and many parameters that we cannot access experimentally.     

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.     

Parasites and Pathogens of the Honeybee (Apis mellifera) and Their Influence on Inter-Colonial Transmission

Pathogens and parasites may facilitate their transmission by manipulating host behavior. Honeybee pathogens and pests need to be transferred from one colony to another if they are to maintain themselves in a host population. Inter-colony transmission occurs typically through honeybee workers not returning to their home colony but entering a foreign colony (“drifting”). Pathogens might enhance drifting to enhance transmission to new colonies. We here report on the effects infection by ten honeybee viruses and Nosema spp., and Varroa mite infestation on honeybee drifting. Genotyping of workers collected from colonies allowed us to identify genuine drifted workers as well as source colonies sending out drifters in addition to sink colonies accepting them. We then used network analysis to determine patterns of drifting. Distance between colonies in the apiary was the major factor explaining 79% of drifting. None of the tested viruses or Nosema spp. were associated with the frequency of drifting. Only colony infestation with Varroa was associated with significantly enhanced drifting. More specifically, colonies with high Varroa infestation had a significantly enhanced acceptance of drifters, although they did not send out more drifting workers. Since Varroa-infested colonies show an enhanced attraction of drifting workers, and not only those infected with Varroa and its associated pathogens, infestation by Varroa may also facilitate the uptake of other pests and parasites.     

The participation of two rhythms in the leaf movements of xanthium plants given various light-dark cycles

We have shown Xanthium strumarium exhibit two distinct leaf movement rhythms with one occurring in continuous light and presumably related to an endogenous rhythm initiated by the “light-on” signal and the other occurring in continuous dark and presumably related to an endogenous rhythm initiated by the “light-off” signal. Characteristic of the light-on rhythm is a sudden and rapid downward movement of the leaf occurring about 16 hours after the light-on signal. Characteristic of the light-off rhythm is an immediate and sudden upward movement following the light-off signal. Under certain photoperiodic treatments, the two movements seem to be in conflict.     

The Sign Rule and Beyond: Boundary Effects,Flexibility, and Noise Correlations in Neural Population Codes

Over repeat presentations of the same stimulus, sensory neurons show variable responses. This “noise” is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population''s ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem – neural tuning curves, etc. – held fixed. This work yields unifying insights into the role of noise correlations. These are summarized in the form of theorems, and illustrated with numerical examples involving neurons with diverse tuning curves. Our main contributions are as follows. (1) We generalize previous results to prove a sign rule (SR) — if noise correlations between pairs of neurons have opposite signs vs. their signal correlations, then coding performance will improve compared to the independent case. This holds for three different metrics of coding performance, and for arbitrary tuning curves and levels of heterogeneity. This generality is true for our other results as well. (2) As also pointed out in the literature, the SR does not provide a necessary condition for good coding. We show that a diverse set of correlation structures can improve coding. Many of these violate the SR, as do experimentally observed correlations. There is structure to this diversity: we prove that the optimal correlation structures must lie on boundaries of the possible set of noise correlations. (3) We provide a novel set of necessary and sufficient conditions, under which the coding performance (in the presence of noise) will be as good as it would be if there were no noise present at all.     

Risk of Exposure to Eastern Equine Encephalomyelitis Virus Increases with the Density of Northern Cardinals

For a variety of infectious diseases, the richness of the community of potential host species has emerged as an important factor in pathogen transmission, whereby a higher richness of host species is associated with a lowered disease risk. The proposed mechanism driving this pattern is an increased likelihood in species-rich communities that infectious individuals will encounter dead-end hosts. Mosquito-borne pathogen systems potentially are exceptions to such “dilution effects” because mosquitoes vary their rates of use of vertebrate host species as bloodmeal sources relative to host availabilities. Such preferences may violate basic assumptions underlying the hypothesis of a dilution effect in pathogen systems. Here, we describe development of a model to predict exposure risk of sentinel chickens to eastern equine encephalitis virus (EEEV) in Walton County, Florida between 2009 and 2010 using avian species richness as well as densities of individual host species potentially important to EEEV transmission as candidate predictor variables. We found the highest support for the model that included the density of northern cardinals, a highly preferred host of mosquito vectors of EEEV, as a predictor variable. The highest-ranking model also included Culiseta melanura abundance as a predictor variable. These results suggest that mosquito preferences for vertebrate hosts influence pathogen transmission.     

Signal Peptide Cleavage from GP5 of PRRSV: A Minor Fraction of Molecules Retains the Decoy Epitope,a Presumed Molecular Cause for Viral Persistence

Porcine reproductive and respiratory syndrome virus (PRRSV) is the major pathogen in the pig industry. Variability of the antigens and persistence are the biggest challenges for successful control and elimination of the disease. GP5, the major glycoprotein of PRRSV, is considered an important target of neutralizing antibodies, which however appear only late in infection. This was attributed to the presence of a “decoy epitope” located near a hypervariable region of GP5. This region also harbors the predicted signal peptide cleavage sites and (dependent on the virus strain) a variable number of potential N-glycosylation sites. Molecular processing of GP5 has not been addressed experimentally so far: whether and where the signal peptide is cleaved and (as a consequence) whether the “decoy epitope” is present in virus particles. We show that the signal peptide of GP5 from the American type 2 reference strain VR-2332 is cleaved, both during in vitro translation in the presence of microsomes and in transfected cells. This was found to be independent of neighboring glycosylation sites and occurred in a variety of porcine cells for GP5 sequences derived from various type 2 strains. The exact signal peptide cleavage site was elucidated by mass spectrometry of virus-derived and recombinant GP5. The results revealed that the signal peptide of GP5 is cleaved at two sites. As a result, a mixture of GP5 proteins exists in virus particles, some of which still contain the “decoy epitope” sequence. Heterogeneity was also observed for the use of glycosylation sites in the hypervariable region. Lastly, GP5 mutants were engineered where one of the signal peptide cleavage sites was blocked. Wildtype GP5 exhibited exactly the same SDS-PAGE mobility as the mutant that is cleavable at site 2 only. This indicates that the overwhelming majority of all GP5 molecules does not contain the “decoy epitope”.     

Dense Percolation in Large-Scale Mean-Field Random Networks Is Provably “Explosive”

Recent reports suggest that evolving large-scale networks exhibit “explosive percolation”: a large fraction of nodes suddenly becomes connected when sufficiently many links have formed in a network. This phase transition has been shown to be continuous (second-order) for most random network formation processes, including classical mean-field random networks and their modifications. We study a related yet different phenomenon referred to as dense percolation, which occurs when a network is already connected, but a large group of nodes must be dense enough, i.e., have at least a certain minimum required percentage of possible links, to form a “highly connected” cluster. Such clusters have been considered in various contexts, including the recently introduced network modularity principle in biological networks. We prove that, contrary to the traditionally defined percolation transition, dense percolation transition is discontinuous (first-order) under the classical mean-field network formation process (with no modifications); therefore, there is not only quantitative, but also qualitative difference between regular and dense percolation transitions. Moreover, the size of the largest dense (highly connected) cluster in a mean-field random network is explicitly characterized by rigorously proven tight asymptotic bounds, which turn out to naturally extend the previously derived formula for the size of the largest clique (a cluster with all possible links) in such a network. We also briefly discuss possible implications of the obtained mathematical results on studying first-order phase transitions in real-world linked systems.