Genetic mechanisms for impaired synaptic plasticity in schizophrenia revealed by computational modelling.

Schizophrenia phenotypes are suggestive of impaired cortical plasticity in the disease, but the mechanisms of these deficits are unknown. Genomic association studies have implicated a large number of genes that regulate neuromodulation and plasticity, indicating that the plasticity deficits have a genetic origin. Here, we used biochemically detailed computational modelling of post-synaptic plasticity to investigate how schizophrenia-associated genes regulate long-term potentiation (LTP) and depression (LTD). We combined our model with data from post-mortem mRNA expression studies (CommonMind gene-expression datasets) to assess the consequences of altered expression of plasticity-regulating genes for the amplitude of LTP and LTD. Our results show that the expression alterations observed post mortem, especially those in anterior cingulate cortex, lead to impaired PKA-pathway-mediated LTP in synapses containing GluR1 receptors. We validated these findings using a genotyped EEG dataset where polygenic risk scores for synaptic and ion channel-encoding genes as well as modulation of visual evoked potentials (VEP) were determined for 286 healthy controls. Our results provide a possible genetic mechanism for plasticity impairments in schizophrenia, which can lead to improved understanding and, ultimately, treatment of the disorder.

Excitatory and inhibitory effects of HCN channel modulation on excitability of layer V pyramidal cells.

Dendrites of cortical pyramidal cells are densely populated by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, a.k.a. Ih channels. Ih channels are targeted by multiple neuromodulatory pathways, and thus are one of the key ion-channel populations regulating the pyramidal cell activity. Previous observations and theories attribute opposing effects of the Ih channels on neuronal excitability due to their mildly hyperpolarized reversal potential. These effects are difficult to measure experimentally due to the fine spatiotemporal landscape of the Ih activity in the dendrites, but computational models provide an efficient tool for studying this question in a reduced but generalizable setting. In this work, we build upon existing biophysically detailed models of thick-tufted layer V pyramidal cells and model the effects of over- and under-expression of Ih channels as well as their neuromodulation. We show that Ih channels facilitate the action potentials of layer V pyramidal cells in response to proximal dendritic stimulus while they hinder the action potentials in response to distal dendritic stimulus at the apical dendrite. We also show that the inhibitory action of the Ih channels in layer V pyramidal cells is due to the interactions between Ih channels and a hot zone of low voltage-activated Ca2+ channels at the apical dendrite. Our simulations suggest that a combination of Ih-enhancing neuromodulation at the proximal part of the apical dendrite and Ih-inhibiting modulation at the distal part of the apical dendrite can increase the layer V pyramidal excitability more than either of the two alone. Our analyses uncover the effects of Ih-channel neuromodulation of layer V pyramidal cells at a single-cell level and shed light on how these neurons integrate information and enable higher-order functions of the brain.

The effect of alterations of schizophrenia-associated genes on gamma band oscillations.

Abnormalities in the synchronized oscillatory activity of neurons in general and, specifically in the gamma band, might play a crucial role in the pathophysiology of schizophrenia. While these changes in oscillatory activity have traditionally been linked to alterations at the synaptic level, we demonstrate here, using computational modeling, that common genetic variants of ion channels can contribute strongly to this effect. Our model of primary auditory cortex highlights multiple schizophrenia-associated genetic variants that reduce gamma power in an auditory steady-state response task. Furthermore, we show that combinations of several of these schizophrenia-associated variants can produce similar effects as the more traditionally considered synaptic changes. Overall, our study provides a mechanistic link between schizophrenia-associated common genetic variants, as identified by genome-wide association studies, and one of the most robust neurophysiological endophenotypes of schizophrenia.

Evidence for Reduced Long-Term Potentiation-Like Visual Cortical Plasticity in Schizophrenia and Bipolar Disorder.

Several lines of research suggest that impairments in long-term potentiation (LTP)-like synaptic plasticity might be a key pathophysiological mechanism in schizophrenia (SZ) and bipolar disorder type I (BDI) and II (BDII). Using modulations of visually evoked potentials (VEP) of the electroencephalogram, impaired LTP-like visual cortical plasticity has been implicated in patients with BDII, while there has been conflicting evidence in SZ, a lack of research in BDI, and mixed results regarding associations with symptom severity, mood states, and medication. We measured the VEP of patients with SZ spectrum disorders (n = 31), BDI (n = 34), BDII (n = 33), and other BD spectrum disorders (n = 2), and age-matched healthy control (HC) participants (n = 200) before and after prolonged visual stimulation. Compared to HCs, modulation of VEP component N1b, but not C1 or P1, was impaired both in patients within the SZ spectrum (χ 2 = 35.1, P = 3.1 × 10-9) and BD spectrum (χ 2 = 7.0, P = 8.2 × 10-3), including BDI (χ 2 = 6.4, P = .012), but not BDII (χ 2 = 2.2, P = .14). N1b modulation was also more severely impaired in SZ spectrum than BD spectrum patients (χ 2 = 14.2, P = 1.7 × 10-4). N1b modulation was not significantly associated with Positive and Negative Syndrome Scale (PANSS) negative or positive symptoms scores, number of psychotic episodes, Montgomery and Åsberg Depression Rating Scale (MADRS) scores, or Young Mania Rating Scale (YMRS) scores after multiple comparison correction, although a nominal association was observed between N1b modulation and PANSS negative symptoms scores among SZ spectrum patients. These results suggest that LTP-like plasticity is impaired in SZ and BD. Adding to previous genetic, pharmacological, and electrophysiological evidence, these results implicate aberrant synaptic plasticity as a mechanism underlying SZ and BD.

Experience-dependent modulation of the visual evoked potential: Testing effect sizes, retention over time, and associations with age in 415 healthy individuals.

Experience-dependent modulation of the visual evoked potential (VEP) is a promising proxy measure of synaptic plasticity in the cerebral cortex. However, existing studies are limited by small to moderate sample sizes as well as by considerable variability in how VEP modulation is quantified. In the present study, we used a large sample (n = 415) of healthy volunteers to compare different quantifications of VEP modulation with regards to effect sizes and retention of the modulation effect over time. We observed significant modulation for VEP components C1 (Cohen's d = 0.53), P1 (d = 0.66), N1 (d=-0.27), N1b (d=-0.66), but not P2 (d = 0.08), and in three clusters of total power modulation, 2-4 min after 2 Hz prolonged visual stimulation. For components N1 (d=-0.21) and N1b (d=-0.38), as well for the total power clusters, this effect was retained after 54-56 min, by which time also the P2 component had gained modulation (d = 0.54). Moderate to high correlations (0.39≤ρ≤0.69) between modulation at different postintervention blocks revealed a relatively high temporal stability in the modulation effect for each VEP component. However, different VEP components also showed markedly different temporal retention patterns. Finally, participant age correlated negatively with C1 (χ2=30.4), and positively with P1 modulation (χ2=13.4), whereas P2 modulation was larger for female participants (χ2=15.4). There were no effects of either age or sex on N1 and N1b potentiation. These results provide strong support for VEP modulation, and especially N1b modulation, as a robust measure of synaptic plasticity, but underscore the need to differentiate between components, and to control for demographic confounders.

A unified computational model for cortical post-synaptic plasticity.

Signalling pathways leading to post-synaptic plasticity have been examined in many types of experimental studies, but a unified picture on how multiple biochemical pathways collectively shape neocortical plasticity is missing. We built a biochemically detailed model of post-synaptic plasticity describing CaMKII, PKA, and PKC pathways and their contribution to synaptic potentiation or depression. We developed a statistical AMPA-receptor-tetramer model, which permits the estimation of the AMPA-receptor-mediated maximal synaptic conductance based on numbers of GluR1s and GluR2s predicted by the biochemical signalling model. We show that our model reproduces neuromodulator-gated spike-timing-dependent plasticity as observed in the visual cortex and can be fit to data from many cortical areas, uncovering the biochemical contributions of the pathways pinpointed by the underlying experimental studies. Our model explains the dependence of different forms of plasticity on the availability of different proteins and can be used for the study of mental disorder-associated impairments of cortical plasticity.

Computational Modeling of Genetic Contributions to Excitability and Neural Coding in Layer V Pyramidal Cells: Applications to Schizophrenia Pathology.

Pyramidal cells in layer V of the neocortex are one of the most widely studied neuron types in the mammalian brain. Due to their role as integrators of feedforward and cortical feedback inputs, they are well-positioned to contribute to the symptoms and pathology in mental disorders-such as schizophrenia-that are characterized by a mismatch between the internal perception and external inputs. In this modeling study, we analyze the input/output properties of layer V pyramidal cells and their sensitivity to modeled genetic variants in schizophrenia-associated genes. We show that the excitability of layer V pyramidal cells and the way they integrate inputs in space and time are altered by many types of variants in ion-channel and Ca2+ transporter-encoding genes that have been identified as risk genes by recent genome-wide association studies. We also show that the variability in the output patterns of spiking and Ca2+ transients in layer V pyramidal cells is altered by these model variants. Importantly, we show that many of the predicted effects are robust to noise and qualitatively similar across different computational models of layer V pyramidal cells. Our modeling framework reveals several aspects of single-neuron excitability that can be linked to known schizophrenia-related phenotypes and existing hypotheses on disease mechanisms. In particular, our models predict that single-cell steady-state firing rate is positively correlated with the coding capacity of the neuron and negatively correlated with the amplitude of a prepulse-mediated adaptation and sensitivity to coincidence of stimuli in the apical dendrite and the perisomatic region of a layer V pyramidal cell. These results help to uncover the voltage-gated ion-channel and Ca2+ transporter-associated genetic underpinnings of schizophrenia phenotypes and biomarkers.

Biophysical Psychiatry-How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders.

The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a "biophysical psychiatry," an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.

Alterations in Schizophrenia-Associated Genes Can Lead to Increased Power in Delta Oscillations.

Genome-wide association studies have implicated many ion channels in schizophrenia pathophysiology. Although the functions of these channels are relatively well characterized by single-cell studies, the contributions of common variation in these channels to neurophysiological biomarkers and symptoms of schizophrenia remain elusive. Here, using computational modeling, we show that a common biomarker of schizophrenia, namely, an increase in delta-oscillation power, may be a direct consequence of altered expression or kinetics of voltage-gated ion channels or calcium transporters. Our model of a circuit of layer V pyramidal cells highlights multiple types of schizophrenia-related variants that contribute to altered dynamics in the delta-frequency band. Moreover, our model predicts that the same membrane mechanisms that increase the layer V pyramidal cell network gain and response to delta-frequency oscillations may also cause a deficit in a single-cell correlate of the prepulse inhibition, which is a behavioral biomarker highly associated with schizophrenia.

A molecule-based genetic association approach implicates a range of voltage-gated calcium channels associated with schizophrenia.

Traditional genome-wide association studies (GWAS) have successfully detected genetic variants associated with schizophrenia. However, only a small fraction of heritability can be explained. Gene-set/pathway-based methods can overcome limitations arising from single nucleotide polymorphism (SNP)-based analysis, but most of them place constraints on size which may exclude highly specific and functional sets, like macromolecules. Voltage-gated calcium (Cav ) channels, belonging to macromolecules, are composed of several subunits whose encoding genes are located far away or even on different chromosomes. We combined information about such molecules with GWAS data to investigate how functional channels associated with schizophrenia. We defined a biologically meaningful SNP-set based on channel structure and performed an association study by using a validated method: SNP-set (sequence) kernel association test. We identified eight subtypes of Cav channels significantly associated with schizophrenia from a subsample of published data (N = 56,605), including the L-type channels (Cav 1.1, Cav 1.2, Cav 1.3), P-/Q-type Cav 2.1, N-type Cav 2.2, R-type Cav 2.3, T-type Cav 3.1, and Cav 3.3. Only genes from Cav 1.2 and Cav 3.3 have been implicated by the largest GWAS (N = 82,315). Each subtype of Cav channels showed relatively high chip heritability, proportional to the size of its constituent gene regions. The results suggest that abnormalities of Cav channels may play an important role in the pathophysiology of schizophrenia and these channels may represent appropriate drug targets for therapeutics. Analyzing subunit-encoding genes of a macromolecule in aggregate is a complementary way to identify more genetic variants of polygenic diseases. This study offers the potential of power for discovery the biological mechanisms of schizophrenia.

A stepwise neuron model fitting procedure designed for recordings with high spatial resolution: Application to layer 5 pyramidal cells.

BACKGROUND: Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level. NEW METHOD: In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca2+ imaging. RESULT: We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model. COMPARISON WITH EXISTING METHODS: Our approach combines features from several previously applied model-fitting strategies. The reduced-morphology neuron model obtained using our approach reliably reproduces the membrane-potential dynamics across the dendrites as predicted by the full-morphology model. CONCLUSIONS: The network models produced using our method are cost-efficient and predict that interconnected L5PCs are able to amplify delta-range oscillatory inputs across a large range of network sizes and topologies, largely due to the medium after hyperpolarization mediated by the Ca2+-activated SK current.

Differential processing in modality-specific Mauthner cell dendrites.

KEY POINTS: The present study examines dendritic integrative processes that occur in many central neurons but have been challenging to study in vivo in the vertebrate brain. The Mauthner cell of goldfish receives auditory and visual information via two separate dendrites, providing a privileged scenario for in vivo examination of dendritic integration. The results show differential attenuation properties in the Mauthner cell dendrites arising at least partly from differences in cable properties and the nonlinear behaviour of the respective dendritic membranes. In addition to distinct modality-dependent membrane specialization in neighbouring dendrites of the Mauthner cell, we report cross-modal dendritic interactions via backpropagating postsynaptic potentials. Broadly, the results of the present study provide an exceptional example for the processing power of single neurons. ABSTRACT: Animals process multimodal information for adaptive behavioural decisions. In fish, evasion of a diving bird that breaks the water surface depends on integrating visual and auditory stimuli with very different characteristics. How do neurons process such differential sensory inputs at the dendritic level? For that, we studied the Mauthner cells (M-cells) in the goldfish startle circuit, which receive visual and auditory inputs via two separate dendrites, both accessible for in vivo recordings. We investigated whether electrophysiological membrane properties and dendrite morphology, studied in vivo, play a role in selective sensory processing in the M-cell. The results obtained show that anatomical and electrophysiological differences between the dendrites combine to produce stronger attenuation of visually evoked postsynaptic potentials (PSPs) than to auditory evoked PSPs. Interestingly, our recordings showed also cross-modal dendritic interaction because auditory evoked PSPs invade the ventral dendrite (VD), as well as the opposite where visual PSPs invade the lateral dendrite (LD). However, these interactions were asymmetrical, with auditory PSPs being more prominent in the VD than visual PSPs in the LD. Modelling experiments imply that this asymmetry is caused by active conductances expressed in the proximal segments of the VD. The results obtained in the present study suggest modality-dependent membrane specialization in M-cell dendrites suited for processing stimuli of different time domains and, more broadly, provide a compelling example of information processing in single neurons.

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons.

Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant-at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis.

Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects.NEW & NOTEWORTHY Standard CSD analysis does not account for ionic diffusion. Using biophysically realistic computer simulations, we show that unaccounted-for diffusive currents can lead to the prediction of spurious current sources. This finding may be of strong interest for in vivo electrophysiologists doing extracellular recordings in general, and CSD analysis in particular.

Pleiotropic effects of schizophrenia-associated genetic variants in neuron firing and cardiac pacemaking revealed by computational modeling.

Schizophrenia patients have an increased risk of cardiac dysfunction. A possible factor underlying this comorbidity are the common variants in the large set of genes that have recently been discovered in genome-wide association studies (GWASs) as risk genes of schizophrenia. Many of these genes control the cell electrogenesis and calcium homeostasis. We applied biophysically detailed models of layer V pyramidal cells and sinoatrial node cells to study the contribution of schizophrenia-associated genes on cellular excitability. By including data from functional genomics literature to simulate the effects of common variants of these genes, we showed that variants of voltage-gated Na+ channel or hyperpolarization-activated cation channel-encoding genes cause qualitatively similar effects on layer V pyramidal cell and sinoatrial node cell excitability. By contrast, variants of Ca2+ channel or transporter-encoding genes mostly have opposite effects on cellular excitability in the two cell types. We also show that the variants may crucially affect the propagation of the cardiac action potential in the sinus node. These results may help explain some of the cardiac comorbidity in schizophrenia, and may facilitate generation of effective antipsychotic medications without cardiac side-effects such as arrhythmia.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue.

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

Functional Effects of Schizophrenia-Linked Genetic Variants on Intrinsic Single-Neuron Excitability: A Modeling Study.

BACKGROUND: Recent genome-wide association studies have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior across SCZ-related genes. METHODS: We applied a biophysically detailed multicompartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used changes in neuron model parameters to represent the effects of these variants. RESULTS: We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree. CONCLUSIONS: Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously proposed deficits in synaptic communication and network behavior.

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model.

We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework.

The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small ([Formula: see text]) networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger ([Formula: see text]) networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.

Balance between noise and information flow maximizes set complexity of network dynamics.

Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure of complexity, namely, the statistical complexity. We show that the networks can be tuned to the regime of maximal complexity by adding a suitable amount of noise to the deterministic Boolean dynamics. In fact, we show that for networks with Poisson degree distributions, all networks ranging from subcritical to slightly supercritical can be tuned with noise to reach maximal set complexity in their dynamics. For networks with a fixed number of inputs this is true for near-to-critical networks. This increase in complexity is obtained at the expense of disruption in information flow. For a large ensemble of networks showing maximal complexity, there exists a balance between noise and contracting dynamics in the state space. In networks that are close to critical the intrinsic noise required for the tuning is smaller and thus also has the smallest effect in terms of the information processing in the system. Our results suggest that the maximization of complexity near to the state transition might be a more general phenomenon in physical systems, and that noise present in a system may in fact be useful in retaining the system in a state with high information content.