Dynamics of a neural system with a multiscale architecture

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.     

Manipulating neural activity in physiologically classified neurons: triumphs and challenges

Understanding brain function requires knowing both how neural activity encodes information and how this activity generates appropriate responses. Electrophysiological, imaging and immediate early gene immunostaining studies have been instrumental in identifying and characterizing neurons that respond to different sensory stimuli, events and motor actions. Here we highlight approaches that have manipulated the activity of physiologically classified neurons to determine their role in the generation of behavioural responses. Previous experiments have often exploited the functional architecture observed in many cortical areas, where clusters of neurons share response properties. However, many brain structures do not exhibit such functional architecture. Instead, neurons with different response properties are anatomically intermingled. Emerging genetic approaches have enabled the identification and manipulation of neurons that respond to specific stimuli despite the lack of discernable anatomical organization. These approaches have advanced understanding of the circuits mediating sensory perception, learning and memory, and the generation of behavioural responses by providing causal evidence linking neural response properties to appropriate behavioural output. However, significant challenges remain for understanding cognitive processes that are probably mediated by neurons with more complex physiological response properties. Currently available strategies may prove inadequate for determining how activity in these neurons is causally related to cognitive behaviour.     

Representation of dynamical stimuli in populations of threshold neurons

Many sensory or cognitive events are associated with dynamic current modulations in cortical neurons. This raises an urgent demand for tractable model approaches addressing the merits and limits of potential encoding strategies. Yet, current theoretical approaches addressing the response to mean- and variance-encoded stimuli rarely provide complete response functions for both modes of encoding in the presence of correlated noise. Here, we investigate the neuronal population response to dynamical modifications of the mean or variance of the synaptic bombardment using an alternative threshold model framework. In the variance and mean channel, we provide explicit expressions for the linear and non-linear frequency response functions in the presence of correlated noise and use them to derive population rate response to step-like stimuli. For mean-encoded signals, we find that the complete response function depends only on the temporal width of the input correlation function, but not on other functional specifics. Furthermore, we show that both mean- and variance-encoded signals can relay high-frequency inputs, and in both schemes step-like changes can be detected instantaneously. Finally, we obtain the pairwise spike correlation function and the spike triggered average from the linear mean-evoked response function. These results provide a maximally tractable limiting case that complements and extends previous results obtained in the integrate and fire framework.     

Local feature analysis: a statistical theory for reproducible essential dynamics of large macromolecules

Multivariate statistical methods are widely used to extract functional collective motions from macromolecular molecular dynamics (MD) simulations. In principal component analysis (PCA), a covariance matrix of positional fluctuations is diagonalized to obtain orthogonal eigenvectors and corresponding eigenvalues. The first few eigenvectors usually correspond to collective modes that approximate the functional motions in the protein. However, PCA representations are globally coherent by definition and, for a large biomolecular system, do not converge on the time scales accessible to MD. Also, the forced orthogonalization of modes leads to complex dependencies that are not necessarily consistent with the symmetry of biological macromolecules and assemblies. Here, we describe for the first time the application of local feature analysis (LFA) to construct a topographic representation of functional dynamics in terms of local features. The LFA representations are low dimensional, and like PCA provide a reduced basis set for collective motions, but they are sparsely distributed and spatially localized. This yields a more reliable assignment of essential dynamics modes across different MD time windows. Also, the intrinsic dynamics of local domains is more extensively sampled than that of globally coherent PCA modes.     

Complex processes from dynamical architectures with time-scale hierarchy

The idea that complex motor, perceptual, and cognitive behaviors are composed of smaller units, which are somehow brought into a meaningful relation, permeates the biological and life sciences. However, no principled framework defining the constituent elementary processes has been developed to this date. Consequently, functional configurations (or architectures) relating elementary processes and external influences are mostly piecemeal formulations suitable to particular instances only. Here, we develop a general dynamical framework for distinct functional architectures characterized by the time-scale separation of their constituents and evaluate their efficiency. Thereto, we build on the (phase) flow of a system, which prescribes the temporal evolution of its state variables. The phase flow topology allows for the unambiguous classification of qualitatively distinct processes, which we consider to represent the functional units or modes within the dynamical architecture. Using the example of a composite movement we illustrate how different architectures can be characterized by their degree of time scale separation between the internal elements of the architecture (i.e. the functional modes) and external interventions. We reveal a tradeoff of the interactions between internal and external influences, which offers a theoretical justification for the efficient composition of complex processes out of non-trivial elementary processes or functional modes.     

Biophysical models of fMRI responses

Functional magnetic resonance imaging (fMRI) is used to investigate where the neural implementation of specific cognitive processes occurs. The standard approach uses linear convolution models that relate experimentally designed inputs, through a haemodynamic response function, to observed blood oxygen level dependent (BOLD) signals. Such models are, however, blind to the causal mechanisms that underlie observed BOLD responses. Recent developments have focused on how BOLD responses are generated and include biophysical input-state-output models with neural and haemodynamic state equations and models of functional integration that explain local dynamics through interactions with remote areas. Forward models with parameters at the neural level, such as dynamic causal modelling, combine both approaches, modelling the whole causal chain from external stimuli, via induced neural dynamics, to observed BOLD responses.     

Minimum-order Wiener modelling of spike-output systems

Systems that generate spike outputs in response to continuous inputs abound in neurophysiology. The study of their dynamics with the use of systems analysis methods has been complicated by the difference in modality of the input and output signals. When the problem is placed in the framework of Wiener's theory in discrete time, an infinite functional series is required for the formal representation of the input-output relation. This has given rise to the belief that a large number of Wiener functionals is needed in practice before a model of reasonable accuracy can be obtained. In this paper, we introduce the concept of minimum-order Wiener models for spike-output systems, and we show that a low-order Wiener model is adequate in many cases for predicting fully the timing of the output spikes.     

Coupling of sympathetic nerve traffic and BP at very low frequencies is mediated by large-amplitude events

This study explores the functional association between renal sympathetic nerve traffic (NT) and arterial blood pressure (BP) in the very-low-frequency range (i.e., <0.1 Hz). NT and BP (n = 6) or BP alone (n = 17) was recorded in unanesthetized rats (n = 6). Data were collected for 2-5 h, and wavelet transforms were calculated from data epochs of up to 1 h. From these transforms, we obtained probability distributions for fluctuation amplitudes over a range of time scales. We also computed the cross-wavelet power spectrum between NT and BP to detect the occurrence in time of large-amplitude transient events that may be important in the autonomic regulation of BP. Finally, we computed a time sequence of cross correlations between NT and BP to follow the relationship between NT and BP in time. We found that NT and BP follow comparable self-similar scaling relationships (i.e., NT and BP fluctuations exhibit a certain type of power law behavior). Scaling of this nature 1) points to underlying dynamics over a wide range of scales and 2) is related to large-amplitude events that contribute to the very-low-frequency variability of NT and BP. There is a strong correlation between NT and BP during many of these transient events. These strong correlations and the uniformity in scaling imply a functional connection between these two signals at frequencies where we previously found no connection using spectral coherence.     

Mode switching of Inositol 1,4,5-trisphosphate receptor channel shapes the Spatiotemporal scales of Ca<Superscript>2+</Superscript> signals

The inositol 1,4,5-trisphosphate (InsP₃) receptor (InsP₃R) channel is crucial for the generation and modulation of highly specific intracellular Ca²⁺ signals performing numerous functions in animal cells. However, the single channel behavior during Ca²⁺ signals of different spatiotemporal scales is not well understood. To elucidate the correlation between the gating dynamics of single InsP₃Rs and spatiotemporal Ca²⁺ patterns, we simulate a cluster of InsP₃Rs under varying ligand concentrations and extract comprehensive gating statistics of all channels during events of different sizes and durations. Our results show that channels gating predominantly in the low activity mode with negligible occupancy of intermediate and high modes leads to single channel Ca²⁺ release event blips. Increasing occupancies of intermediate and high modes results in events with increasing size. When the channel has more than 50% probability of gating in the intermediate and high modes, the cluster generates very large puffs that would most likely result in global Ca²⁺ signals. The size, duration and frequency of Ca²⁺ signals all increase linearly with the total probability of channel gating in the intermediate and high modes. To our knowledge, this is the first study that quantitatively relates the modal characteristics of InsP₃R to the shaping of different spatiotemporal scales of Ca²⁺ signals.     

Coping with variability in small neuronal networks

Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.     

Syntactic sequencing in Hebbian cell assemblies

Hebbian cell assemblies provide a theoretical framework for the modeling of cognitive processes that grounds them in the underlying physiological neural circuits. Recently we have presented an extension of cell assemblies by operational components which allows to model aspects of language, rules, and complex behaviour. In the present work we study the generation of syntactic sequences using operational cell assemblies timed by unspecific trigger signals. Syntactic patterns are implemented in terms of hetero-associative transition graphs in attractor networks which cause a directed flow of activity through the neural state space. We provide regimes for parameters that enable an unspecific excitatory control signal to switch reliably between attractors in accordance with the implemented syntactic rules. If several target attractors are possible in a given state, noise in the system in conjunction with a winner-takes-all mechanism can randomly choose a target. Disambiguation can also be guided by context signals or specific additional external signals. Given a permanently elevated level of external excitation the model can enter an autonomous mode, where it generates temporal grammatical patterns continuously.     

Task-Driven Activity Reduces the Cortical Activity Space of the Brain: Experiment and Whole-Brain Modeling

How a stimulus or a task alters the spontaneous dynamics of the brain remains a fundamental open question in neuroscience. One of the most robust hallmarks of task/stimulus-driven brain dynamics is the decrease of variability with respect to the spontaneous level, an effect seen across multiple experimental conditions and in brain signals observed at different spatiotemporal scales. Recently, it was observed that the trial-to-trial variability and temporal variance of functional magnetic resonance imaging (fMRI) signals decrease in the task-driven activity. Here we examined the dynamics of a large-scale model of the human cortex to provide a mechanistic understanding of these observations. The model allows computing the statistics of synaptic activity in the spontaneous condition and in putative tasks determined by external inputs to a given subset of brain regions. We demonstrated that external inputs decrease the variance, increase the covariances, and decrease the autocovariance of synaptic activity as a consequence of single node and large-scale network dynamics. Altogether, these changes in network statistics imply a reduction of entropy, meaning that the spontaneous synaptic activity outlines a larger multidimensional activity space than does the task-driven activity. We tested this model’s prediction on fMRI signals from healthy humans acquired during rest and task conditions and found a significant decrease of entropy in the stimulus-driven activity. Altogether, our study proposes a mechanism for increasing the information capacity of brain networks by enlarging the volume of possible activity configurations at rest and reliably settling into a confined stimulus-driven state to allow better transmission of stimulus-related information.     

Coupling between global dynamics and signal transduction pathways: a mechanism of allostery for chaperonin GroEL

Despite significant efforts toward understanding the molecular basis of allosteric communication, the mechanisms by which local energetic and conformational changes cooperatively diffuse from ligand-binding sites to distal regions across the 3-dimensional structure of allosteric proteins remain to be established. Recent experimental and theoretical evidence supports the view that allosteric communication is facilitated by the intrinsic ability of the biomolecules to undergo collective changes in structure, triggered by ligand binding. Two groups of studies recently proved to provide insights into such intrinsic, structure-induced effects: elastic network models that permit us to visualize the cooperative changes in conformation that are most readily accessible near native state conditions, and information-theoretic approaches that elucidate the most efficient pathways of signal transmission favored by the overall architecture. Using a combination of these two approaches, we highlight, by way of application to the bacterial chaperonin complex GroEL-GroES, how the most cooperative modes of motion play a role in mediating the propagation of allosteric signals. A functional coupling between the global dynamics sampled under equilibrium conditions and the signal transduction pathways inherently favored by network topology appears to control allosteric effects.     

Combined experimental and computational analysis of DNA damage signaling reveals context‐dependent roles for Erk in apoptosis and G1/S arrest after genotoxic stress

Following DNA damage, cells display complex multi‐pathway signaling dynamics that connect cell‐cycle arrest and DNA repair in G1, S, or G2/M phase with phenotypic fate decisions made between survival, cell‐cycle re‐entry and proliferation, permanent cell‐cycle arrest, or cell death. How these phenotypic fate decisions are determined remains poorly understood, but must derive from integrating genotoxic stress signals together with inputs from the local microenvironment. To investigate this in a systematic manner, we undertook a quantitative time‐resolved cell signaling and phenotypic response study in U2OS cells receiving doxorubicin‐induced DNA damage in the presence or absence of TNFα co‐treatment; we measured key nodes in a broad set of DNA damage signal transduction pathways along with apoptotic death and cell‐cycle regulatory responses. Two relational modeling approaches were then used to identify network‐level relationships between signals and cell phenotypic events: a partial least squares regression approach and a complementary new technique which we term ‘time‐interval stepwise regression.’ Taken together, the results from these analysis methods revealed complex, cytokine‐modulated inter‐relationships among multiple signaling pathways following DNA damage, and identified an unexpected context‐dependent role for Erk in both G1/S arrest and apoptotic cell death following treatment with this commonly used clinical chemotherapeutic drug.     

Dynamics of spiking neurons: between homogeneity and synchrony

Randomly connected networks of neurons driven by Poisson inputs are often assumed to produce “homogeneous” dynamics, characterized by largely independent firing and approximable by diffusion processes. At the same time, it is well known that such networks can fire synchronously. Between these two much studied scenarios lies a vastly complex dynamical landscape that is relatively unexplored. In this paper, we discuss a phenomenon which commonly manifests in these intermediate regimes, namely brief spurts of spiking activity which we call multiple firing events (MFE). These events do not depend on structured network architecture nor on structured input; they are an emergent property of the system. We came upon them in an earlier modeling paper, in which we discovered, through a careful benchmarking process, that MFEs are the single most important dynamical mechanism behind many of the V1 phenomena we were able to replicate. In this paper we explain in a simpler setting how MFEs come about, as well as their potential dynamic consequences. Although the mechanism underlying MFEs cannot easily be captured by current population dynamics models, this phenomena should not be ignored during analysis; there is a growing body of evidence that such collaborative activity may be a key towards unlocking the possible functional properties of many neuronal networks.     

Multimodal sensory integration in insects--towards insect brain control architectures

Although a variety of basic insect behaviours have inspired successful robot implementations, more complex capabilities in these 'simple' animals are often overlooked. By reviewing the general architecture of their nervous systems, we gain insight into how they are able to integrate behaviours, perform pattern recognition, context-dependent learning, and combine many sensory inputs in tasks such as navigation. We review in particular what is known about two specific 'higher' areas in the insect brain, the mushroom bodies and the central complex, and how they are involved in controlling an insect's behaviour. While much of the functional interpretation of this information is still speculative, it nevertheless suggests some promising new approaches to obtaining adaptive behaviour in robots.     

Resting-State Temporal Synchronization Networks Emerge from Connectivity Topology and Heterogeneity

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain’s anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.     

Functional Connectivity in MRI Is Driven by Spontaneous BOLD Events

Functional brain signals are frequently decomposed into a relatively small set of large scale, distributed cortical networks that are associated with different cognitive functions. It is generally assumed that the connectivity of these networks is static in time and constant over the whole network, although there is increasing evidence that this view is too simplistic. This work proposes novel techniques to investigate the contribution of spontaneous BOLD events to the temporal dynamics of functional connectivity as assessed by ultra-high field functional magnetic resonance imaging (fMRI). The results show that: 1) spontaneous events in recognised brain networks contribute significantly to network connectivity estimates; 2) these spontaneous events do not necessarily involve whole networks or nodes, but clusters of voxels which act in concert, forming transiently synchronising sub-networks and 3) a task can significantly alter the number of localised spontaneous events that are detected within a single network. These findings support the notion that spontaneous events are the main driver of the large scale networks that are commonly detected by seed-based correlation and ICA. Furthermore, we found that large scale networks are manifestations of smaller, transiently synchronising sub-networks acting dynamically in concert, corresponding to spontaneous events, and which do not necessarily involve all voxels within the network nodes oscillating in unison.     

Covariations between pupil diameter and supplementary eye field activity suggest a role in cognitive effort implementation

In both human and nonhuman primates (NHP), the medial prefrontal region, defined as the supplementary eye field (SEF), can indirectly influence behavior selection through modulation of the primary selection process in the oculomotor structures. To perform this oculomotor control, SEF integrates multiple cognitive signals such as attention, memory, reward, and error. As changes in pupil responses can assess these cognitive efforts, a better understanding of the precise dynamics by which pupil diameter and medial prefrontal cortex activity interact requires thorough investigations before, during, and after changes in pupil diameter. We tested whether SEF activity is related to pupil dynamics during a mixed pro/antisaccade oculomotor task in 2 macaque monkeys. We used functional ultrasound (fUS) imaging to examine temporal changes in brain activity at the 0.1-s time scale and 0.1-mm spatial resolution concerning behavioral performance and pupil dynamics. By combining the pupil signals and real-time imaging of NHP during cognitive tasks, we were able to infer localized cerebral blood volume (CBV) responses within a restricted part of the dorsomedial prefrontal cortex, referred to as the SEF, an area in which antisaccade preparation activity is also recorded. Inversely, SEF neurovascular activity measured by fUS imaging was found to be a robust predictor of specific variations in pupil diameter over short and long-time scales. Furthermore, we directly manipulated pupil diameter and CBV in the SEF using reward modulations. These results bring a novel understanding of the physiological links between pupil and SEF, but it also raises questions about the role of anterior cingulate cortex (ACC), as CBV variations in the ACC seems to be negligible compared to CBV variations in the SEF.

Ultrafast functional imaging reveals short- and long-term covariations between pupil diameter and activity in the Supplementary Eye Field (SEF) of awake behaving non-human primates, yielding a novel understanding of the physiological links between the pupil and SEF.