Nonlinear Dynamics of Emotion-Cognition Interaction: When Emotion Does not Destroy Cognition?

Emotion (i.e., spontaneous motivation and subsequent implementation of a behavior) and cognition (i.e., problem solving by information processing) are essential to how we, as humans, respond to changes in our environment. Recent studies in cognitive science suggest that emotion and cognition are subserved by different, although heavily integrated, neural systems. Understanding the time-varying relationship of emotion and cognition is a challenging goal with important implications for neuroscience. We formulate here the dynamical model of emotion-cognition interaction that is based on the following principles: (1) the temporal evolution of cognitive and emotion modes are captured by the incoming stimuli and competition within and among themselves (competition principle); (2) metastable states exist in the unified emotion-cognition phase space; and (3) the brain processes information with robust and reproducible transients through the sequence of metastable states. Such a model can take advantage of the often ignored temporal structure of the emotion-cognition interaction to provide a robust and generalizable method for understanding the relationship between brain activation and complex human behavior. The mathematical image of the robust and reproducible transient dynamics is a Stable Heteroclinic Sequence (SHS), and the Stable Heteroclinic Channels (SHCs). These have been hypothesized to be possible mechanisms that lead to the sequential transient behavior observed in networks. We investigate the modularity of SHCs, i.e., given a SHS and a SHC that is supported in one part of a network, we study conditions under which the SHC pertaining to the cognition will continue to function in the presence of interfering activity with other parts of the network, i.e., emotion.     

Metastable states, phase transitions, and persistent neural activity

A new mathematical model to describe the spiking rate of a neural population is derived, which considers both the mean and the variance of the activity. Bifurcation analysis identifies a critical interval of parameter values in which the standard bistability regime coexists with an additional third attractor corresponding to the metastable state of bounded mean activity and high variance. To understand the structure of spatio-temporal activity in the metastable state, we study a simple discrete-time model of binary elements with random noise locally coupled on the grid, which produces rich dynamics including metastability. A critical value of the noise amplitude is identified; in the vicinity of this value the system is flexible and can easily generate transitions between UP and DOWN metastable states, either autonomously or in response to a control process. These metastable states and phase transitions provide a proper basis for the modelling of persistent neural activity reported in many experimental studies.     

Critical slowing down and noise-induced intermittency in bistable perception: bifurcation analysis

Stochastic dynamics and critical slowing down were studied experimentally and numerically near the onset of dynamical bistability in visual perception under the influence of noise. Exploring the Necker cube as the essential example of an ambiguous figure, and using its wire contrast as a control parameter, we measured dynamical hysteresis in two coexisting percepts as a function of both the velocity of the parameter change and the background luminance. The bifurcation analysis allowed us to estimate the level of cognitive noise inherent to brain neural cells activity, which induced intermittent switches between different perception states. The results of numerical simulations with a simple energy model are in good qualitative agreement with psychological experiments.     

A modular latching chain

Many cognitive tasks involve transitions between distinct mental processes, which may range from discrete states to complex strategies. The ability of cortical networks to combine discrete jumps with continuous glides along ever changing trajectories, dubbed latching dynamics, may be essential for the emergence of the unique cognitive capacities of modern humans. Novel trajectories have to be followed in the multidimensional space of cortical activity for novel behaviours to be produced; yet, not everything changes: several lines of evidence point at recurring patterns in the sequence of activation of cortical areas in a variety of behaviours. To extend a mathematical model of latching dynamics beyond the simple unstructured auto-associative Potts network previously analysed, we introduce delayed structured connectivity and hetero-associative connection weights, and we explore their effects on the dynamics. A modular model in the small-world regime is considered, with modules arranged on a ring. The synaptic weights include a standard auto-associative component, stabilizing distinct patterns of activity, and a hetero-associative component, favoring transitions from one pattern, expressed in one module, to the next, in the next module. We then study, through simulations, how structural parameters, like those regulating rewiring probability, noise and feedback connections, determine sequential association dynamics.     

In vivo calcium dynamics during neural crest cell migration and patterning using GCaMP3

Examining calcium dynamics within the neural crest (NC) has the potential to shed light on mechanisms that regulate complex cell migration and patterning events during embryogenesis. Unfortunately, typical calcium indicators are added to culture media or have low signal to noise after microinjection into tissue that severely limit analyses to cultured cells or superficial events. Here, we studied in vivo calcium dynamics during NC cell migration and patterning, using a genetically encoded calcium sensor, GCaMP3. We discovered that trunk NC cells displayed significantly more spontaneous calcium transients than cranial NC cells, and during cell aggregation versus cell migration events. Spontaneous calcium transients were more prevalent during NC cell aggregation into discrete sympathetic ganglia (SG). Blocking of N-cadherin activity in trunk NC cells near the presumptive SG led to a dramatic decrease in the frequency of spontaneous calcium transients. Detailed analysis and mathematical modeling of cell behaviors during SG formation showed NC cells aggregated into clusters after displaying a spontaneous calcium transient. This approach highlights the novel application of a genetically encoded calcium indicator to study subsets of cells during ventral events in embryogenesis.     

The logical analysis of continuous, non-linear biochemical control networks

We propose a mapping to study the qualitative properties of continuous biochemical control networks which are invariant to the parameters used to describe the networks but depend only on the logical structure of the networks. For the networks, we are able to place a lower limit on the number of steady states and strong restrictions on the phase relations between components on cycles and transients. The logical structure and the dynamical behavior for a number of simple systems of biological interest, the feedback (predator-prey) oscillator, the bistable switch, the phase dependent switch, are discussed. We discuss the possibility that these techniques may be extended to study the dynamics of large many component systems.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

Sudden Shifts in Ecological Systems: Intermittency and Transients in the Coupled Ricker Population Model

Many real ecological systems show sudden changes in behavior, phenomena sometimes categorized as regime shifts in the literature. The relative importance of exogenous versus endogenous forces producing regime shifts is an important question. These forces’ role in generating variability over time in ecological systems has been explored using tools from dynamical systems. We use similar ideas to look at transients in simple ecological models as a way of understanding regime shifts. Based in part on the theory of crises, we carefully analyze a simple two patch spatial model and begin to understand from a mathematical point of view what produces transient behavior in ecological systems. In particular, since the tools are essentially qualitative, we are able to suggest that transient behavior should be ubiquitous in systems with overcompensatory local dynamics, and thus should be typical of many ecological systems. This work has been supported by NSF Grant EF-0434266.     

The control of seizure-like activity in the rat hippocampal slice

The sudden and transient hypersynchrony of neuronal firing that characterizes epileptic seizures can be considered as the transitory stabilization of metastable states present within the dynamical repertoire of a neuronal network. Using an in vitro model of recurrent spontaneous seizures in the rat horizontal hippocampal slice preparation, we present an approach to characterize the dynamics of the transition to seizure, and to use this information to control the activity and avoid the occurrence of seizure-like events. The transition from the interictal activity (between seizures) to the seizure-like event is aborted by brief (20-50 s) low-frequency (0.5 Hz) periodic forcing perturbations, applied via an extracellular stimulating electrode to the mossy fibers, the axons of the dentate neurons that synapse onto the CA3 pyramidal cells. This perturbation results in the stabilization of an interictal-like low-frequency firing pattern in the hippocampal slice. The results derived from this work shed light on the dynamics of the transition to seizure and will further the development of algorithms that can be used in automated devices to stop seizure occurrence.     

Stochastic Dynamics Underlying Cognitive Stability and Flexibility

Cognitive stability and flexibility are core functions in the successful pursuit of behavioral goals. While there is evidence for a common frontoparietal network underlying both functions and for a key role of dopamine in the modulation of flexible versus stable behavior, the exact neurocomputational mechanisms underlying those executive functions and their adaptation to environmental demands are still unclear. In this work we study the neurocomputational mechanisms underlying cue based task switching (flexibility) and distractor inhibition (stability) in a paradigm specifically designed to probe both functions. We develop a physiologically plausible, explicit model of neural networks that maintain the currently active task rule in working memory and implement the decision process. We simplify the four-choice decision network to a nonlinear drift-diffusion process that we canonically derive from a generic winner-take-all network model. By fitting our model to the behavioral data of individual subjects, we can reproduce their full behavior in terms of decisions and reaction time distributions in baseline as well as distractor inhibition and switch conditions. Furthermore, we predict the individual hemodynamic response timecourse of the rule-representing network and localize it to a frontoparietal network including the inferior frontal junction area and the intraparietal sulcus, using functional magnetic resonance imaging. This refines the understanding of task-switch-related frontoparietal brain activity as reflecting attractor-like working memory representations of task rules. Finally, we estimate the subject-specific stability of the rule-representing attractor states in terms of the minimal action associated with a transition between different rule states in the phase-space of the fitted models. This stability measure correlates with switching-specific thalamocorticostriatal activation, i.e., with a system associated with flexible working memory updating and dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences.     

Increased Firing Irregularity as an Emergent Property of Neural-State Transition in Monkey Prefrontal Cortex

Flexible behaviors are organized by complex neural networks in the prefrontal cortex. Recent studies have suggested that such networks exhibit multiple dynamical states, and can switch rapidly from one state to another. In many complex systems such as the brain, the early-warning signals that may predict whether a critical threshold for state transitions is approaching are extremely difficult to detect. We hypothesized that increases in firing irregularity are a crucial measure for predicting state transitions in the underlying neuronal circuits of the prefrontal cortex. We used both experimental and theoretical approaches to test this hypothesis. Experimentally, we analyzed activities of neurons in the prefrontal cortex while monkeys performed a maze task that required them to perform actions to reach a goal. We observed increased firing irregularity before the activity changed to encode goal-to-action information. Theoretically, we constructed theoretical generic neural networks and demonstrated that changes in neuronal gain on functional connectivity resulted in a loss of stability and an altered state of the networks, accompanied by increased firing irregularity. These results suggest that assessing the temporal pattern of neuronal fluctuations provides important clues regarding the state stability of the prefrontal network. We also introduce a novel scheme that the prefrontal cortex functions in a metastable state near the critical point of bifurcation. According to this scheme, firing irregularity in the prefrontal cortex indicates that the system is about to change its state and the flow of information in a flexible manner, which is essential for executive functions. This metastable and/or critical dynamical state of the prefrontal cortex may account for distractibility and loss of flexibility in the prefrontal cortex in major mental illnesses such as schizophrenia.     

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.     

Ultrafast dynamics-driven biomolecular recognition where fast activities dictate slow events

In general, biological macromolecules require significant dynamical freedom to carry out their different functions, including signal transduction, metabolism, catalysis and gene regulation. Effectors (ligands, DNA and external milieu, etc) are considered to function in a purely dynamical manner by selectively stabilizing a specific dynamical state, thereby regulating biological function. In particular, proteins in presence of these effectors can exist in several dynamical states with distinct binding or enzymatic activity. Here, we have reviewed the efficacy of ultrafast fluorescence spectroscopy to monitor the dynamical flexibility of various proteins in presence of different effectors leading to their biological activity. Recent studies demonstrate the potency of a combined approach involving picosecond-resolved Förster resonance energy transfer, polarisation-gated fluorescence and time-dependent stokes shift for the exploration of ultrafast dynamics in biomolecular recognition of various protein molecules. The allosteric protein–protein recognition following differential protein–DNA interaction is shown to be a consequence of some ultrafast segmental motions at the C-terminal of Gal repressor protein dimer with DNA operator sequences O_E and O_I. Differential ultrafast dynamics at the C-terminal of λ-repressor protein with two different operator DNA sequences for the protein–protein interaction with different strengths is also reviewed. We have also systemically briefed the study on the role of ultrafast dynamics of water molecules on the functionality of enzyme proteins α-chymotrypsin and deoxyribonuclease I. The studies on the essential ultrafast dynamics at the active site of the enzyme α-chymotrypsin by using an anthraniloyl fluorescent extrinsic probe covalently attached to the serine-195 residue for the enzymatic activity at homeothermic condition has also been reviewed. Finally, we have highlighted the evidence that a photoinduced dynamical event dictates the molecular recognition of a photochromic ligand, dihydroindolizine with the serine protease α-chymotrypsin and with a liposome (L-α-phosphatidylcholine).     

Generation and reshaping of sequences in neural systems

The generation of informational sequences and their reorganization or reshaping is one of the most intriguing subjects for both neuroscience and the theory of autonomous intelligent systems. In spite of the diversity of sequential activities of sensory, motor, and cognitive neural systems, they have many similarities from the dynamical point of view. In this review we discus the ideas, models, and mathematical image of sequence generation and reshaping on different levels of the neural hierarchy, i.e., the role of a sensory network dynamics in the generation of a motor program (hunting swimming of marine mollusk Clione), olfactory dynamical coding, and sequential learning and decision making. Analysis of these phenomena is based on the winnerless competition principle. The considered models can be a basis for the design of biologically inspired autonomous intelligent systems.     

The nature of folded states of globular proteins.

We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.     

An optimization framework of biological dynamical systems

Different biological dynamics are often described by different mathematical equations. On the other hand, some mathematical models describe many biological dynamics universally. Here, we focus on three biological dynamics: the Lotka-Volterra equation, the Hopfield neural networks, and the replicator equation. We describe these three dynamical models using a single optimization framework, which is constructed with employing the Riemannian geometry. Then, we show that the optimization structures of these dynamics are identical, and the differences among the three dynamics are only in the constraints of the optimization. From this perspective, we discuss the unified view for biological dynamics. We also discuss the plausible categorizations, the fundamental nature, and the efficient modeling of the biological dynamics, which arise from the optimization perspective of the dynamical systems.     

Computing the heteroclinic bifurcation curves in predator–prey systems with ratio-dependent functional response

Predator-prey models with Michaelis-Menten-Holling type ratio- dependent functional response exhibit very rich and complex dynamical behavior, such as the existence of degenerate equilibria, appearance of limit cycles and heteroclinic loops, and the coexistence of two attractive equilibria. In this paper, we study heteroclinic bifurcations of such a predator-prey model. We first calculate the higher order Melnikov functions by transforming the model into a Hamiltonian system and then provide an algorithm for computing higher order approximations of the heteroclinic bifurcation curves.