Two-phase strategy of controlling motor coordination determined by task performance optimality

A quantitative model of optimal coordination between hand transport and grip aperture has been derived in our previous studies of reach-to-grasp movements without utilizing explicit knowledge of the optimality criterion or motor plant dynamics. The model’s utility for experimental data analysis has been demonstrated. Here we show how to generalize this model for a broad class of reaching-type, goal-directed movements. The model allows for measuring the variability of motor coordination and studying its dependence on movement phase. The experimentally found characteristics of that dependence imply that execution noise is low and does not affect motor coordination significantly. From those characteristics it is inferred that the cost of neural computations required for information acquisition and processing is included in the criterion of task performance optimality as a function of precision demand for state estimation and decision making. The precision demand is an additional optimized control variable that regulates the amount of neurocomputational resources activated dynamically. It is shown that an optimal control strategy in this case comprises two different phases. During the initial phase, the cost of neural computations is significantly reduced at the expense of reducing the demand for their precision, which results in speed-accuracy tradeoff violation and significant inter-trial variability of motor coordination. During the final phase, neural computations and thus motor coordination are considerably more precise to reduce the cost of errors in making a contact with the target object. The generality of the optimal coordination model and the two-phase control strategy is illustrated on several diverse examples.     

Coordination dynamics: (in)stability and metastability in the behavioural and neural systems

For more than 20 years, coordination dynamics have provided research on human movement science with new views about the nonlinear relationships between behavioral and neural dynamics. A number of studies across various experimental settings including bimanual, postural or interpersonal coordination, and also coordination between movements of a limb and an external event in the environment revealed the self-organized nature of human coordination. Here we review an extensive body of literature - in the human movement science and the neuroscience fields - that has investigated the coordination dynamics of brain and behavior when individuals are involved in two rhythmic coordination patterns: synchronization (on-the-beat movements) and syncopation (in-between beats movements). When the frequency of movement approaches 2 Hz, the syncopation mode is destabilized and synchronization is spontaneously adopted. The abrupt change between the two patterns illustrates a phenomenon known as non-equilibrium phase transition. Phase transitions offer a novel entry point into the investigation of pattern formation (and dissolution) at both the behavioral and the cerebral levels as they illustrate the loss of stability of the system. Brain imaging methods (MEG, EEG and fMRI) were used to reveal the neural signatures of (in)stability underlying the differences between behavioral coordination patterns, and pointed at the role of self-organization and metastability principles in brain functioning. Relationships between behavioral and brain dynamics can therefore be investigated within a unified empirical and theoretical framework.     

A Common Neurodynamical Mechanism Could Mediate Externally Induced and Intrinsically Generated Transitions in Visual Awareness

The neural correlates of conscious visual perception are commonly studied in paradigms of perceptual multistability that allow multiple perceptual interpretations during unchanged sensory stimulation. What is the source of this multistability in the content of perception? From a theoretical perspective, a fine balance between deterministic and stochastic forces has been suggested to underlie the spontaneous, intrinsically driven perceptual transitions observed during multistable perception. Deterministic forces are represented by adaptation of feature-selective neuronal populations encoding the competing percepts while stochastic forces are modeled as noise-driven processes. Here, we used a unified neuronal competition model to study the dynamics of adaptation and noise processes in binocular flash suppression (BFS), a form of externally induced perceptual suppression, and compare it with the dynamics of intrinsically driven alternations in binocular rivalry (BR). For the first time, we use electrophysiological, biologically relevant data to constrain a model of perceptual rivalry. Specifically, we show that the mean population discharge pattern of a perceptually modulated neuronal population detected in electrophysiological recordings in the lateral prefrontal cortex (LPFC) during BFS, constrains the dynamical range of externally induced perceptual transitions to a region around the bifurcation separating a noise-driven attractor regime from an adaptation-driven oscillatory regime. Most interestingly, the dynamical range of intrinsically driven perceptual transitions during BR is located in the noise-driven attractor regime, where it overlaps with BFS. Our results suggest that the neurodynamical mechanisms of externally induced and spontaneously generated perceptual alternations overlap in a narrow, noise-driven region just before a bifurcation where the system becomes adaptation-driven.     

Six types of multistability in a neuronal model based on slow calcium current

Background

Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings

Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions

We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.     

A neural network model for stroboscopic alternative motion

A neural network which models multistable perception is presented. The network consists of sensor and inner neurons. The dynamics is established by a stochastic neuronal dynamics, a formal Hebb-type coupling dynamics and a resource mechanism that corresponds to saturation effects in perception. From this a system of coupled differential equations is derived and analyzed. Single stimuli are bound to exactly one percept, even in ambiguous situations where multistability occurs. The network exhibits discontinuous as well as continuous phase transitions and models various empirical findings, including the percepts of succession, alternative motion and simultaneity; the percept of oscillation is explained by oscillating percepts at a continuous phase transition. Received: 13 September 1995 / Accepted: 3 June 1996     

Variability of perceptual multistability: from brain state to individual trait

Few phenomena are as suitable as perceptual multistability to demonstrate that the brain constructively interprets sensory input. Several studies have outlined the neural circuitry involved in generating perceptual inference but only more recently has the individual variability of this inferential process been appreciated. Studies of the interaction of evoked and ongoing neural activity show that inference itself is not merely a stimulus-triggered process but is related to the context of the current brain state into which the processing of external stimulation is embedded. As brain states fluctuate, so does perception of a given sensory input. In multistability, perceptual fluctuation rates are consistent for a given individual but vary considerably between individuals. There has been some evidence for a genetic basis for these individual differences and recent morphometric studies of parietal lobe regions have identified neuroanatomical substrates for individual variability in spontaneous switching behaviour. Moreover, disrupting the function of these latter regions by transcranial magnetic stimulation yields systematic interference effects on switching behaviour, further arguing for a causal role of these regions in perceptual inference. Together, these studies have advanced our understanding of the biological mechanisms by which the brain constructs the contents of consciousness from sensory input.     

How do neural connectivity and time delays influence bimanual coordination?

Multilevel crosstalk as a neural basis for motor control has been widely discussed in the literature. Since no natural process is instantaneous, any crosstalk model should incorporate time delays, which are known to induce temporal coupling between functional elements and stabilize or destabilize a particular mode of coordination. In this article, we systematically study the dynamics of rhythmic bimanual coordination under the influence of varying connection topology as realized by callosal fibers, cortico-thalamic projections, and crossing peripheral fibers. Such connectivity contributes to various degrees of neural crosstalk between the effectors which we continuously parameterize in a mathematical model. We identify the stability regimes of bimanual coordination as a function of the degree of neural crosstalk, movement amplitude and the time delays involved due to signal processing. Prominent examples include explanations of the decreased stability of the antiphase mode of coordination in split brain patients and the role of coupling in mediating bimanual coordination.     

Dynamics and bifurcations of two coupled neural oscillators with different connection types

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.     

Multistability property in cardiac ionic models of mammalian and human ventricular cells

The underlying mechanisms of irregular cardiac rhythms are still poorly understood. Many experimental and modeling studies are aimed at identifying factors which cause cardiac arrhythmias. However, a lack of understanding of heart rhythm dynamical properties makes it difficult to uncover precise mechanisms of electrical instabilities, and hence to predict the onset of heart rhythm disorders. We review and compare the existing methods of studying cardiac dynamics, including restitution protocol (S1-S2), dynamic restitution protocol and multistability test protocol (S1-CI-S2). We focus on cardiac cell dynamics to elucidate regularities of heart rhythm. We demonstrate the advantages of our newly proposed systematic approach of analysis of cardiac cell dynamics using mammalian Luo Rudy 1991 and human ventricular Ten Tusscher 2006 single cell models under healthy and diseased conditions such as altered K⁺ or Ca²⁺ related currents. We investigate the role of ionic properties and the shape of an action potential on the nonlinear dynamics of electrical processes in periodically stimulated cardiac cells. We show the existence of multistability property for human ventricular cells. Moreover, the multistability is proposed to be an intrinsic property of cardiac cells, and is also suggested to be one of the mechanisms which could underlie the sudden triggering of life-threatening ventricular arrhythmias in the human heart.     

Quantifying the impact of ecological memory on the dynamics of interacting communities

Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications.Recent modeling studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can be introduced in such models using the framework of fractional calculus. We study how the dynamics of a well-characterized interaction model is affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity.Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory introduces inertia into the dynamics. This favors species coexistence under perturbation, enhances system resistance to state shifts, mitigates hysteresis, and can affect system resilience both ways depending on the time scale considered. Memory also promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Our study highlights the fundamental role of memory in communities, and provides quantitative tools to introduce it in ecological models and analyse its impact under varying conditions.     

Observation of Optical Bistability in a Polaritonic Material Doped with Nanoparticles

We study the optical bistability and multistability in a defect structure doped with polaritonic materials and three-level nanoparticles. It is realized that the threshold of optical bistability can be manipulated by some controllable parameters such as Rabi frequency, line width of upper level, and thickness of defect structure. Due to dense doping of three-level nanoparticles, the dipole-dipole interactions (DDI) between nanoparticles become important. Therefore, the DDI has been considered as an interesting mechanism for transition from optical bistability to multistability. The line width effect of upper level and thickness of defect structure on threshold of optical multistability has also been investigated. We hope that our proposed model may be useful for developing the future all-optical devices in nanoscales.

     

Collective decision‐making and fission–fusion dynamics: a conceptual framework

Sociality exists in an extraordinary range of ecological settings. For individuals to accrue the benefits associated with social interactions, they are required to maintain a degree of spatial and temporal coordination in their activities, and make collective decisions. Such coordination and decision‐making has been the focus of much recent research. However, efforts largely have been directed toward understanding patterns of collective behaviour in relatively stable and cohesive groups. Less well understood is how fission–fusion dynamics mediate the process and outcome of collective decisions making. Here, we aim to apply established concepts and knowledge to highlight the implications of fission–fusion dynamics for collective decisions, presenting a conceptual framework based on the outcome of a small‐group discussion INCORE meeting (funded by the European Community's Sixth Framework Programme). First, we discuss how the degree of uncertainty in the environment shapes social flexibility and therefore the types of decisions individuals make in different social settings. Second, we propose that the quality of social relationships and the energetic needs of each individual influence fission decisions. Third, we explore how these factors affect the probability of individuals to fuse. Fourth, we discuss how group size and fission–fusion dynamics may affect communication processes between individuals at a local or global scale to reach a consensus or to fission. Finally, we offer a number of suggestions for future research, capturing emerging ideas and concepts on the interaction between collective decisions and fission–fusion dynamics.     

Neurodynamics: nonlinear dynamics and neurobiology

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.     

New analysis technique for multistability detection

Systems with counter-clockwise input-output (I-O) dynamics were recently introduced in order to study the convergence of positive feedback loops (possibly to many different equilibrium states). The author shows how this notion can be used to perform bifurcation analysis and globally predict multistability of a closed-loop feedback interconnection just by using the knowledge of steady-state I-O responses of the systems. To illustrate the theory, this method is then applied to a recently published model of mitogen activated protein kinase (MAPK) cascade. Furthermore, some examples (mainly motivated by molecular biology) of systems that enjoy the property are presented and discussed.     

Nonlinear transient computation as a potential "kernel trick" in cortical processing

Evidence has been found for the presence of chaotic dynamics at all levels of the mammalian brain. This has led to some searching questions about the potential role that nonlinear dynamics may have in neural information processing. We propose that chaos equips the brain with the equivalent of a kernel trick for solving hard nonlinear problems. The approach presented, which is described as nonlinear transient computation, uses the dynamics of a well known chaotic attractor. The paper provides experimental results to show that this approach can be used to solve some challenging pattern recognition tasks. The paper also offers evidence to suggest that the efficacy of nonlinear transient computation for nonlinear pattern classification is dependent only on the generic properties of chaotic attractors and is not sensitive to the particular dynamics of specific sub-regions of chaotic phase space. If, as this work suggests, nonlinear transient computation is independent of the particulars of any given chaotic attractor, then it could be offered as a possible explanation of how the chaotic dynamics that have been observed in brain structures contribute to neural information processing tasks.     

Dynamics of excitable neural networks with heterogeneous connectivity

A central issue of neuroscience is to understand how neural units integrates internal and external signals to create coherent states. Recently, it has been shown that the sensitivity and dynamic range of neural assemblies are optimal at a critical coupling among its elements. Complex architectures of connections seem to play a constructive role on the reliable coordination of neural units. Here we show that, the synchronizability and sensitivity of excitable neural networks can be tuned by diversity in the connections strengths. We illustrate our findings for weighted networks with regular, random and complex topologies. Additional comparisons of real brain networks support previous studies suggesting that heterogeneity in the connectivity may play a constructive role on information processing. These findings provide insights into the relationship between structure and function of neural circuits.     

An approximate stochastic optimal control framework to simulate nonlinear neuro-musculoskeletal models in the presence of noise

Optimal control simulations have shown that both musculoskeletal dynamics and physiological noise are important determinants of movement. However, due to the limited efficiency of available computational tools, deterministic simulations of movement focus on accurately modelling the musculoskeletal system while neglecting physiological noise, and stochastic simulations account for noise while simplifying the dynamics. We took advantage of recent approaches where stochastic optimal control problems are approximated using deterministic optimal control problems, which can be solved efficiently using direct collocation. We were thus able to extend predictions of stochastic optimal control as a theory of motor coordination to include muscle coordination and movement patterns emerging from non-linear musculoskeletal dynamics. In stochastic optimal control simulations of human standing balance, we demonstrated that the inclusion of muscle dynamics can predict muscle co-contraction as minimal effort strategy that complements sensorimotor feedback control in the presence of sensory noise. In simulations of reaching, we demonstrated that nonlinear multi-segment musculoskeletal dynamics enables complex perturbed and unperturbed reach trajectories under a variety of task conditions to be predicted. In both behaviors, we demonstrated how interactions between task constraint, sensory noise, and the intrinsic properties of muscle influence optimal muscle coordination patterns, including muscle co-contraction, and the resulting movement trajectories. Our approach enables a true minimum effort solution to be identified as task constraints, such as movement accuracy, can be explicitly imposed, rather than being approximated using penalty terms in the cost function. Our approximate stochastic optimal control framework predicts complex features, not captured by previous simulation approaches, providing a generalizable and valuable tool to study how musculoskeletal dynamics and physiological noise may alter neural control of movement in both healthy and pathological movements.