CHAOS REALITY IN THE BRAIN

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Neuroscience, quantum indeterminism and the Cartesian soul

Quantum indeterminism is frequently invoked as a solution to the problem of how a disembodied soul might interact with the brain (as Descartes proposed), and is sometimes invoked in theories of libertarian free will even when they do not involve dualistic assumptions. Taking as example the Eccles-Beck model of interaction between self (or soul) and brain at the level of synaptic exocytosis, I here evaluate the plausibility of these approaches. I conclude that Heisenbergian uncertainty is too small to affect synaptic function, and that amplification by chaos or by other means does not provide a solution to this problem. Furthermore, even if Heisenbergian effects did modify brain functioning, the changes would be swamped by those due to thermal noise. Cells and neural circuits have powerful noise-resistance mechanisms, that are adequate protection against thermal noise and must therefore be more than sufficient to buffer against Heisenbergian effects. Other forms of quantum indeterminism must be considered, because these can be much greater than Heisenbergian uncertainty, but these have not so far been shown to play a role in the brain.

Systems biology approaches and tools for analysis of interactomes and multi-target drugs

Systems biology is essentially a proteomic and epigenetic exercise because the relatively condensed information of genomes unfolds on the level of proteins. The flexibility of cellular architectures is not only mediated by a dazzling number of proteinaceous species but moreover by the kinetics of their molecular changes: The time scales of posttranslational modifications range from milliseconds to years. The genetic framework of an organism only provides the blue print of protein embodiments which are constantly shaped by external input. Indeed, posttranslational modifications of proteins represent the scope and velocity of these inputs and fulfil the requirements of integration of external spatiotemporal signal transduction inside an organism. The optimization of biochemical networks for this type of information processing and storage results in chemically extremely fine tuned molecular entities. The huge dynamic range of concentrations, the chemical diversity and the necessity of synchronisation of complex protein expression patterns pose the major challenge of systemic analysis of biological models. One further message is that many of the key reactions in living systems are essentially based on interactions of moderate affinities and moderate selectivities. This principle is responsible for the enormous flexibility and redundancy of cellular circuitries. In complex disorders such as cancer or neurodegenerative diseases, which initially appear to be rooted in relatively subtle dysfunctions of multimodal physiologic pathways, drug discovery programs based on the concept of high affinity/high specificity compounds ("one-target, one-disease"), which has been dominating the pharmaceutical industry for a long time, increasingly turn out to be unsuccessful. Despite improvements in rational drug design and high throughput screening methods, the number of novel, single-target drugs fell much behind expectations during the past decade, and the treatment of "complex diseases" remains a most pressing medical need. Currently, a change of paradigm can be observed with regard to a new interest in agents that modulate multiple targets simultaneously, essentially "dirty drugs." Targeting cellular function as a system rather than on the level of the single target, significantly increases the size of the drugable proteome and is expected to introduce novel classes of multi-target drugs with fewer adverse effects and toxicity. Multiple target approaches have recently been used to design medications against atherosclerosis, cancer, depression, psychosis and neurodegenerative diseases. A focussed approach towards "systemic" drugs will certainly require the development of novel computational and mathematical concepts for appropriate modelling of complex data. But the key is the extraction of relevant molecular information from biological systems by implementing rigid statistical procedures to differential proteomic analytics.

Spatial-temporal dynamics of chaotic behavior in cultured hippocampal networks

Using multiple nonlinear techniques, we revealed the existence of chaos in the spontaneous activity of neuronal networks in vitro. The spatial-temporal dynamics of these networks indicated that emergent transition between chaotic behavior and superburst occurred periodically in low-frequency oscillations. An analysis of network-wide activity indicated that chaos was synchronized among different sites. Moreover, we found that the degree of chaos increased as the number of active sites in the network increased during long-term development (over three months in vitro). The chaotic behavior of the dissociated networks had similar spatial-temporal characteristics (rapid transition, periodicity, and synchronization) as the intact brain; however, the degree of chaos depended on the number of active sites at the mesoscopic level. This work could provide insight into neural coding and neurocybernetics.

Learning to imitate stochastic time series in a compositional way by chaos

This study shows that a mixture of RNN experts model can acquire the ability to generate sequences that are combination of multiple primitive patterns by means of self-organizing chaos. By training the model, each expert learns a primitive sequence pattern, and a gating network learns to imitate stochastic switching of the multiple primitives via chaotic dynamics, utilizing a sensitive dependence on initial conditions. As a demonstration, we present a numerical simulation in which the model learns Markov chain switching among some Lissajous curves by chaotic dynamics. Our analysis shows that by using a sufficient amount of training data, balanced with the network memory capacity, it is possible to satisfy the conditions for embedding the target stochastic sequences into a chaotic dynamical system. It is also shown that reconstruction of a stochastic time series by a chaotic model can be stabilized by adding a negligible amount of noise to the dynamics of the model.

Invariant template matching in systems with spatiotemporal coding: A matter of instability

We consider the design principles of algorithms that match templates to images subject to spatiotemporal encoding. Both templates and images are encoded as temporal sequences of samplings from spatial patterns. Matching is required to be tolerant to various combinations of image perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, and, as special cases, invariant transformation groups such as translation and rotations, as well as unmodeled uncertainties (noise). For a system to deal with such perturbations in an efficient way, they are to be handled through a minimal number of channels and by simple adaptation mechanisms. These normative requirements can be met within the mathematical framework of weakly attracting sets. We discuss explicit implementation of this principle in neural systems and show that it naturally explains a range of phenomena in biological vision, such as mental rotation, visual search, and the presence of multiple time scales in adaptation. We illustrate our results with an application to a realistic pattern recognition problem.