Behavioural robustness and the distributed mechanisms hypothesis

A current challenge in neuroscience and systems biology is to better understand properties that allow organisms to exhibit and sustain appropriate behaviours despite the effects of perturbations (behavioural robustness). There are still significant theoretical difficulties in this endeavour, mainly due to the context-dependent nature of the problem. Biological robustness, in general, is considered in the literature as a property that emerges from the internal structure of organisms, rather than being a dynamical phenomenon involving agent-internal controls, the organism body, and the environment. Our hypothesis is that the capacity for behavioural robustness is rooted in dynamical processes that are distributed between agent ‘brain’, body, and environment, rather than warranted exclusively by organisms’ internal mechanisms. Distribution is operationally defined here based on perturbation analyses. Evolutionary Robotics (ER) techniques are used here to construct four computational models to study behavioural robustness from a systemic perspective. Dynamical systems theory provides the conceptual framework for these investigations. The first model evolves situated agents in a goalseeking scenario in the presence of neural noise perturbations. Results suggest that evolution implicitly selects neural systems that are noise-resistant during coupling behaviour by concentrating search in regions of the fitness landscape that retain functionality for goal approaching. The second model evolves situated, dynamically limited agents exhibiting minimalcognitive behaviour (categorization task). Results indicate a small but significant tendency toward better performance under most types of perturbations by agents showing further cognitivebehavioural dependency on their environments. The third model evolves experience-dependent robust behaviour in embodied, one-legged walking agents. Evidence suggests that robustness is rooted in both internal and external dynamics, but robust motion emerges always from the systemin-coupling. The fourth model implements a historically dependent, mobile-object tracking task under sensorimotor perturbations. Results indicate two different modes of distribution, one in which inner controls necessarily depend on a set of specific environmental factors to exhibit behaviour, then these controls will be more vulnerable to perturbations on that set, and another for which these factors are equally sufficient for behaviours. Vulnerability to perturbations depends on the particular distribution. In contrast to most existing approaches to the study of robustness, this thesis argues that behavioural robustness is better understood in the context of agent-environment dynamical couplings, not in terms of internal mechanisms. Such couplings, however, are not always the full determinants of robustness. Challenges and limitations of our approach are also identified for future studies

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Geometry of gene regulatory dynamics

Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data

Neural Cartography: Computer Assisted Poincare Return Mappings for Biological Oscillations

This dissertation creates practical methods for Poincaré return mappings of individual and networked neuron models. Elliptic bursting models are found in numerous biological systems, including the external Globus Pallidus (GPe) section of the brain; the focus for studies of epileptic seizures and Parkinson\u27s disease. However, the bifurcation structure for changes in dynamics remains incomplete. This dissertation develops computer-assisted Poincaré ́maps for mathematical and biologically relevant elliptic bursting neuron models and central pattern generators (CPGs). The first method, used for individual neurons, offers the advantage of an entire family of computationally smooth and complete mappings, which can explain all of the systems dynamical transitions. A complete bifurcation analysis was performed detailing the mechanisms for the transitions from tonic spiking to quiescence in elliptic bursters. A previously unknown, unstable torus bifurcation was found to give rise to small amplitude oscillations. The focus of the dissertation shifts from individual neuron models to small networks of neuron models, particularly 3-cell CPGs. A CPG is a small network which is able to produce specific phasic relationships between the cells. The output rhythms represent a number of biologically observable actions, i.e. walking or running gates. A 2-dimensional map is derived from the CPGs phase-lags. The cells are endogenously bursting neuron models mutually coupled with reciprocal inhibitory connections using the fast threshold synaptic paradigm. The mappings generate clear explanations for rhythmic outcomes, as well as basins of attraction for specific rhythms and possible mechanisms for switching between rhythms

Contraction Analysis of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria and Plasmodium within Mosquitoes.

We propose and analyze an extension to the classic Competitive Lotka-Volterra (CLV) model. The goal is to model competition between species, with a response from the environment. This response is a function of the population of all species and can represent numerous physical phenomena including resource limitation and immune response of a host due to infection. We name this new system a Functional Competitive Lotka-Volterra (FCLV) model. We mainly use the construction of contraction metrics, to determine global properties of the model. We use this result to analyze the competition between Plasmodium sp. and genetically engineered bacteria within the midgut of a mosquito. We find that the effect of the immune response of the mosquito on invaders has a significant effect on whether Plasmodium or the genetically engineered bacteria dominates, but that under certain conditions the bacterium can eliminate the Plasmodium from the mosquito