July 30-August 2, 2008
Society for Mathematical Biology Conference

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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8) Does neuroscience have a logic? - Limitations of brain and machine information processing
Principal organiser: Dr. Jose Luis Perez Velazquez
Assistant Professor, Department of Paediatrics and Institute of Medical Science, University of Toronto
Associate Scientist, Neuroscience and Mental Health Programme, Brain & Behaviour Centre
Hospital for Sick Children Research Institute

Luis Garcia Dominguez
Neuroscience and Mental Health Programme, Brain & Behaviour Centre, Hospital for Sick Children

One of the main goals of neuroscience is to understand consciousness, and of particular interest is the question of self-consciousness. This scheme contains the implicit assumption that brain states (or some specific cognitive states) like the "self" can be reached. But is this so? Are all brain states reachable and/or observable? Some aspects of neuroscience research have developed in close parallel to some aspects of mathematical research. Specifically, the view of mathematics as a consistent and complete system of logic, and the demise of this programme by the works of K. Gödel and A. Turing, ran in parallel to the notions of a deterministic nervous system function through classical Cartesian reflexes, a viewpoint that not many neuroscientists would adopt today. Thus, some results in mathematical logic can offer insight to the neuroscientists involved in seeking answers to these questions that are at the forefront of neuroscientific research these days. Along these lines, issues to be discussed in the symposium could be the limitations imposed by certain results in (meta)mathematics, and the queries relating complexity measures to neuronal activity and its relation to behaviour: if brain is complex, what kind of complexity is applicable to it? Many words have been devoted to discuss whether some of the aforementioned mathematical results reveal something about the brain and brain information processing associated with the sense of self and consciousness, and our plan is to gather workers in several disciplines (mathematics, logic, philosophy, and neuroscience) that could express their opinions and, perhaps, find an (approximate) answer to some of those queries.

Speakers and Abstracts

Information Processing Limits on Generating Neuroanatomy
Christopher Cherniak, University of Maryland

An apparent paradox is emerging regarding models of brain-wiring: Available connectivity in, e.g., cerebrum, is stringently limited; yet deployment of the interconnections attains fine grained optimization, sometimes without detectable limits. Neuroconnectivity architecture sometimes shows virtually perfect network optimization, rather than just network satisficing. Such connection cost-minimization problems are a major hurdle of microcircuit design, and are known to be NP-complete. How does biology effectively solve them? Briefly, some anomalies of the computational realm seem to be exploited; for instance, some "butterfly effects". This line of thought suggests extensions to the Anthropic Principle of cosmology, that is, further possible constraints on models of a brain-friendly Universe in which our intelligence can arise.

The Logic of Neuroscience and Goedel's incompleteness theorems
Jeff Buechner, Rutgers University-Newark and The Saul Kripke Center, CUNY, The Graduate Center

If neuroscience has a logic, then if it is strong enough to express arithmetic, it is subject to the Goedel incompleteness theorems. Distinguish between the logic of neurological processes and the logic of mental processes that are dependent upon (in some way: either reducible to or supervenient upon) those neurological processes. There are various possibilities: the logic(s) of mental processes and neurological processes are subject to the Goedel theorems, neither are, or one is while the other is not. I argue that even if the logic of either is subject to the Goedel theorems, that there is a way out. This has to do with the connection between mathematical certainty and the Goedel incompleteness theorems, one little recognized by logicians, mathematicians, philosophers, neuroscientists, cognitive scientists.

Rumbling about Brain Noise
AR McIntosh, PhD, Rotman Research Institute - Baycrest Centre

When we measure brain dynamics, noise is often considered as a nuisance variable that needs to be factored out of the equation. However, given the brain is almost always active, it is quite likely that this "noise" may serve a vital role in normal function. Following from the perspective of stochastic resonance, local noise fluctuations are key in extracting relevant signal from the barrage of noisy input. At a network level, optimal noise would facilitate the transmission of information between neural elements. Ongoing noise fluctuations, which may be captured in the oft observed "resting-state" network, would thus sculpt the moment-to-moment response of the network. From a developmental perspective, the emergence of optimal noise can be related to structural changes in myelin and synaptic density, resulting in a paradoxical increase in measured noise as the system matures. So too, as the system ages and brain structures deteriorate, the noise profile is similarly changed having broad, and seemingly unrelated, behavioural effects. Thus, in addition to a connectivity structure that can be characterized in terms of optimal small world properties, the tuning of internal noise may be a second factor that produces a system with optimal capacity for information segregation and integration – in other words, optimal complexity.

Nonliner Cable-like Properties of Microtubules and Their Potential for Neuronal Processing
Jack Tuszynski, University of Alberta

Recently, it has become apparent that neurons may utilize microtubules (MT) networks in cognitive processing via associated proteins (MAPs), including MAP-tau and MAP2, in such neuronal processes as learning and memory (Kaech et al., PNAS 98:7086-7092, 2001). MTs are also linked to the regulation of a number of ion channels, thus contributing to the electrical activity of excitable cells. Hence, MTs may play a role in the processing of electrical signals within the cell. Cytoskeletal alterations may reflect changes of neural circuits in response to learning and experience, and they must involve highly dynamic regulatory mechanisms.
Little is known, however about the intrinsic electrical properties of MTs, and in particular as to how these electrical properties are modulated. We recently reported novel features of MTs in solution (Priel et al., Biophys. J. 90:4639-4643, 2006). Namely, MTs behave as bio-molecular transistors capable of amplifying electrical signals. In that report, we used taxol-stabilized, polymerized tubulin, which were electrically manipulated with a modified dual "patch-clamp" setup. Our data provided the first direct experimental proof that MTs sustain novel biomolecular transistor capabilities, which likely play a yet unknown role in cell function.
To elucidate the electrodynamic properties of MTs and gain insight into the regulatory role that MTs play in cellular activity, we shall present a model intended to explain the ionic conductive properties of an MT based on a nonlinear electrical circuit, which mimics the behavior of an MT in solution. Using the theory of polyelectrolytes for ionic condensation along the stretch of a polymer, we assess that the cylindrical volume of depleted ions outside the ionic cloud surrounding the MT serves as an electrical shield. Hence, we expect this cloud to act as a dielectric medium between the two providing both resistive and capacitive components for the MT dimers. The inductive component is due to the MT's helical structure that should induce a helical ionic flow in a solenoidal manner.
There are a number of potential biological implications for a MT-based electrical device, e.g., MT-supported phenomena such as fast axonal transport. Interestingly, while axonal MTs are highly polarized, the MTs in dendrites have both plus and minus ends pointing outward. It is entirely possible that electrical amplification may provide a novel means for directionality in MTs. It has been postulated that electrical sorting may be suitable mechanism of vesicle trafficking. Thus electrical amplification by MTs, can provide novel means for explaining relevant cellular features in neuronal function, and likely other aspects of cell biology at large.

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