AMS-ASL Special Session on Applications of Logic, Model Theory, and Theoretical Computer Science to Systems Biology

        Saturday January 9, 2016, 1:00 p.m.-5:40 p.m.
Room 602, Washington State Convention Center
James Lynch, Clarkson University
Leo Marcus, Santa Monica, CA

o   1:00 p.m.
Many-sorted first-order model theory as a conceptual framework for complex dynamical systems.
Solomon Feferman, Stanford University

When complex biological systems (among others) are conceived reductively, they are modeled in set-theoretical hierarchical terms from the bottom up. But the point of view of Systems Biology (SB) is to deal with such systems from the top down. So in this talk I will suggest the use of many-sorted first-order structures with downward nested sorts as an alternative conceptual framework for modeling them. In particular, the notion of a nested substructure allows one to study parts of a structure in isolation from the rest, while the notion of restriction allows one to study a structure relative to some of its parts treated as black boxes. The temporal dimension can be incorporated both as an additional sort and in the indexing of sorts, allowing for both static and dynamic views of a system. Furthermore, one may make use of a quite general theory of recursion on many-sorted first-order structures that includes both discrete and continuous computation. Some possible applications of this model-theoretic approach to SB include excision or substitution of a part as operations on structures, similarity of biological systems via similarity notions for structures, and homeostasis via fixed point recursion.

Many-sorted first-order model theory as a conceptual framework for biological and other complex dynamical systems (draft)

o   2:00 p.m.
Neural Algebra and Modelling.
Erwin Engeler, ETH Zurich

The mathematical model introduced in this paper attempts to explain how complex scripts of behavior and conceptual contents can reside in, combine and interact on large networks of interconnected basic actors. The approach derives from modeling the neural structure and dynamics of the connectome of a brain. The neurological hypothesis attributes functions of the brain to sets of firing neurons, dynamically as sets of cascades of such firings, typically visualized by imaging technologies. Such sets are represented as the elements of what we call a neural algebra, and their interaction as its basic operation. In particular we analyze the representation of perception and of control in its various forms, distributed, hierarchical, recursive and especially reflexive control, the latter modeling the concept of self-reflecting control. The main thrust of this paper develops from the fact that characteristic properties of these suggestive notions can be cast in the form of equations of the neural algebra. Analyzing the solutions leads to a complete description of the necessary structure of their neural correlates.

Neural Algebra A MODEL OF INTERACTING BRAIN FUNCTIONS (Manuscript draft)

o   3:00 p.m.
Dependence logic and biology.
Jouko A Vaananen, Department of Mathematics and Statistics, University of Helsinki, Finland

An essential part of science is detecting variation in data. I will give an introduction to dependence logic (1), an approach to logic emphasizing the detection of variation and dependences between variables. I will discuss algorithmic and model theoretic properties of dependence logic, and its relation to other notions of dependence e.g. dependence in biology, model theory, computer science, quantum physics, and economics. In science it is natural to consider probabilities of formulas rather than just the truth values true/false. Suppose we have a set of assignments of fixed variables into the domain of a first order structure. We call such sets teams. Semantics based on teams is the underlying concept of dependence logic. We may ask, what is the probability that a randomly chosen assignment in a team satisfies a given first-order formula in the structure? The Hardy-Weinberg Theorem is an example of such a first order property of probabilities in teams. In (2) we give axioms for making inferences about first-order properties of probabilities, and prove the completeness of our axioms.

o   4:00 p.m.
Probabilistic Boolean Networks as Models of Gene Regulatory Networks.
Ilya Shmulevich, Institute for Systems Biology

I will present Probabilistic Boolean Networks (PBNs), which are models of genetic regulatory networks that i) incorporate rule-based dependencies between genes; ii) allow the systematic study of global system dynamics; iii) are able to cope with uncertainty; iv) permit the quantification of the relative influence and sensitivity of genes in their interactions with other genes. PBNs share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. The dynamics of PBNs can be studied in the context of Markov Chains, with standard Boolean networks being special cases. I will also discuss the relationship between PBNs and Bayesian networks -- a family of graphical models that explicitly represent probabilistic relationships between the variables. A major objective is the development of computational tools for the identification of potential targets for therapeutic intervention in diseases such as cancer. I will describe several approaches for finding the best genes with which to intervene in order to elicit desirable network behavior.

o   5:00 p.m.
Datum Logic: A Formal Executable Semantics for Experimental Evidence.
Carolyn L Talcott, SRI International

Executable symbolic models of signal transduction have been successfully used to analyze networks of biological reactions. Such models can provide insights into how cells work, and a means to understand and predict the effects of perturbations and mutations, key for cellular understanding of disease and therapeutics. Pathway Logic (PL) is a formal system for representing and reasoning with executable models of cellular processes. Developing models requires significant expertise and time to collect, organize and interpret experimental evidence; and to infer rules representing hypothesized biochemical reaction that make up a signaling network. There is a great need for tools to help automate the curation of executable models. The problem of automatically constructing executable models from experimental evidence has several aspects including: (1) formal representation of experimental findings, (2) formal representation of rules as elements of executable models, (3) extracting findings from papers, and (4) algorithms for inferring rules from findings and for assembly of executable models. The PL representation system is a solution for (2). Datum Logic is a solution to (1,4). We will describe the representation, and an approach to inferring rules from datums.

Inferring Executable Models from Formalized Experimental Evidence (related article)