MS06 - MFBM-1
Brutus Buckeye Room (#3044) in The Ohio Union

Algebra, Combinatorics, and Topology in Modern Biology

Thursday, July 20 at 10:30am

SMB2023 SMB2023 Follow Thursday during the "MS06" time block.
Room assignment: Brutus Buckeye Room (#3044) in The Ohio Union.
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Daniel A. Cruz,Margherita Maria Ferrari


Over the last several years, research at the interface of mathematics and biology has proven to be a powerful catalyst for advancing each of the individual fields by yielding new tools, discoveries, and open questions. In particular, techniques from algebra, combinatorics, topology, and related areas have complemented more mainstream approaches in mathematical biology while becoming natural tools for understanding biological structures and interactions. This mini-symposium will focus on recent developments and open problems in algebra, combinatorics, and topology inspired by and/or applied to biological processes. Specific topics include DNA assembly and recombination, biopolymer structure analysis, and phylogenetics, among others. Our intention is not only to facilitate discussion and collaboration but also to promote inclusivity within the associated research communities. As such, we have invited a diverse group of junior and senior speakers with complementary expertise which includes a significant number of women mathematicians.

Lina Fajardo Gomez

University of South Florida (Mathematics)
"Homology for Directed Graphs with Applications to DNA Recombination"
We propose custom made cell complexes, in particular prodsimplicial complexes, in order to analyze data consisting of directed graphs. These are constructed by attaching cells that are products of simplices and are suited to study data of acyclic directed graphs, called here consistently directed graphs. We investigate possible values of the first and second Betti numbers and the types of cycles that generate nontrivial homology. We apply these tools to graphs associated with DNA recombination processes in certain species of ciliates and we study the effects of changes in the directed graphs on the homology.
Additional authors: Margherita Maria Ferrari - University of Manitoba; Nataša Jonoska - University of South Florida; Masahico Saito - University of South Florida.

Puttipong Pongtanapaisan

Arizona State University (Mathematics and statistics)
"On the scarcity of split links spanning a lattice tube"
Frisch, Wasserman, and Delbrück conjectured that as the length of a polymer chain tends to infinity, the probability of knotting approaches 1. Similar questions regarding the entanglement complexity of multiple closed curves can also be addressed with lattice models. In this talk, I will show that all but exponentially few sufficiently large spanning pairs of self-avoiding polygons in the (2x1)-tube are linked.
Additional authors: Jeremy Eng (Saskatchewan Polytechnic); Rob Scharein (Hypnagogic Software); Chris Soteros (University of Saskatchewan)

Caitlin Lienkaemper

Boston University (Department of Mathematics and Statistics)
"Combinatorial coexpression in mosquito olfaction"
Across species, the olfactory system follows a stereotyped organization: each olfactory receptor neuron expresses a single type of olfactory receptor, and responses of olfactory sensory neurons which express the same receptor are pooled before they are sent to higher regions of the brain. Mosquitoes have recently been shown to violate this organization: olfactory sensory neurons coexpress multiple receptor types, thus mixing information about activation of different receptors from the start. We describe the properties of this pattern of receptor expression as a combinatorial code, consider from an information-theoretic perspective how coexpression helps mosquitoes perform as olfactory-guided predators, and investigate how the pattern of coexpression must be tuned to the pattern of stimulus statistics.
Additional authors: Gabriel Koch Ocker, Meg A. Younger

Radmila Sazdanovic

NC State University (Mathematics)
"Categorified chromosome aberration model"
Graphs are ubiquitous in mathematics and widely used to model physical phenomena in science and engineering. One such model was developed by Sachs and collaborators to analyze exchange type chromosome aberrations. In this talk we introduce a 'categorification' of this model where chromosomes (and their aberrant versions) are modeled as objects and the aberrations causing exchange processes as morphisms in a thin-surface cobordism category. This new framework allows for interpreting and analyzing patterns of chromosome aberrations observed in radiation experiments.
Additional authors: J. Arsuaga, S. Ardanza-Trevijano

Margherita Maria Ferrari

University of Manitoba (Department of Mathematics)
"Graph theory for DNA self-assembly"
The chemical and physical properties of DNA strands contain a high degree of information which allows DNA to serve as building material for assembling nanostructures. These complexes have a wide range of applications, including drug delivery and molecular scaffolding. In this talk, we focus on assembling graph-like structures using branched junction DNA molecules which are star-shaped molecules that join together through adhesion sites at the end of their arms. We describe a combinatorial representation of these molecules and consider the problem of optimally building a target graph under different laboratory settings. We show how this question give rises to new graph invariants and how these invariants can be studied through edge-colorings and graph decompositions.

#SMB2023 Follow
Annual Meeting for the Society for Mathematical Biology, 2023.