Discrete Mathematical Biology, Part I
Org: Torin Greenwood
and Christine Heitsch
(Georgia Institute of Technology)
- SHARLEE CLIMER, University of Missouri - St. Louis
Embracing the complexity of combinatorial GWAS [PDF]
Unlike monogenic traits, complex traits typically arise due to combinations of genetic factors, and standard genome-wide association studies (GWAS) can miss these interactions. An additional challenge is genetic heterogeneity, in which different subsets of individuals acquire the trait due to different combinations of genetic factors, muddling associations between markers and trait status. We have developed a network-based approach, BlocBuster, to address these confounding properties. Two key characteristics differentiate BlocBuster from conventional methods: a vector-based correlation measure captures heterogeneity and an expanded network scaffold increases information retention. This approach has facilitated the discovery of overlooked patterns for several diverse complex traits.
- JOANNA ELLIS-MONAGHAN, Saint Michael's College
Ins and Outs of DNA Self-Assembly [PDF]
New areas of mathematical investigation arise from determining optimal design strategies for self-assembling DNA nanostructures, particularly in developing graph-theoretical models for assembling the target molecules. The various DNA assembly methods may be grouped roughly into the areas of double-coverings, tile assembly (flexible and rigid), and DNA origami (filled and skeletal). As these have become increasingly sophisticated, the question of automating design processes arise, particularly for biomolecular computing applications, where existence and computational complexity questions must be addressed for both designing the input structures and reading the output. We present hardness results for some common strategies and discuss their implications.
- TORIN GREENWOOD, Georgia Institute of Technology
Using Experimental Data to Deconvolve Structural Signals [PDF]
The combinatorial arrangement of RNA base pairings encodes functional information, and a sequence is typically predicted to fold to a single minimum free energy conformation. But, an increasing number of RNA molecules are now known to fold into multiple stable structures. Discrete optimization methods are commonly used to predict foldings, and adding experimental data as auxiliary information improves prediction accuracy when there is a single dominant conformation. In this talk, we describe the challenges of extending the thermodynamic prediction approaches with experimental data to multimodal structural distributions, and we discuss alternative methods, such as those with stochastic context free grammars.
- EZRA MILLER, Duke University
Fruit fly wing veins as embedded planar graphs [PDF]
The topology of fruit fly wing veins is a model highly canalized (rarely varying) discrete feature. The question here is whether
evolutionary forces can nonetheless generate topologically new features with enough frequency for selection to act. Our analysis
summarizes the metrically embedded planar vein graphs in a way that allows graphs with different topologies to be compared in a single
statistical analysis. Multiparameter persistent homology serves as a natural data structure in this case. We recast and greatly extend the algebraic, combinatorial, and algorithmic foundations of persistence for this biological investigation, but the resulting methodology is general and widely applicable.
- SONJA PETROVIC, Illinois Institute of Technology
Discrete methods for statistical network analysis in biology [PDF]
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network
data. Through the running examples of protein-protein interaction and neuronal networks, this talk will offer a brief overview of open
problems in this area of discrete mathematics from the point of view of a particular family of statistical models for networks called exponential random graph models. The emphasis will be on statistical relevance of the discrete problems.