Georgia Institute of Technology College of Sciences

Morphogenesis is the biological process that causes cells, tissues, or organisms to develop their shape. The theory of morphogenesis, proposed by Alan Turning, is a chemical model where biological cells differentiate and form patterns through intercellular reaction-diffusion mechanisms. Various reaction-diffusion models can produce a chemical pattern that mimics natural patterns. However, while they provide a plausible prepattern, they do not describe a mechanism in which the pattern is expressed. An alternative model is a mechanical model of the skin, initially described by Murray, Oster, and Harris. This model used mechanical interactions between cells without a chemical prepattern to produce structures like those observed in a Turing model. In this talk, we derive a modified version of the Murray, Oster, and Harris model incorporating nonlinear deformation effects. Since it is observed in some experiments that chemicals present in developing skin can cause or disrupt pattern formation, the mechanical model is coupled with a single diffusing chemical. Furthermore, it is observed that the interaction between tissue deformations with a diffusing chemical can cause a previously undescribed instability. This instability could describe both the pattern’s chemical patterning and mechanical expression without the need for a reaction-diffusion system.

Reaction networks are commonly used to model a variety of physical systems ranging from the microscopic world like cell biology and chemistry, to the macroscopic world like epidemiology and evolution biology. A biologically relevant property that reaction networks can have is absolute concentration robustness (ACR), which refers to when a steady-state species concentration is maintained even when initial conditions are changed. Networks with ACR have been observed experimentally, for example, in E. coli EnvZ-OmpR and IDHKP-IDH systems. Another reaction network property that might be desirable is multistationarity-the capacity for two or more steady states, since it is often associated with the capability for cellular signaling and decision-making.

While the two properties seem to be opposite, having both properties might be favorable as a biochemical network may require robustness in its internal operation while maintaining flexibility as a signal-response mechanism. As such, our driving motivation is to explore what network structures can produce ACR and multistationarity. We show that it is highly atypical for both properties to coexist in very small and very large reaction networks without special structures. However, it is possible for them to coexist in certain classes of reaction networks. I will discuss in detail one such class of networks, which consists of multisite phosphorylation-dephosphorylation cycles with a ``paradoxical enzyme".

The phylogenetic birth-death process is a probabilistic model of evolution that
is widely used to analyze genetic data. In a striking result, Louca & Pennell
(Nature, 2020) recently showed that this model is statistically unidentifiable,
meaning that an arbitrary number of different evolutionary hypotheses are
consistent with any given data set. This grave finding has called into question
the conclusions of a large number of evolutionary studies which relied on this
model.

In this talk, I will give an introduction to the phylogenetic birth-death
process, and explain Louca and Pennell's unidentifiability result. Then, I will
describe recent positive results that we have obtained, which establish that, by
restricting the evolutionary hypothesis space in certain biologically plausible
ways, statistical identifiability is restored. Finally, I will discuss some
complementary hardness-of-estimation results which show that, even in identifiable
model classes, obtaining reliable inferences from finite amounts of data may be
extremely challenging.

No background in this area is assumed, and the talk will be accessible to a
mathematically mature audience. This is joint work with Brandon Legried.

Zoom link:  https://gatech.zoom.us/j/99936668317

A central goal of biological experiments that generate omics time-course data is the discovery of patterns, or signatures, of response. A natural representation of such data is in the form of a third-order tensor. For example, if the dataset is from a bulk RNASeq experiment, which measures tissue-level gene expression collected at multiple time points, the data can be structured into a gene-by-subject-by-time tensor. We consider the use of a non-negative CANDECOMP/PARAFAC (CP) decomposition (NCPD) on the tensor to derive rank-one components that correspond to biologically meaningful signatures.  To assess whether over-factoring has occurred in a model, we develop the maximum internal n-similarity score (mINS) score. We use the mINS as well as other metrics to choose a model rank for downstream analysis. We show that on time-course data profiling vaccination responses against the Influenza and Bordetella Pertussis pathogens, our NCPD pipeline yields novel and informative signatures of response. We finish with outstanding research challenges in the application of tensor decomposition to modern biological datasets.