Past Mathematical Biology and Ecology Seminar

23 October 2020
14:00
Abstract

Multi-modal data sets are growing rapidly in single cell genomics, as well as other fields in science and engineering. We introduce MultiMAP, an approach for dimensionality reduction and integration of multiple datasets. MultiMAP embeds multiple datasets into a shared space so as to preserve both the manifold structure of each dataset independently, in addition to the manifold structure in shared feature spaces. MultiMAP is based on the rich mathematical foundation of UMAP, generalizing it to the setting of more than one data manifold. MultiMAP can be used for visualization of multiple datasets as well as an integration approach that enables subsequent joint analyses. Compared to other integration for single cell data, MultiMAP is not restricted to a linear transformation, is extremely fast, and is able to leverage features that may not be present in all datasets. We apply MultiMAP to the integration of a variety of single-cell transcriptomics, chromatin accessibility, methylation, and spatial data, and show that it outperforms current approaches in run time, label transfer, and label consistency. On a newly generated single cell ATAC-seq and RNA-seq dataset of the human thymus, we use MultiMAP to integrate cells across pseudotime. This enables the study of chromatin accessibility and TF binding over the course of T cell differentiation.

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  • Mathematical Biology and Ecology Seminar
16 October 2020
14:00
Abstract

 Inherent fluctuations may play an important role in biological and chemical systems when the copy number of some chemical species is small. This talk will present the recent work on the stochastic modeling of reaction-diffusion processes in biochemical systems. First, I will introduce several stochastic models, which describe system features at different scales of interest. Then, model reduction and coarse-graining methods will be discussed to reduce model complexity. Next, I will show multiscale algorithms for stochastic simulation of reaction-diffusion processes that couple different modeling schemes for better efficiency of the simulation. The algorithms apply to the systems whose domain is partitioned into two regions with a few molecules and a large number of molecules.

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  • Mathematical Biology and Ecology Seminar
19 June 2020
14:00
Abstract

Femoral neck response to physiological loading during level walking can be better understood, if personalized muscle and bone anatomy is considered. Finite element (FE) models of in vivo cadaveric bones combined with gait data from body-matched volunteers were used in the earlier studies, which could introduce errors in the results. The aim of the current study is to report the first fully personalized multiscale model to investigate the strains predicted at the femoral neck during a full gait cycle. CT-based Finite element models (CT/FE) of the right femur were developed following a validated framework. Muscle forces estimated by the musculoskeletal model were applied to the CT/FE model. For most of the cases, two overall peaks were predicted around 15% and 50% of the gait. Maximum strains were predicted at the superior neck region in the model. Anatomical muscle variations seem to affect femur response leading to considerable variations among individuals, both in term of the strains level and the trend at the femoral neck.
 

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  • Mathematical Biology and Ecology Seminar
12 June 2020
14:00
Dr Berta Verd
Abstract

Pattern formation emerges during development from the interplay between gene regulatory networks (GRNs) acting at the single cell level and cell movements driving tissue level morphogenetic changes. As a result, the timing of cell specification and the dynamics of morphogenesis must be tightly cross-regulated. In the developing zebrafish, mesoderm progenitors will spend varying amounts of time (from 5 to 10hrs) in the tailbud before entering the pre-somitic mesoderm (PSM) and initiating a stereotypical transcriptional trajectory towards a mesodermal fate. In contrast, when dissociated and placed in vitro, these progenitors differentiate synchronously in around 5 hours. We have used a data-driven mathematical modelling approach to reverse-engineer a GRN that is able to tune the timing of mesodermal differentiation as progenitors leave the tailbud’s signalling environment, which also explains our in vitro observations. This GRN recapitulates pattern formation at the tissue level when modelled on cell tracks obtained from live-imaging a developing PSM. Our “live-modelling” framework also allows us to simulate how perturbations to the GRN affect the emergence of pattern in zebrafish mutants. We are now extending this analysis to cichlid fishes in order to explore the regulation of developmental time in evolution.

 

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  • Mathematical Biology and Ecology Seminar
5 June 2020
14:00
Professor Alan Garfinkel
Abstract

There is a need for a new kind of maths course, to be taught, not to mathematics students, but to biologists with little or no maths background. There have been many recent calls for an upgrade to the mathematical background of biologists: undergraduate biology students need to understand the role of modeling and dynamics in understanding ecological systems, evolutionary dynamics, neuroscience, physiology, epidemiology, and the modeling that underlies the concept of climate change. They also need to understand the importance of feedback, both positive and negative, in creating dynamical systems in biology.

 Such a course is possible. The most important foundational development was the 20th century replacement of the vague and unhelpful concept of a differential equation by the rigorous geometric concept of a vector field, a function from a multidimensional state space to its tangent space, assigning “change vectors” to every point in state space. This twentieth-century concept is not just more rigorous, but in fact makes for superior pedagogy. We also discuss the key nonlinear behaviors that biological systems display, such as switch-like behavior, robust oscillations and even chaotic behavior.

 This talk will outline such a course. It would have a significant effect on the conduct of biological research and teaching, and bring the usefulness of mathematical modeling to a wide audience.

 

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  • Mathematical Biology and Ecology Seminar
6 March 2020
14:00
Professor Adriana Dawes
Abstract

During development, cells take on specific fates to properly build tissues and organs. These cell fates are regulated by short and long range signalling mechanisms, as well as feedback on gene expression and protein activity. Despite the high conservation of these signalling pathways, we often see different cell fate outcomes in similar tissues or related species in response to similar perturbations. How these short and long range signals work to control patterning during development, and how the same network can lead to species specific responses to perturbations, is not yet understood. Exploiting the high conservation of developmental pathways, we theoretically and experimentally explore mechanisms of cell fate patterning during development of the egg laying structure (vulva) in nematode worms. We developed differential equation models of the main signalling networks (EGF/Ras, Notch and Wnt) responsible for vulval cell fate specification, and validated them using experimental data. A complex, biologically based model identified key network components for wild type patterning, and relationships that render the network more sensitive to perturbations. Analysis of a simplified model indicated that short and long range signalling play complementary roles in developmental patterning. The rich data sets produced by these models form the basis for further analysis and increase our understanding of cell fate regulation in development.

  • Mathematical Biology and Ecology Seminar

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