Oxford University

Thu 18 Jan 2018, 11:00am
SPECIAL
Mathematical Biology Seminar / Probability Seminar
Math 126

Modelling mutations: mechanisms and evolutionary consequences

Math 126
Thu 18 Jan 2018, 11:00am12:00pm
Abstract
As the source of new genetic variation, mutations constitute a fundamental process in evolution. While most mutations lower fitness, rare beneficial mutations are essential for adaptation to changing environments. Thus, understanding the effects of mutations and estimating their rate is of strong interest in evolutionary biology. The necessity to treat rare mutational events stochastically has also stimulated a rich mathematical literature. Typically, mutations are modelled simply as an instantaneous change of type, occurring at a fixed rate. However, the underlying biology is more complex. I will present two recent projects delving deeper into mutational mechanisms and their consequences. Firstly, mutations can exhibit a multigenerational delay in phenotypic expression. Secondly, individuals within a population can vary in their propensity to mutate. Through analytical and simulation methods, we investigated the impact of these biological complexities on (a) population fitness and capacity to evolve, and (b) our ability to accurately infer mutation rates from data. I will conclude by discussing some future directions to incorporate these insights into more realistic models and to quantify the distribution of mutation rate empirically.
hide

Eotvos Lorand University, Budapest

Fri 19 Jan 2018, 2:00pm
Harmonic Analysis Seminar
MATH 126

Furstenbergtype estimates for unions of affine subspaces

MATH 126
Fri 19 Jan 2018, 2:00pm3:00pm
Abstract
A plane set is called a tFurstenberg set for some t in (0,1), if it has an at least tdimensional intersection with some line in each direction (here and in the sequel dimension refers to Hausdorff dimension). Classical results are that every tFurstenberg set has dimension at least 2t, and at least t + 1/2.
We generalize these estimates for families of affine subspaces. As a result, we prove that the union of any sdimensional family of kdimensional affine subspaces is at least k + s/(k+1) dimensional, and is exactly k + s dimensional if s is at most 1.
Based on joint work with Tamas Keleti and Andras Mathe.
hide

Oxford University

Fri 19 Jan 2018, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

Stochastic population dynamic models with applications to pathogen evolution

ESB 2012
Fri 19 Jan 2018, 3:00pm4:00pm
Abstract
Biological populations facing severe environmental change must adapt in order to avoid extinction. This socalled “evolutionary rescue” scenario is relevant to many applied problems, including pathogen evolution of drug resistance during the treatment of infectious diseases. Understanding what drives the rescue process gives rise to interesting mathematical modelling challenges arising from two key features: demographic and evolutionary processes occur on the same timescale, and stochasticity is inherent in the emergence of rare welladapted mutants. In this talk, I will present recent work on population dynamics in changing environments, merging biological realism with tractable stochastic models. Firstly, I will describe a model of drug resistance evolution in chronic viral infections, which serves as a case study for a novel mathematical approach yielding analytical approximations for the probability of rescue. Secondly, I will present a combined theoretical and experimental investigation of the classical problem of establishment (nonextinction) of new lineages, using antibioticresistant bacteria as a model system. Finally, I will discuss some future directions in modelling antibiotic treatment to predict optimal dosing strategies, and in developing a general theoretical framework for evolutionary rescue that unites approaches to distinct applied problems.
hide

University of North Carolina, Chapel Hill

Mon 22 Jan 2018, 12:00pm
SPECIAL
ESB 4133 (PIMS Lounge)

Seminar Talk in Math Biology, Applied Stochastics: How molecular crowding is changing our understanding of spatial patterning in living cells

ESB 4133 (PIMS Lounge)
Mon 22 Jan 2018, 12:00pm1:00pm
Details
Molecular crowding has recognized consequences for biological function. However, there are also circumstances in which uncrowding is important that is, when molecules must evacuate from a region before a given process can occur. One example is offered by the T cell, where large surface molecules must evacuate from a region to allow for the T cell to interact with its target, thereby facilitating immune function. Evacuation is fundamentally stochastic and spatial, since diffusion is a major driver. Studies of molecular evacuation present mathematical and computational challenges. For example, in some scenarios, it is a "rare event", making straightforward simulation unfeasible. To obtain a complete picture of diffusional evacuation, we use a combination of perturbation theory and numerical simulation. I will also show evidence of persistent uncrowding in living fungal cells. Based on our understanding of diffusional evacuation, we know that diffusion alone cannot explain these observations. I will discuss our current efforts to quantify and resolve how fungal cells control uncrowding.
hide

Cornell Statistical Science and Biological Statistics & Computational Biology

Mon 22 Jan 2018, 3:00pm
SPECIAL
Institute of Applied Mathematics
ESB 2012

An ODE to Statistics: Inference about Nonlinear Dynamics

ESB 2012
Mon 22 Jan 2018, 3:00pm4:00pm
Abstract
Ordinary differential equation models are used extensively within mathematics as descriptions of processes in the real world. However, they are rarely employed by statisticians and there is a paucity of methods for combining differential equation models with data. This talk provides a survey of recently developed statistical methods for estimating parameters from data, conducting model criticism and improvement for differential equation models in the light of data, and designing experiments that yield optimal estimates of parameters. It ends with some perspectives on the current state of the field and open problems.
hide

Saskatchewan

Mon 22 Jan 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126

Asymptotic geometry of hyperpolygons

MATH 126
Mon 22 Jan 2018, 4:00pm5:00pm
Abstract
Nakajima quiver varieties lie at the interface of geometry and representation theory. I will discuss a particular example, hyperpolygon space, which arises from starshaped quivers. The simplest of these varieties is a noncompact complex surface admitting the structure of an "instanton", and therefore fits nicely into the KronheimerNakajima classification of ALE hyperkaehler 4manifolds, which is a geometric realization of the McKay correspondence for finite subgroups of SU(2). For more general hyperpolygon spaces, we speculate on how this classification might be extended by studying the asymptotic geometry of the variety. In modulitheoretic terms, this involves driving the stability parameter for the quotient to an irregular value. This is joint work in progress with Harmut Weiss, building on previous work with Jonathan Fisher.
hide

University of North Carolina, Chapel Hill

Tue 23 Jan 2018, 3:45pm
SPECIAL
Department Colloquium
ESB 2012 (PIMS)

Weaker is better: how weak transient molecular interactions give rise to robust, dynamic immune protection

ESB 2012 (PIMS)
Tue 23 Jan 2018, 3:45pm4:45pm
Abstract
The longstanding view in chemistry and biology is that highaffinity, tightbinding interactions are optimal for many essential functions, such as receptorligand interactions. Yet, an increasing number of biological systems are emerging that challenge this view, finding instead that lowaffinity, rapidly unbinding dynamics can be essential for optimal function. These mechanisms have been poorly understood in the past due to the inability to directly observe such fleeting interactions and the lack of a theoretical framework to mechanistically understand how they work. In fact, it is only by tracking the motion of effector nanoprobes that afford detection of multiple such interactions simultaneously, coupled with inferences by stochastic modeling, Bayesian statistics, and bioimaging tools, that we recently begin to obtain definitive evidence substantiating the consequences of these interactions. A common theme has begun to emerge: rapidly diffusing thirdparty molecular anchors with weak, shortlived affinities play a major role for self organization of micronscale living systems. My talk will demonstrate how these ideas can answer a longstanding question: how mucosal barriers selectively impede transport of pathogens and toxic particles, while allowing diffusion of nutrients.
hide

UBC

Wed 24 Jan 2018, 3:10pm
Probability Seminar
LSK 460

Heat flow on snowballs

LSK 460
Wed 24 Jan 2018, 3:10pm4:10pm
Abstract
Quasisymmetric maps are fruitful generalizations of conformal maps. Quasisymmetric uniformization problem seeks for extensions of uniformization theorem beyond the classical context of Riemann surfaces.
The goal of this talk is to show that quasisymmetric uniformization problem is closely related to random walks and diffusions. I will explain how the existence of quasisymmetric maps is equivalent to heat kernel estimates for the simple random walk on a family of planar graphs. The same methods also apply to diffusions on a class of fractals homeomorphic to the 2sphere.
These ideas will be illustrated using snowballs and their graph approximations. Snowballs are high dimensional analogues of Koch snowflake.
hide

Courant Institute, NYU

Wed 24 Jan 2018, 3:15pm
Mathematical Biology Seminar
PIMS Lounge, ESB 4133

Mechanical Positioning of Multiple Myonuclei in Muscle Cells

PIMS Lounge, ESB 4133
Wed 24 Jan 2018, 3:15pm4:15pm
Abstract
Many types of large cells have multiple nuclei. In long muscle cells, nuclei are distributed almost uniformly along their length, which is crucial for cell function. However, the underlying positioning mechanisms remain unclear. We examine computationally the hypothesis that a force balance generated by microtubules positions the nuclei. Rather than assuming what the forces are, we allow for various types of forces between pairs of nuclei and between the nuclei and the cell boundary. Mathematically, this means that we start with a great number of potential models. We then use a reverse engineering approach by screening the models and requiring their predictions to fit imaging data on nuclei positions from hundreds of muscle cells of Drosophila larva. Computational screens result in a small number of feasible models, the most adequate of which suggests that the nuclei repel each other and the cell boundary with forces that decrease with distance.
This suggests that microtubules growing from nuclear envelopes push on neighboring nuclei and the cell boundary. We support this hypothesis with stochastic microscopic simulations. Using statistical and analytical tools such as correlation and bifurcation analysis, we make several nontrivial predictions: An increased nuclear density near the cell poles, zigzag patterns in wider cells, and correlations between the cell width and elongated nuclear shapes, all of which we confirm by image analysis of the experimental data.
This is joint work with Mary Baylies, Alex Mogilner and Stefanie Windner.
hide

Seminar Information Pages

Note for Attendees
Math 126 is behind a locked glass door. Latecomers without access should knock loudly!