Mathematical Biology

Alan Turing and the Patterns of Life

Speaker: 
Przemysław Prusinkiewicz
Date: 
Tue, Oct 9, 2012
Location: 
PIMS, University of Calgary
Conference: 
Alan Turing Year
Abstract: 
In 1952, Turing published his only paper spanning chemistry and biology: "The chemical basis of morphogenesis". In it, he proposed a hypothetical mechanism for the emergence of complex patterns in chemical reactions, called reaction-diffusion. He also predicted the use of computational models as a tool for understanding patterning. Sixty years later, reaction-diffusion is a key concept in the study of patterns and forms in nature. In particular, it provides a link between molecular genetics and developmental biology. The presentation will review the concept of reaction-diffusion, the tumultuous path towards its acceptance, and its current place in biology.

2012 IGTC Summit: Prof. Steve Krone (Part II)

Author: 
Prof. Steve Krone
Date: 
Sun, Oct 14, 2012
Location: 
Naramata Centre
Abstract: 
Spontaneous pattern formation in spatial populations with cyclic dynamics

There are many examples in nature where a system goes through a succession of states that are cyclically related. Examples include ecological succession in a forest and SIRS models of epidemics. When such populations are spatially arranged (as are *all* populations to some degree), these cyclic dynamics can sometimes lead to the spontaneous formation of spatial patterns such as spiral waves. We will explore this phenomenon via interacting particle system models and related differential equations.

2012 IGTC Summit: Prof. Steve Krone (Part I)

Author: 
Prof. Steve Krone
Date: 
Sat, Oct 13, 2012
Location: 
Naramata Centre
Abstract: 
Individual-based stochastic spatial models and population biology

These talks will provide an introduction to individual-based stochastic spatial models (sometimes called interacting particle systems or stochastic cellular automata). We will proceed from very simple basic models to more elaborate ones, illustrating the ideas with examples of spatial biological population dynamics. We will compare these models and results with analogous differential equations (ODE and PDE) and see how they are connected. Biological topics will include spatial population growth and spread, epidemics, evolution of pathogens, and antibiotic resistance plasmids. Throughout, we will point out situations in which spatial structure can dramatically influence the ecology and evolution of populations.

Mechanical Simulations of Cell Motility

Speaker: 
Leah Edelstein-Keshet
Date: 
Fri, May 25, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
Here I survey a broad range of recent computational models for 2D and 3D cell motility. Some of these models depict chemical activation on the perimeter of a (static or deforming) domain. Others consider fluid and/or mechanical elements and/or biochemical signalling on the interior of a deforming 2D region representing a cell. Examples of platforms include the immersed-boundary method and level set methods. I describe some of the computational challenges and how these have been addressed by various researchers.

Polymer Size Distributions (continued)

Speaker: 
Leah Edelstein-Keshet
Date: 
Wed, May 9, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
We continue the discussion from last time, and solve the polymer size distribution equations, which are linear in the case of constant monomer level. In a distinct case, when monomer is depleted, we show that the size distribution evolves in two phases, where in the first, the entire distribution appears to satisfy a transport equation, and then, later on, once monomer is at its critical level, the process of length adjustment appears to be governed by an effective diffusion (in size-class). Next, I introduce the problem of determining features of polymer assembly from experimental polymerization versus time data. (Based on work by Flybjerg et al, this leads to an extended homework exercise carried out by the students.) Finally, I revisit microtubule growth and shrinking by discussing the Dogterom-Leibler equations and their steady state exponential solutions. I illustrate the use of XPP software to solve several problems in this lecture.

On growth and form: geometry, physics and biology

Speaker: 
Lakshminarayanan Mahadevan
Date: 
Thu, May 24, 2012
Location: 
PIMS, University of British Columbia
Conference: 
2012 Niven Lecture
Abstract: 
The diversity of form in living beings led Darwin to state that it is "enough to drive the sanest man mad". How can we describe this variety? How can we predict it? Motivated by biological observations on different scales from molecules to tissues, I will show how a combination of biological and physical experiments, mathematical models and simple computations allow us to begin to unravel the physical basis for morphogenesis.

Mathematical Cell Biology Summer Course Lecture 36

Speaker: 
Dimitrios Vavylonis
Date: 
Thu, May 24, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
TBA

Mathematical Cell Biology Summer Course Lecture 35

Speaker: 
Dimitrios Vavylonis
Date: 
Thu, May 24, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
  • Regulatory circuits in Bacterial Chemotaxis and motility
  • Introduction to molecular motors, porters vs rowers and cooperativity of myosin in muscle
  • Microtubule dynamics
  • Cytokinesis
  • FRAP studies of microtubule dynamics in the mitotic spindle
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