Timetable (SDBW01)

The generation of directed movement of cellular components frequently requires the rectification of Brownian motion. In this talk, we discuss mathematical models that track bias generation by nano machine constructs. These dynamic constructs work during cell division and their efficient operation requires specific interactions with dynamic bio polymers. We use first passage techniques to derive mesoscale properties for these motor constructs using microscale rates and reactions. 

Co-authors: David F. Anderson (University of Wisconsin-Madison), Yu Sun (University of Wisconsin-Madison)

I will analyze and compare the computational complexity of different simulation strategies for continuous time Markov chains. I consider the task of approximating the expected value of some functional of the state of the system over a compact time interval. This task is a bottleneck in many large-scale computations arising in biochemical kinetics and cell biology. In this context, the terms 'Gillespie's method', 'The Stochastic Simulation Algorithm' and 'The Next Reaction Method' are widely used to describe exact simulation methods. For example, Google Scholar records more than 6,000 citations to Gillespie's seminal 1977 paper. I will look at the use of standard Monte Carlo when samples are produced by exact simulation and by approximation with tau-leaping or an Euler-Maruyama discretization of a diffusion approximation. In particular, I will point out some possible pitfalls when computational complexity is analysed. Appropriate modifications o f recently proposed multilevel Monte Carlo algorithms will then be studied for the tau-leaping and Euler-Maruyama approaches. I will pay particular attention to a parameterization of the problem that, in the mass action chemical kinetics setting, corresponds to the classical system size scaling.

Related Links

• http://personal.strath.ac.uk/d.j.higham/

Co-authors: Brian Drawert (UC Santa Barbara), Michael Lawson (Uppsala University), Tau-Mu Yi (UC Santa Barbara), Mustafa Khammash (ETH Zurich), Otger Campas (UC Santa Barbara), Michael Trogdon (UC Santa Barbara) AbstractPolarization is an essential behavior of living cells, yet the dynamics of this symmetry-breaking process are not fully understood. Previously, noise was thought to interfere with this process; however, we show that stochastic dynamics plan an essential role in robust cell polarization and the dynamic response to changing cues. 

To further our understanding of polarization, we have developed a spatial stochastic model of cellular polarization during mating of Saccharomyces cerevisiae. Specifically we investigate the ability of yeast cells to sense a spatial gradient of mating pheromone and respond by forming a projection in the direction of the mating partner. Our mechanistic model integrates three components of the polarization process: the G-protein cycle activated by pheromone bound receptors, the focusing of a Cdc42 polarization cap, and the formation of the tight localization of proteins on the membrane known as the polarisome. 

Our results demonstrate that higher levels of stochastic noise result in increased robustness, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function. Additionally, our simulations predict that two positive feedback loops are required to generate the spatial amplification to produce focal polarization. We combined our modeling with experiments to explore the critical role of the polarisome scaffold protein Spa2 during yeast mating, and as a result, have characterized a novel positive feedback loop critical to focal polarization via the stabilization of actin cables. 

Co-authors: Clive Bowsher (), Margaritis Voliotis (University of Bristol)

To understand how cells control and exploit biochemical fluctuations, we must identify the sources of stochasticity, quantify their effects, and distinguish informative variation from confounding "noise". I will present an analysis that allows fluctuations of biochemical networks to be decomposed into multiple components, gives conditions for the design of experimental reporters to measure all components, and provides a technique to predict the magnitude of these components from models. Further, I will identify a particular component of variation that can be used to quantify the efficacy of information flow through a biochemical network. 

In adult, tissues are maintained and repaired by stem cells, which divide and differentiate to generate more specialized progeny. The mechanisms that control the balance between proliferation and differentiation promise fundamental insights into the origin and design of multi-cellular organisms. Using epidermis as a model system, we show how the combination of genetic lineage tracing assays in transgenic mouse models with simple ideas from non-equilibrium statistical physics provide a quantitative platform to resolve the stochastic fate behaviour of stem cells and their progeny in both healthy and diseased states. Furthermore, we describe how these methods can be adapted to address exome deep-sequening data, providing a new and general method to resolve the pattern of normal stem cell fate, and detect and characterize the mutational signature of rare field transformations in human tissues, with implications for the early detection of preneoplasia.

The last twenty years have seen a revolution in tracking data of biological agents across unprecedented spatial and temporal scales. An important observation from these studies is that path trajectories of living organisms can appear random, but are often poorly described by classical Brownian motion. The analysis of this data can be controversial because practitioners tend to rely on summary statistics that can be produced by multiple, distinct stochastic process models. Furthermore, these summary statistics inappropriately compress the data, destroying details of non-Brownian characteristics that contain vital clues to mechanisms of transport and interaction. In this talk, I will survey the mathematical and statistical challenges that have arisen from recent work on the movement of foreign agents, including viruses, antibodies, and synthetic microparticle probes, in human mucus. 

This is a fast 45 minutes tutorial of the passage time and narrow escape theory with various application in cell biology.
Asymptotic method for the Laplace equation, boundary layer analysis, Dire strait time and Brownian motion in cusp geometry.

The development of technology to read and write DNA quickly and cheaply is enabling new opportunities for programming biological systems. One example of this is DNA computing, a field devoted to implementing computation in purely biological materials. The hope is that this would enable computation to be performed inside cells, which could pave the way for so-called “smart therapeutics”. Naturally, what we have learned in computer science can be applied to DNA computing systems, and has enabled the implementation of a wide variety of examples of performing computation. Examples include DNA circuits for computing a square root, implementing artificial neural networks, and a general scheme for describing arbitrary chemical reaction networks (CRNs), which itself can be thought of as a compiler.

We have used such a CRN compiler of DNA circuitry to implement the approximate majority (AM) algorithm, which seeks to determine the initial majority of a population of agents holding different beliefs. In its simplest form, the algorithm can be described by three chemical reactions. In this talk, I will describe how we implemented, characterized and modelled a purely DNA implementation of the AM reactions. Along the way, I will demonstrate our software platform for programming biological computation. The platform brings together a variety of stochastic methods that are relevant for both programming and understanding biochemical systems, including stochastic simulation, integration of the chemical master equation, a linear noise approximation, and Markov chain Monte Carlo methods for parameter inference. I will also show preliminary work on synthesizing CRNs with specified probabilistic behaviours.

Related Links

• http://research.microsoft.com/en-us/people/ndalchau/ - Personal website
• http://research.microsoft.com/en-us/projects/dna/ - 'Programming DNA circuits' project

Bacterial persistence is probably the best-established example of a system where noisy gene expression provides a fitness benefit. By inducing switching between two phenotypes, one well-adapted to growth-promoting conditions and one adapted to survival in hostile conditions, noise allows provides a mechanism that allows a population to deal with unpredictable environmental conditions. In the talk I will discuss the gene circuits and feedback underlying persistence, aspects of the evolution of these circuits as well as how such heterogeneity of the population can be advantageous for the spreading of a population in space.

Related Links

• http://www.mpikg.mpg.de/th/people/klumpp/ - home page 

This lecture follows Part 1 of (Lecture 1/3)