Applied/ACMS/absS11: Difference between revisions

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== Alex Kiselev, UW-Madison (Mathematics) ==
== Tatiana M$aacute;rquez-Lago, ETH-Zurich ===


<center>
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
|-
| bgcolor="#DDDDDD" align="center"| '''Biomixing by chemotaxis and enhancement of biological reactions'''
| bgcolor="#DDDDDD" align="center"| '''Stochastic models in systems and synthetic biology'''
|-
|-
| bgcolor="#DDDDDD"|   
| bgcolor="#DDDDDD"|   
Many processes in biology involve both reactions and chemotaxis.
Cells prevail as efficient decision makers, despite the intrinsic
However, to the best of our knowledge, the question of interaction between chemotaxis and reactions has not yet been addressed either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction (fertilization). The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization
uncertainty in the occurrence of chemical events, and being embedded
rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that  in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the
within fluctuating environments. The underlying mechanisms of this
estimates in chemotactic case is that rates and timescales of the reaction
ability remain widely unknown, but they are critical for the correct
(fertilization) process do not depend on the reaction amplitude coefficient.  
understanding of biological systems output and predictability. Some
advances have been achieved by considering biological processes as
modular units, but the conclusions in many studies vary alongside
experimental conditions, or easily break down once the system is no
longer isolated. Moreover, sets of seemingly simple biochemical
reactions can generate a wide range of highly non-linear complex
behaviours, even in the absence of crosstalk.
 
<br><br>
 
To illustrate some of these challenges, encountered in everyday
biological/pharmaceutical research, I will present three short stories
showing how iterations between mathematicians, computer scientists and
biologists can generate successful ideas, testable in the laboratory.
 
<br><br>
 
The first story revolves around a tunable synthetic mammalian
oscillator, from the individual cell perspective and population
behavior. The long term importance of this work lies in discerning
whether it is possible to influence the underlying genetic clockwork
to tune the expression of key genes. Answering this question may prove
to be central in the design of future gene therapies, particularly
those requiring a periodic input.
 
<br><br>
 
In the second story I will show how closures on master equations
describing negative self-regulation may yield diametrically opposed
noise effects to those expected by exact solutions, discovering how
any noise profile (and correlations between mRNA transcription and
protein synthesis) can be created by the consideration of specific
kinetic rates and network topologies.
 
<br><br>
 
Lastly, I will illustrate in a third story how chemical adaptation can
many times be considered a purely emergent property of a collective
system (even in simple linear settings), how a simple linear
adaptation scheme displays fold-change detection properties, and how
rupture of biological ergodicity prevails in scenarios where
transitions between protein states are mediated by other molecular
species in the system.
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</center>
</center>
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<br>
<br>


== Alex Kiselev, UW-Madison (Mathematics) ==


<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#DDDDDD" align="center"| '''Biomixing by chemotaxis and enhancement of biological reactions'''
|-
| bgcolor="#DDDDDD"| 
Many processes in biology involve both reactions and chemotaxis.
However, to the best of our knowledge, the question of interaction between chemotaxis and reactions has not yet been addressed either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction (fertilization). The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization
rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that  in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the
estimates in chemotactic case is that rates and timescales of the reaction
(fertilization) process do not depend on the reaction amplitude coefficient.
|}                                                                       
</center>
<br>


== James Rossmanith, UW-Madison (Mathematics) ==
== James Rossmanith, UW-Madison (Mathematics) ==

Revision as of 14:15, 5 February 2011

Cynthia Vinzant, UC Berkeley

The central curve in linear programming

The central curve of a linear program is an algebraic curve specified by the associated hyperplane arrangement and cost vector. This curve is the union of the various central paths for minimizing or maximizing the cost function over any region in this hyperplane arrangement. Here we will discuss the algebraic properties of this curve and its beautiful global geometry. In the process, we'll need to study the corresponding matroid of the hyperplane arrangement. This will let us give a refined bound on the total curvature of the central curve, a quantity relevant for interior point methods. This is joint work with Jesus De Loera and Bernd Sturmfels appearing in arXiv:1012.3978.


József Farkas, University of Stirling, Scotland

Analysis of a size-structured cannibalism model with infinite dimensional environmental feedback

First I will give a brief introduction to structured population dynamics. Then I will consider a size-structured cannibalism model with the model ingredients depending on size (ranging over an infinite domain) and on a general function of the standing population (environmental feedback). Our focus is on the asymptotic behavior of the system. We show how the point spectrum of the linearised semigroup generator can be characterized in the special case of a separable attack rate and establish a general instability result. Further spectral analysis allows us to give conditions for asynchronous exponential growth of the linear semigroup.


Tatiana M$aacute;rquez-Lago, ETH-Zurich =

Stochastic models in systems and synthetic biology

Cells prevail as efficient decision makers, despite the intrinsic uncertainty in the occurrence of chemical events, and being embedded within fluctuating environments. The underlying mechanisms of this ability remain widely unknown, but they are critical for the correct understanding of biological systems output and predictability. Some advances have been achieved by considering biological processes as modular units, but the conclusions in many studies vary alongside experimental conditions, or easily break down once the system is no longer isolated. Moreover, sets of seemingly simple biochemical reactions can generate a wide range of highly non-linear complex behaviours, even in the absence of crosstalk.



To illustrate some of these challenges, encountered in everyday biological/pharmaceutical research, I will present three short stories showing how iterations between mathematicians, computer scientists and biologists can generate successful ideas, testable in the laboratory.



The first story revolves around a tunable synthetic mammalian oscillator, from the individual cell perspective and population behavior. The long term importance of this work lies in discerning whether it is possible to influence the underlying genetic clockwork to tune the expression of key genes. Answering this question may prove to be central in the design of future gene therapies, particularly those requiring a periodic input.



In the second story I will show how closures on master equations describing negative self-regulation may yield diametrically opposed noise effects to those expected by exact solutions, discovering how any noise profile (and correlations between mRNA transcription and protein synthesis) can be created by the consideration of specific kinetic rates and network topologies.



Lastly, I will illustrate in a third story how chemical adaptation can many times be considered a purely emergent property of a collective system (even in simple linear settings), how a simple linear adaptation scheme displays fold-change detection properties, and how rupture of biological ergodicity prevails in scenarios where transitions between protein states are mediated by other molecular species in the system.


Tim Reluga, Penn State University

Title

Abstract


Alex Kiselev, UW-Madison (Mathematics)

Biomixing by chemotaxis and enhancement of biological reactions

Many processes in biology involve both reactions and chemotaxis. However, to the best of our knowledge, the question of interaction between chemotaxis and reactions has not yet been addressed either analytically or numerically. We consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction (fertilization). The model is motivated, in particular, by studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We prove that in the framework of our model, chemotaxis plays a crucial role. There is a rigid limit to how much the fertilization efficiency can be enhanced if there is no chemotaxis but only advection and diffusion. On the other hand, when chemotaxis is present, the fertilization rate can be arbitrarily close to being complete provided that the chemotactic attraction is sufficiently strong. Moreover, an interesting feature of the estimates in chemotactic case is that rates and timescales of the reaction (fertilization) process do not depend on the reaction amplitude coefficient.


James Rossmanith, UW-Madison (Mathematics)

High-order relaxation schemes for hyperbolic conservation laws

Abstract


Anne Gelb, Arizona State University

Title

Abstract


Vageli Coutsias, University of New Mexico

Title

Abstract


Smadar Karni, University of Michigan

Title

Abstract


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