# Scientific

## A Particle Based Model for Healthy and Malaria Infected Red Blood Cells

In this talk, I will describe a smoothed particle hydrodynamics method for simulating the motion and deformation of red blood cells. After validating the model and numerical method using the dynamics of healthy red cells in shear and channel flows, we focus on the loss of red cell deformability as a result of malaria infection. The current understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of about 3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out 3D numerical simulations of RBC stretching tests by optical tweezers to demonstrate this mechanism. Our results show that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. Thus, the previous interpretation of RBC-deformation data in terms of membrane stiffness alone is flawed. With the solid inclusion, the apparently contradictory data can be reconciled, and the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.

## Switches, Oscillators (and the Cell Cycle)

By incorporating positive and negative feedback into phosphorylation cycles of proteins such as GTPases (described in Lecture 2), one arrives at a biochemical mini-circuits with properties of a switch or an oscillator. I provide examples from papers by Boris Kholodenko. I also show the connection between bistability and hysteresis and relaxation oscillations (e.g. in the Fitzhugh-Nagumo model). I briefly

discuss applications of such ideas to models of the cell cycle proposed over the years by John Tyson.

## Mathematical Cell Biology Summer Course Lecture 5

- Cell biology imaging techniques
- 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
- 2. Fluorescence microscopy: Fluorescent labelling biological samples |

Epifluorescence microscopy |

Confocal fluorescence microscopy - 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging

(time permitting) - 4. FRAP data and modelling integrin dynamics

## Simple biochemical motifs (1, 2, & 3)

This triplet of introductory lectures summarizes a few of the most basic biochemical models with the simple rate equations that they satisfy. I describe production-decay, with Michaelis-Menten and sigmoidal terms, showing how the latter can lead to bistable behaviour and hysteresis. I describe two bistable genetic circuits: the toggle switch by Gardner et al (2000) Nature 403, and the phage-lambda gene by Hasty et al (2000) PNAs 97. The idea of bifurcations is discussed. Finally, I introduce

phosphorylation cycles, and show that sharp responses can arise when the enzymes responsible (kinase and phosphatase) operate near saturation. (This is the so called Goldbeter-Koshland ultrasensitivity).

## Mathematical Cell Biology Summer Course Lecture 3

- Cell biology imaging techniques
- 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
- 2. Fluorescence microscopy: Fluorescent labelling biological samples |

Epifluorescence microscopy |

Confocal fluorescence microscopy - 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging

(time permitting) - 4. FRAP data and modelling integrin dynamics

## Mathematical Cell Biology Summer Course Lecture 2

- Cell biology imaging techniques
- 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
- 2. Fluorescence microscopy: Fluorescent labelling biological samples |

Epifluorescence microscopy |

Confocal fluorescence microscopy - 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging

(time permitting) - 4. FRAP data and modelling integrin dynamics

## Introduction

This opening lecture lists some of the questions and issues propelling current research in Cell Biology and modelling in this field. I introduce basic features of eukaryotic cells that can crawl, and explain briefly the role of the actin cytoskeleton in cell motility. I also introduce the biochemical signalling that regulates the cytoskeleton and the concept of cell polarization. By simplifying the

enormously complex signalling networks, and applying tools of mathematics (nonlinear dynamics, scaling, bifurcations), we can hope to get some understanding of a few of the basic mechanisms that areresponsible for symmetry breaking, robustness, pattern formation, self-assembly, and other cell-level phenomena.

- Read more about Introduction
- 5324 reads

## Alan Turing and Enigma

Central to Alan Turing's posthumous reputation is his work with British codebreaking during the Second World War. This relationship is not well understood, largely because it stands on the intersection of two technical fields, mathematics and cryptology, the second of which also has been shrouded by secrecy. This lecture will assess this relationship from an historical cryptological perspective. It treats the mathematization and mechanization of cryptology between 1920-50 as international phenomena. It assesses Turing's role in one important phase of this process, British work at Bletchley Park in developing cryptanalytical machines for use against Enigma in 1940-41. It focuses on also his interest in and work with cryptographic machines between 1942-46, and concludes that work with them served as a seed bed for the development of his thinking about computers.

### Turing 2012 - Calgary

This talk is part of a series celebrating the Alan Turing Centenary in Calgary. The following mathtube videos are part of this series

- Alan Turing and the Decision Problem,
*Richard Zach*. - Turing's Real Machine,
*Michael R. Williams*. - Alan Turing and Enigma, John R. Ferris.

- Read more about Alan Turing and Enigma
- 9907 reads

## Turing's Real Machines

While Turing is best known for his abstract concept of a "Turing Machine," he did design (but not build) several other machines - particularly ones involved with code breaking and early computers. While Turing was a fine mathematician, he could not be trusted to actually try and construct the machines he designed - he would almost always break some delicate piece of equipment if he tried to do anything practical.

The early code-breaking machines (known as "bombes" - the Polish word for bomb, because of their loud ticking noise) were not designed by Turing but he had a hand in several later machines known as "Robinsons" and eventually the Colossus machines.

After the War he worked on an electronic computer design for the National Physical Laboratory - an innovative design unlike the other computing machines being considered at the time. He left the NPL before the machine was operational but made other contributions to early computers such as those being constructed at Manchester University.

This talk will describe some of his ideas behind these machines.

### Turing 2012 - Calgary

This talk is part of a series celebrating The Alan Turing Centenary in Calgary. The following mathtube videos are also part of this series

- Alan Turing and the Decision Problem,
*Richard Zach*. - Turing's Real Machine,
*Michael R. Williams*. - Alan Turing and Enigma,
*John R. Ferris*.

- Read more about Turing's Real Machines
- 12082 reads

## Alan Turing and the Decision Problem

Many scientific questions are considered solved to the best possible degree when we have a method for computing a solution. This is especially true in mathematics and those areas of science in which phenomena can be described mathematically: one only has to think of the methods of symbolic algebra in order to solve equations, or laws of physics which allow one to calculate unknown quantities from known measurements. The crowning achievement of mathematics would thus be a systematic way to compute the solution to any mathematical problem. The hope that this was possible was perhaps first articulated by the 18th century mathematician-philosopher G. W. Leibniz. Advances in the foundations of mathematics in the early 20th century made it possible in the 1920s to first formulate the question of whether there is such a systematic way to find a solution to every mathematical problem. This became known as the decision problem, and it was considered a major open problem in the 1920s and 1930s. Alan Turing solved it in his first, groundbreaking paper "On computable numbers" (1936). In order to show that there cannot be a systematic computational procedure that solves every mathematical question, Turing had to provide a convincing analysis of what a computational procedure is. His abstract, mathematical model of computability is that of a Turing Machine. He showed that no Turing machine, and hence no computational procedure at all, could solve the Entscheidungsproblem.

### Turing 2012 - Calgary

This talk is part of a series celebrating the Alan Turing Centenary in Calgary. The following mathtube videos are also part of this series

- Alan Turing and the Decision Problem,
*Richard Zach*. - Turing's Real Machine,
*Michael R. Williams*. - Alan Turing and Enigma,
*John R. Ferris*.