The SMB Annual Meeting was held at the University of Toronto July 13-17. It was held in conjunction with SIAM's Annual and Discrete Mathematics Meetings. The meeting was well attended; by my estimate over 1000 registered, and over 100 attendees participated in the SMB meeting/poster session/reception on Wednesday evening at the Fields Institute.

A brief summary of each talk is included where possible.

A short course, "Introduction to Computational Genomics" by Mark W. Perlin preceded the meeting on Sunday.

An introduction to what genomics is included current efforts in information science and chemistry, the goal to understand the cellular operating system and organisms as well as diagnosis and treatment of disease, and methods used: informatics as well as the physical and biological sciences. The rudiments of biotechnology included informatics and chemistry of DNA, hybridization, and the polymerase chain reaction. The mathematical perspective included information processing as central to genomics plus experimental design, analysis and examples of applications.

Genetic mapping was described, including recombination, linkage maps, markers and traits followed by microsatellite genotyping, laboratory experiments and data interpretation methods and examples.

Radiation hybrid mapping discussed included association of DNA markers to locations, mathematical methods used and sample maps.

Plenary talks during the week included:

G. M. Crippen, "A Mixed Integer Program for Deducing Objective Models of Drug Receptor Sites from Experimental Binding Data".

That small drug molecules must bind to a particular site on a large receptor protein is an essential step to producing a desired biological response in drug discovery. The speaker presented an objective way of finding a range of models that deduce receptor site's shape and energetics of interaction to predict the binding of other molecules with estimated uncertainties.

Jurg Ott, "Statistical Aspects of Genetic Mapping in Human Families".

Approaches to gene mapping using nonparametric statistics and open problems were discussed.

Richard M. Karp, "Discrete Mathematics as a Tool for Molecular Biology"

Combinatorial problems that arise in radiation hybrid mapping, sequence-tagged-site mapping and restriction mapping were discussed as well as combinatorial problems that arise in the analysis of gene expression data.

Minisymposia of special interest included the following:

Fisheries (Organizer: Ransom Myers; Speakers: Robert McKelvey, Russell Millar, Michael Fogarty, Ransom Myers)

DNA Computing: Arrival of Biological Mathematics (Organizer: Lila Kari; Speakers: Lila Kari, Masami Hagiya, John Reif, Laura Landweber)

Lila Kari, in "DNA Computing: Arrival of Biological Mathematics", addressed two questions proposed by Adleman [Molecular computation of solutions to combinatorial problems. Science. 1994 Nov 11; 266(5187): 1021-1024], namely:

1. Does EVERY computing problem have a DNA-based solution? and
2. Is it possible, at least theoretically, to construct programmable "test-tube" DNA computers?

Mathematical Biology (Organizer Suzanne Lenhart; Speakers: Meghan Burke, Zhilian Feng, Ramit Mehr, Rebecca Tyson)

Ramit Mehr, in "Modelling the Metadynamics of Lymphocyte Repertoires", described how receptor genes rearrange from segment libraries to create highly diverse repertoires to recognize most antigens. The biology was described for modelling repertoire metadynamics, from the stochastic generation of new clones, through competition between clones, through competition between clones to emergent properties including learning and memory.

Discrete Math/Modeling (Organizer: Brigitte Servatius; Speakers: Katherine St. John, Sharon Crook, Joan Remski, Graciela Cerezo)

Sharon Crook, in "Modelling Cortical Oscillations with Networks of Coupled Phase Oscillators", used such models to examine mechanisms that affect cortical dynamics.

Graciela Cerezo, in "Modelling the Distributional Dynamics of a Clam Population along the Coasts of Argentina", presented a model of the life cycle of Mesodesma mactroides integrated with a model of the physical environment. Results of a discrete model and a continuous model that couples the coastal population dynamics of the species with transport processes in the ocean were shown, as was how these may help to create restoration and conservation of the species.

Time Delays in Physiological and Neural Systems (Organizer: Jacques Belair; Speakers: Coraci Malta, Harold Layton, John Milton, Jacques Belair)

Harold Layton, in "Oscillations in the Tubuloglomerular Feedback System", described a model of the TGF pathway that shows oscillations arising from two distributed delays; namely, the time for fluid to travel up the thick ascending loop of Henle, and the time for macula densa cells to sense the fluid composition delivered to the distal tubules. Model results predict that for a sufficiently large feedback loop gain magnitude, the oscillations have the potential to decouple water and NaCl delivery to the distal nephron.

John Milton, in ";Multistability in Neural Computer Devices (NCD)", discussed multistability in prototype NCDs involving Aplysia motoneurons and the human pupil light reflex.

Jacques Belair, in "Timing and Delays in Drug Administration", described the need to take into account time delays due to circulation in the design of theraputic drug treatments. Examples were given of both beneficial as well as undesirable oscillations due to treatment strategies.

Interactive Mathematical Biology's Role in Curriculum Reform (Organizer: John Jungck; Speakers: John Jungck, James Haefner, Evans Afenya, James Cornette)

Theoretical Population Biology: Examples at Multiple Scales (Organizer: Denise Kirschner; Speakers: Suzanne Lenhart, Ramit Mehr, James Sneyd, Michael Savageau)

Ramit Mehr, in "Modeling B Cell Repertoire Shift", described how antibodies dominating the secondary immune response are often produced by different B cell lineage from that which dominated the primary response. A mathematical model and computer simulations of the dynamics of competing B cell clones was used to examine the various hypotheses that attempt to explain repertoire shift. In combination with experimental data, the suggestion was made that differentiation of mature B cells and their earlier development may use the same mechanisms.

James Sneyd, in "Talking with Nonlinear Waves: Coordination in Cell Populations", described how the theory of nonlinear waves can be used to study intracellular communication, and how the mathematical problems differ for different cell types. Examples included cardiac tissue, the liver, the hippocampus, and the trachea.

Michael Savageau, in "Function, Design and Evolution of Gene Circuitry", presented a quantitative theory to predict selection of the mode of control as well as minimum, maximum and nominal values for gene cycle time in an organism.

Unstable Periodic Orbits in Biology: Identification and Control (Organizers: Daniel Kaplan and James Collins; Speakers: William Ditto, Frank Moss, Daniel Gauthier, James Collins)

William Ditto, in "Unstable Fixed Points in Biological Systems: Tips, Traps and Techniques", demonstrated control of fixed points in human atrial and canine ventricular fibrilation and in rat hippocampal slices.

Employment Opportunities for Applied Mathematicians in Biotechnology (Organizer: Leon Glass; Speakers: Jamie Cuticchia, Thomas Paterson, Frank Tobin, Jeffrey Sachs)

Mathematical Modeling in Physiology (Organizers: Jonathan Bell and Bruce Pitman; Speakers: James Collins, Timothy Lewis, Arthur Sherman, Gregory Smith)

James Collins, in "Noise-Enhanced Dynamics in Sensory Neurons", showed how noise can enhance the detection and transmission of weak signals in certain nonlinear systems. Stochastic resonance behavior was demonstrated in single model neurons, networks of model neurons, rat cutaneous motor neurons and the human-touch sensation system.

Timothy Lewis, in "The Effects of Nonexcitable Regions on Signal Propagation in Excitable Media: Propagation Failure and Reflection", demonstrated and gave examples of dynamical mechanisms that form the basis of arrythmia-generating phenomena of propagation failure and reflection in a cardiac tissue model.

Arthur Sherman, in "Heterogeneous Patterns of Pancreatic Beta-Cell Activity Studied with Modelling and Dynamic Current Clamp" describes how pancreatic islet response might be constructed from isolated cell activity,

Gregory Smith, in "Fourier Analysis of Sinusoidally Driven Thalamocortical Relay Neurons and a Minimal Integrate-and-Fire-or-Burst Model", showed results of a minimal IFB model that reproduces many of the features of thalamocortical relay cell responses to sinusoidal current injection. The model is constrained using Fourier analysis of intracellular records from cat thalamic slices and experimental observations.

Contributed presentations of special interest included:

Gerda de Vries, in "Effect of Noise on the Emergent Collective Behaviour of Diffusively Coupled Biological Oscillators", demonstrated that the addition of noise produces a stochastic resonance-like phenomenon that increases the coupling range over which bursting develops from tonically spiking isolated cells.

Rebecca Tyson, in "Model and Analysis of Chemotactic Salmonella Typhimurium Patterns in Semi-Solid Medium", presented a mathematical model of a chemotactic phenomenon that induces bacteria to form large spatial patterns. A nonlinear analysis predicted the parameter regions in which certain limited pattern types exist, namely, spots and stripes, and it was shown how these patterns relate to patterns obtained experimentally.

Carl Panetta, in "Mathematically Modeling the Effects of Paclitaxel and Cisplatin on Cancer", described models to study the cell kinetics of the cancer and the pharmacokinetics of the two drugs paclitaxel and cisplatin, and used the models to explain results seen clinically and suggest effective treatment regimens.

Jonathan Bell, in "Direct and Inverse Problems Associated with Modeling the Dynamics of a Skin Receptor", described the development of a non-classical cable model for the nerve ending and the appropriate oblique boundary conditions. Conditions for the boundary potential to reach threshold were given, and initial work on recovering properties of the stimulus based on additional boundary and voltage measurements was presented.

Jonathan Rubin, in "Synchronization Mechanisms in Neuronal Network Models with Fast Inhibitory Synapses", used new neuronal models and more complicated neuronal architectures to show that stable, synchronous oscillations can be produced by fast inhibitory coupling. Crucial qualitative differences in inhibitory synchronization mechanisms were shown when additional network complexity is considered.