Math 449Dynamical systems in Biology

and Medicine.D. Gurarie

Overview

Structure/Organization

Genom

Cell

Tissue

System

Organism

Population

Eco system

Environment

Function/Process

Signaling:chemical (enzyme kinetics)neural

Expression ReproductionRegulation

Species interaction:competition/cooperation(symbiosis, parasitism)

Anatomy, physiology, behavior(e.g. locomotionadaptation, migration, invasion)

EpithelialConnectiveMuscularnervous

SkeletalDigestiveRespiratoryEndocrinal

Immune …

Pathogens/Diseases

Living world

Dynamic Modeling

• Model Structure:

– State space (variables and parameters)

– Model type: discrete, continuous, deterministic, stochastic,…

– Mathematical tools/techniques: differential equations, discrete

eq-ns, combinatorial structures (graphs, networks, etc.)

– Computer tools

Objectives, strategies:

•Build “mathematical cartoons” of real (physical, chemical, biological)

systems

•analyze, identify dynamic patterns (e.g. equilibria, cycles, chaos).

•Develop math. concepts, tools and techniques (analytic, numeric,

exact, qualitative)

•Solution methods for predicting outcomes

•Parameter estimation and model validate

Applications:

•explain data

•make predictions

•test hypotheses

•run numeric (virtual) experiments, compare with real/

data/experiments