# Topics in detail

## Introduction to biocybernetics

Definition of systems. Comparison of natural and artificial systems. Applicability of systems theory and engineering in biology. Components of biological systems. Biological time series. Modelling biological phenomena.

#### Supporting material

: CoCalc Primer (PDF), Python primer (PDF).## First-order kinetics

Stock-and-flow model of inflation. First-order chemical reactions and reaction networks. Systems of linear ordinary differential equations. Solving linear ODE systems by finding the eigenvalues and eigenvectors of the coefficient matrix. Qualitative behaviour of linear systems.

#### Supporting material

: Linear algebra with CoCalc (PDF), Solving differential equations with CoCalc (PDF).## Biochemical kinetics

Bulk-phase mass action kinetics. Reversible reactions, equilibrium. Isomerisation catalysis. Enzyme kinetics models: steady-state approximation, Michaelis-Menten rate equation. Competitive and noncompetitive inhibition.

## Principles of genomic regulation

The molecules of life: DNA, RNAs, proteins. The "central dogma": transcription and translation. The differences between prokaryotic and eukaryotic organisms.

Prokaryotic genome regulation: the *E. coli* lac operon,
the lambda phage bistable switch, the "Repressilator" synthetic genetic network.

Eukaryotic genome organisation: chromosome structure, splicing, epigenetic regulation. The self-regulatory Hes1 network.

## Oscillations and chaos

Periodic phenomena in living systems. The Byelousov-Zhabotinsky chemical oscillator. Biological examples of oscillatory phenomena: glycolysis, mitotic oscillations, predator-prey interactions (Lotka-Volterra models).

Chaotic dynamics. The Lorenz attractor and the logistic map. Chaos in enzyme-catalysed reactions. Qualitative behaviour of nonlinear differential equations, the linearisation approach. Detecting chaotic behaviour with Lyapunov exponents.

## Stochastic biochemical kinetics

Basic probability theory. Rolling dice in software. Bayes' Rule. Principles of stochastic kinetics. Master equation approach, the Gillespie stochastic simulation algorithm. Properties of Markov chains. "Convergence" of stochastic kinetic trajectories to the bulk kinetics model in the limit of very large number of molecules.

## Systems modelling

How to construct mechanistic hypotheses from observations. Popper's falsifiability theory. Kinetic indistinguishability. System analysis by structural or parameter perturbation. Robustness of genetic networks. Self-regulation in biochemical networks: metabolic control theory, flux balance analysis.

## The theory of evolution

Fundamental concepts. Lamarckian and Darwinian evolution. Evolution of macromolecular sequences, molecular phylogeny. Epigenetic inheritance.

## Genetic algorithms

Genetic algorithm optimisation techniques. Genetic programming, symbolic regression.

## Computing with biomolecules

Quasi-digital approaches: Adleman's DNA-based solution of the travelling salesman problem and related efforts. Molecular implementations of Boolean logic gates. Computing with enzymatic reaction networks. Simple learning phenomena.

## Fourier analysis

Scalar product of functions. Orthogonal decomposition. Polynomial and trigonometric bases. The Fourier series and the Fourier transform. Signal processing in the inner ear. Solving differential equations with the Fourier transformation. Power spectral density, Wiener-Khinchin theorem. Rate constants from noise in chemical equilibrium: the Feher-Weissman method.

## Regulation in spacetime

Algorithmic models of
plant growth, applications in computer graphics.
Turing's theory of morphogenesis.
Modelling reaction-diffusion networks with partial differential equations.
Solving the diffusion equation with Fourier transformation techniques.
The Gierer-Meinhardt model
of pattern formation in *Dictyostelium discoideum*.
Robustness of pattern formation in living systems.

## Artificial life

Chemoton theory: self-reproducing autocatalytic reaction networks. Cellular automata, Conway's "The Game of Life". In silico models of simulated evolution: the Tierra and Avida systems.