Syllabus
MTH994, Biological Modeling and Computation I
Fundamentals of biological sciences. (1) Mechanical foundation: Quantum
mechanics of biomolecules. The Schrodinger equation; Interaction potentials;
Chemical bondings; Intermolecular forces; Classical mechanics and its role
in biology; Interconnection between classical mechanics and quantum mechanics.
(2) Structure and catalysis: Protein structure and function; DNA and RNA
sequences and structures; carbohydrates; Lipids; Enzyme and chemical dynamics;
Membranes and transport; Biosignaling; (3) Bioenergetics and metabolism:
Principles of bioenergetics; Glycolysis; Fatty acid catabolism; Carbohydrate
biosynthesis in plants and bacteria; Metabolic regulations. (4) Information
pathways: Genes and chromosomes, Metabolism of DNA, RNA and protein;
Regulation of gene expression. (5) Cellular structure and function; Cellular
dynamics and transport.
-------------------------------------------------------------------------
MTH994, Biological Modeling and Computation II
Principles of thermodynamics; Statistical ensembles; Maxwell-Boltzmann
statistics; Fermi-Dirac and Bose-Einstein statistics; Random work; Stochastic
process; Markov process; Master equation; Fokker-Planck equation; Brownian
motion and Langevin equation; Autocorrelation; Density matrix; Liouvelle
equation; Zwanzig's equation; Linear response theory; Boltzmann equation;
Theory of liquids; Brownian ratchets; Molecular motor; Biomechanics; Protein
membrane interaction; Evolutionary genomics; mathematical approaches to the
discovery of gene motifs; Gene regulation; Explanatory and predictive models
of cellular growth and interaction; Metabolic circuitry and dynamics; Signal
transduction and enzyme dynamics; Phylogenetic analysis; Biosensors;
Neuroscience; Electrostatics in metabolic process; Fluid-macromolecule
interaction and impact to metabolism; Molecular dynamics and force fields;
Monte Carlo; Implicit solvent modeling; Poisson-Boltzmann equation.