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AMS 537, Biological Dynamics and Networks

This course will provide a solid foundation in key theoretical concepts for the study of dynamics in biological systems and networks at different scales ranging from the molecular level to metabolic and gene regulatory networks. Topics of this course include but are not limited to: Physical kinetics; Diffusion/Smoluchowskii; Random flights; Waiting times; Poisson; Brownian ratchets; Chemical kinetics; Transition states; Stability, bifurcations, pattern development; Noise in cells: intrinsic and Extrinsic; Feedback; Biological Osciillators; Recurrence, period doubling, chaos; Networks; Topologies; Degree distribution, betweenness; Models of nets: Erdos-Renyi, scale-free, social, Watts-Strogatz, agents; Robustness, highly-optimized tolerance, bowties, epidemics; Biological networks: Protein-protein nets, regulatory and metabolic nets; Known biological circuits and their behaviors; How networks evolve: Preferential attachment, rewiring; Power laws; Fluxed through networks; Information and communication, entropy; Metabolic flux analysis; Artificial and Natural selection for traits; Darwinian evolution; Population dynamics.

Offered in the Spring semester, 3 credits, ABCF grading

Crosslisted with PHY 559 and CHE 559

No course materials selected


Learning Outcomes:

1) Understand basic concepts in statistical thermodynamics: Physical kinetics, Diffusion/Smoluchowski, random flights, Brownian ratchets, Chemical kinetics. 

2) Biochemical networks and enzyme kinetics:
      * Become familiar with basic concepts: rate laws and basic properties of reactions;
      * Model and analyze the reversible linear and bilinear reaction;
      * Understand existing models of autocatalysis and dynamical stability;
      * Comprehend Michaelis-Menten and Hill kinetics for enzyme regulation.

3) Network measurements and models of network evolution:
      * Understand measures of networks such as degree distribution and centrality;
      * Become familiar with the small-world effect, power laws and scale-free networks;
      * Be able to apply models of network evolution such as preferential attachment.

4) Metabolic network modeling:
      * Understand how large metabolic networks can be modeled using stoichiometry matrices;
      * Model the process of glycolysis using the Sel’kov model.

5) Gene regulatory networks:
      * Acquire a basic knowledge of gene regulation and transcription network models;
      * Understand relevant gene network measures such as network motifs;
      * Model oscillations and autoregulation of gene expression.

6) Robustness:
      * Understand robustness in signaling networks using the bacterial chemotaxis model;
      * Analyze the process of development and understand the role of robustness.

7) The role of noise in biological systems:
      * Understand the difference between intrinsic and extrinsic noise in cells;
      * Become familiar with the Gillespie algorithm for stochastic biochemical simulations.

8) Population genetics:
      * Learn to model irreversible and reversible mutation processes;
      * Understand coalescence theory and the calculations relating to coalescent events.