Models and methods in systems biology Daniel Kluesing Algorithms in Biology Spring 2009

Engineering Principles Simple primitives Abstraction layers Composable Systems Robust and well characterized Manage complexity Should also work in biology

Executable Cell Biology Jasmin Fisher, Thomas Henzinger Nature Biotechnology, November 2007

Mathematical v Computational Mathematical –Describe relationships between quantities –Differential equations, probability models –Composition of transfer functions –Simulated, quantitative Computational –Sequence of steps –State machines –Transitions between states –Executed, qualitative, abstractions

Mathematical model Describe changes in quantities over time Need an algorithm for simulating and solving Differential equations

Computational Models Large number of states Non-linear, non-deterministic Hard to model mathematically Executes itself Abstraction layers

Populations Organism Organ Tissue Cell Signaling networks Metabolic pathways Protien-protien interaction Genes DNA segment Base pairs Molecules Network Program Class Function Variable Bits Logic gates Transistors Atoms

Model Checking Given a model Test if model meets specification Systematically analyze the outcomes of a computational model without executing them individually Explore states rather than all executions Efficient

Model Checking Computational models can be analyzed by model checking –Yields a proof Mathematical models can often only be simulated –Only as good as your data, edge cases

Formal Verification Fsu.edu We know exactly what this chip does, for all input We can prove that it works correctly for all conditions Can make guarantees about its operation No data mining required

Executable cell biology Many of the algorithms covered in class –Gather a bunch of data –Train a model –Model explains data –May not reflect biology –Looking inside an SVM isn’t useful Would like to have a model of the underlying system Algorithms that mimic biological phenomena

Executable Biology Fisher et al

Boolean Models Each gene or protein is either on or off Activation level determines state at next time step Gene regulatory networks

Boolean Models Easy to build, efficient to analyze Show causal and temporal relationships Deterministic But –Difficult to compose –Cannot build larger models from several small ones

Petri Nets Used to model distributed systems Two types of nodes –Places (resources) –Transitions (events) Edges connection places to transitions and transitions to places Multiple tokens on the graph More than one token can move at a time

Petri Nets Animation: Wikipedia

Petri Nets

Petri Nets Generalization of Boolean networks Visual design and analysis Non-deterministic Colored tokens, stochastic nets But –Still can’t compose networks

Interacting state machines

Interacting state machines Multiple state machines Communication between machines Fisher et al

Interacting state machines Fisher et al

Interacting State machines Natural abstraction and hierarchy Qualitative Easy to run model checking on Mature and well tested tools and languages

Process calculi Languages that model communicating processes Interactions between molecules Process is a state machine –Some state changes are events –Events allow communication between processes

Process calculi Interactions as message passing –No shared variables Small set of primitives –Operators to combine primitives Algebraic laws Parallel and sequential composition Directed communication

Hybrid Models Combine computational and mathematical models Discrete state changes update differential equations Fisher et al

Challenges and Open Questions What about GFP? What are the biological abstraction layers?

Quantitative measures Experimental data is often unit less ratios Direct measurements make parameter setting easier Need better experimental methods to get direct measurement of signals Convert observed fluorescence into number of molecules

Bio Logic Gates Fisher et al

Biology as engineering Design and build systems Very large scale integration Hierarchy and levels of abstraction Robust and fully characterized

Regulation of Gene Expression in Flux Balance Models of Metabolism Markus Covert, Christophe Schilling, Bernhard Palsson Journal of Theoretical Biology, 2001

Flux Balance Analysis Cells obey the laws of physics and chemistry We can write down the reactions We know the basic governing laws –Conservation of mass –Conservation of energy –Redox potential So, cell behavior is constrained

Flux Balance Analysis

Flux Balance Analysis Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Advances in flux balance analysis, 2003 Kenneth J Kauffman, Purusharth Prakash and Jeremy S Edwards

Flux Balance Analysis

Regulation FBA assumes all gene products are available to contribute to a solution E. Coli has 600 metabolic genes 400 regulatory genes High levels of transcriptional regulation

Regulation Constraints change shape of solution space Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Representing transcriptional Regulatory Constraints Boolean logic equations If all products present, flux determined by FBA If all products not present, place a temporary constraint Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Carbon core metabolic network Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Simulating different Conditions Two carbon sources, aerobic Two carbon sources, diauxic shift Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Amino Acid biosynthesis Picture: Regulation of Gene Expression in Flux Balance Models of Metabolism, Covert et al

Further Advances Explicit incorporation of thermodynamics Different objective functions –Maximization of biomass –Maximization of ATP –Maximizing rate of synthesis of a product

Takeaways Quantitative dynamic simulation of –Substrate uptake –Cell growth –By-product secretion Qualitative simulation of gene transcription and proteins in cell Explore system effects of regulatory constraints

Metabolic modeling of microbes: the flux-balance approach, Environmental Microbiology, 2002 Jeremy S. Edwards, Markus Covert and Bernhard Palsson