Models and methods in systems biology

Daniel KluesingAlgorithms in Biology

Spring 2009

http://www.estudisbarbera.es/hardware/articles/cpu/imatges/big/2000_Pentium4.jpg

Engineering Principles

• Simple primitives• Abstraction layers• Composable Systems• Robust and well characterized• Manage complexity

Should also work in biology

http://pworldrworld.com/blog/wp-content/uploads/2008/07/hummingbird.jpg

http://science.howstuffworks.com/ten-bungled-flight-attempt.htm

http://www.efluids.com/efluids/gallery_problems/gallery_images/fighter.jpg

Executable Cell BiologyJasmin 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

Abstraction layersPopulations

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

www.ra.cs.uni-tuebingen.de

www.zaik.uni-koeln.de

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

http://upload.wikimedia.org/wikipedia/commons/f/fe/Detailed_petri_net.png

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

www.odetocode.com/Articles/460.aspx

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?

http://www.snl-c.salk.edu/DavidLyon/Virus_Transport_DSRED_GFP.jpg

http://www.wormbook.org/chapters/www_germlinegenomics/germlinegenomicsfig1.jpg

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

http://covertlab.stanford.edu/projects/iFBA/

Flux Balance Analysis

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

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

Flux Balance Analysis

http://covertlab.stanford.edu/projects/iFBA/

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, 2002Jeremy S. Edwards, Markus Covert and Bernhard Palsson