BMCB625:Mathematics in Biology

Overview of Topic

1.) Take Home Message (Big Picture / Themes):

A.) Common Languages for Quantitative Biology

B.) Probability in Gene Expression

2.) Important Experimental Details

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Papers

Outline of Talk and Discussion

• Introduction: Perspectives between disciplines and the Language of Biology

Can we develop a common language? Is it mathematics? Should it be? In what cases?

• Classic Biological Underpinning by Mathematical (Statistical) Arguments

Luria-Delbrück Fluctuation Analysis

• Static Picture of Dynamic Pathways

The Lac Operon as a Model of Bistability and Stochastic Events

• Discussion

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PAPERS:

• MAIN PAPER: "Multistability in the lactose utilization network of Escherichia coli"

EM Ozbudak, et al, Nature 427, 737-740 (19 February 2004)

Main Paper

• CLASSIC: "Mutations of Bacteria from Virus Sensitivity to Virus Resistance"

S. E. Luria and M. Delbrück, Genetics. 1943 November; 28(6): 491–511

Classic Paper 1943 Luria & Delbruck

• See Below: "Biologists Fixing Radios"

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Chris - Bonus Materials

Ranking:

• Critical Read/of Outstanding Interest (oo)
• Importand Read (o)
• Of Interest (no label)

1. (o) A good primer on how biologists and engineers look at a problem in different ways; while many comments do not address the complexity of biochemistry and genetics, it does provide an interesting perspective on what we consider "important." Also, of importance, in my opinion, is developing a common language by which numerous disciplines can communicate. I'll touch more on this particular topic during my talk.

Y. Lazebnik, "Can a Biologist Fix a Radio? or, What I Learned while Studying Apoptosis" "Biologists Fixing Radios"

• Math in Bio Presentation 7 June 2007

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Unresolved Questions for Followup

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Discussion/Homework Questions

Mahta

Q1. (not to steal Jon's question) BUT - The authors state, "In this respect, the behaviour of the lac system closely resembles that of thermodynamic systems: the discontinuous transition from low to high induction is analogous to a first-order phase transition such as evaporation in a liquid-gas system, with chemical noise instead of thermal noise driving stochastic transitions between these states." All i have to ask is WHAT?

Q2. From "Can a Biologist Fix a Radio? - or, What I Learned while Studying Apoptosis" - Sorry to be anti-beauty pageant but isn't trying to create a universal language for biologists equivalent to achieving peace on earth?

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Larry

1. As a reductionist, I would attempt to explain the behavior of such circuits in terms of the behavior of the components, what are the limitations of this approach (reductionist view)?

2. "Despite many molecular components of biological organisms being identified and characterized using genetic and biochemical techniques, it is still not possible to predict system behavior except in the simplest systems."( pmid=17170763 ) What needs to happen in the field in order to be able to model more complex systems?

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Chayne

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Jon

The author's state: "The discontinuous transition from low to high induction is analogous to a first-order phase transition such as evaporation in a liquid-gas system, with chemical noise instead of thermal noise driving stochastic transition between these states"

Q: What is chemical noise and how is diffrent than thermal noise?

A: I think they mean the sugar - promoter interaction is "chemical noise" and it is analagous to the phase transition due to thermal noise.

Q:

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Jeremy

Q1. Thermodynamically speaking, why might it not be surprising that biological events exhibit hysteresis and bimodal behavior?

Part 1. Considering that the majority of protein-protein interactions or protein-ligand interactions take place at concentrations close to or near the Kd suggests that most processes exhibit bimodal like behavior. In other words, a small change in ligand concentration results in a large change in activity within the cell. The authors observe linear graded activity only when the concentration of protein (lacI) is reduced. The authors achieve this by introducing multiple lacI sites on a plasmid - titrating away protein and effectively reducing the concentration of free lacI.

Part 2. Kinetically speaking, if a protein ligand interaction has a slow off-rate.. the state of the complex depends on it's history and therefore exhibits hysteresis.

When comparing protein-ligand interactions it's often easy to forget the importance of comparing on and off rates. Two ligands may have similar affinities but have very different on and off rates. A ligand with a slow off rate would have a longer lasting effect.

Faculty Questions and Comments