The Structure, Function, and Evolution of Biological Systems

1. The Structure, Function, and Evolution of Biological Systems Instructor: Van Savage Spring 2010 Quarter 4/13/2010

2. Recent papers using models of epistasis: Michel, Yeh, Chait, Moellering, Kishony

3. Measuresofepistasis Since covariance is as fundamental as fitness, why not define relative covariance instead of relative fitness. We define it relative to tri-modally binned covariance that itself varies, so relative to a shifting baseline. Absolute covariance Relative covariance

4. Measures of epistasis—based onFBA predictions in yeast Sort of unimodal distribution goes to trimodal distribution Opposite of Lenki et al. because synergy is enriched. Why?

5. ….and some pathogens grow very quickly a1-phm-gro.wmv

6. They can be killed by antibiotics… a1-phm-kil.wmv

7. X X …but some bacteria can become resistant to the drug Antibiotic Resistant Bacterium Sensitive Bacterium

8. X X Resistance confers a large fitness advantage in the presence of the drug Resistant bacteria, CFP compDOX.mpg Sensitive bacteria, YFP

9. Antibiotic resistance a growing public health threat Years

10. Main Questions • How do drugs interact with each other, and how can we use their interactions to determine their mechanisms of action? • How do drug interactions affect the evolution of drug-resistant bacteria? • Future Directions: What role do birds play in the transmission of drug-resistant bacteria?

11. Multiple drugs combine to fight bacteria Drug A Drug B Two drugs can interact with each other to produce varying effects

12. Can we do reverse and cluster monochromatically to find functional groups? Construct network for all pairwise interactions, Start with each gene in its own group. Cluster by pairs if they interact with other genes in same way. Require monochromaticity, each group must interact with all other groups in same way Within a group there is no requirement for monochromaticity Make cluster sizes as large as possible Cluster Movie How clusterable are networks? Is clustering unique? If not, which instantiation is chosen?

13. Drug-Drug Network  Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006

14. Drug-Drug Network  Functional Classification Cell Wall DNA Aminoglycosides Folic Acid Functional classification of a new drug 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006

15. Drug-Drug Network  Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006

16. Drug-Drug Network  Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006

17. Drug-Drug Network  Functional Classification Cell Wall DNA Aminoglycosides Folic Acid Putative novel action mechanisms 50S 30S Protein Synthesis Yeh et al. – Nature Genetics 2006

18. Conclusions (part 1) • Drugs can be classified by their underlying mechanism of action based only on properties of their interaction network. • Drugs with novel mechanism of action can be identified as drugs that cannot be classified with any existing groups.

19. How do drug interactions affect the evolution of resistance? Main result: Antagonism, typically avoided in clinical settings, better slows the emergence of resistant bacteria

20. wild type Mutant Selection Window Some drug concentrations select for resistance 1 10-4 Frequency of resistance 10-8 0 0 MIC MPC Drug concentration The Mutant Selection Window is one measure of the potential to evolve resistance MPC: Mutant Prevention Concentration MIC: Minimal Inhibitory Concentration Dong et al. 1999, Drlica 2003

21. Multi-drug 1 Mutant Selection Window 10-4 Frequency of resistance 10-8 0 0 MIC MPC Drug concentration Concentration of drug Y Concentration of drug X In two-drug treatments, the “Mutant Selection Window” becomes an “area” of drug concentrations. Single Drug Michel,Yeh, et al. – PNAS 2008 Dong et al. 1999, Drlica 2003

22. We want to minimize the area that resistant mutants can grow. For distance, we choose straight lines drawn through the origin. Why? Concentration of drug Y Concentration of drug X These lines imply constant ratio of drug concentrations. This is what would be designed in a single pill and the amount prescribed would push you up and down this line. It would signal how much more of drug to prescribe to kill of resistants and not just wild type. Could also look for lowest dosage that gives MPC.

23. Imaging platform delivers resistance frequencies on 2-D drug gradient Michel,Yeh, et al. – PNAS 2008

24. 103 103 102 102 MSW MSW 10 10 1 ERY ERY:FUS FUS 1 Drug ratio AMI AMI:FUS FUS Drug ratio Selection for resistance strongly depends on the drug combination Michel,Yeh, et al. – PNAS 2008

25. MICB MICB MICB MICA MICA MICA Another view of antibiotic interactions Isobolograms Loewe additivity Effect of drugs are independent, so all that matters is total concentration. Can imagine then that Cx+Cy=Cx,MIC or Cy,MIC. Every drug is normalized to its MIC, so the combined MIC line is defined by

26. MICB MICB MICB MICA MICA MICA Loewe additivity and epistaticadditivity Loewe additivity Fitness is scaled by MIC line for each drug independently. Combination is product of the two, and then just set Fxy equal to 0.

27. Suppression Antagonism Additivity Synergy Synergy The shape of equal inhibition lines in the dose-dose space defines the interaction between the drugs [B] Growth rate Growth rate [A] MIC Minimal Inhibitory Concentration

28. wild-type growth MICB MICA A simple multiplicative model FAB = FA*FBdoes not work Synergy Antagonism MICB FAB<<1 Concentration of drug B FAB=1 MICA Concentration of drug A FA=1, FB=1 Multiplicative model predicts FAB=1 Michel,Yeh, et al. – PNAS 2008

29. There are many different resistance mechanisms • efflux pump • target affinity • drug degradation resistant mutants see lower levels of drug

30. Rescaling Resistant mutants “see” lower effective drug concentrations Concentration of drug B wild type resistant mutant Concentration of drug A Chait, Craney, Kishony – Nature 2007

31. Model for single drug Can also use theta/heaviside/step function or their eta function Can express frequency of bacteria at concentration Cxas Recognize the probability density

32. Model for two drugs By analogy, Can directly measure and enforce MIC curve. Trying to use this and other information to predict MPC curve and thus mutant selection window. How do we approximate the joint probability distribution. Two extremes. Independent probability distribution If drugs are the same, this is extreme correlation in probability distribution. Does NOT imply additive epistasis at all.

33. Model for two drugs Choose actual probability density to be linear combination of these twowith free parameter ξ to tune model to data. Measure px, py, and ηxyand all of these are experimentally tractable Free parameter ξ is only part of model fit Important to build simple models in terms of measurable parameters and only a few free parameters

34. measurements single drug resistance drug interactions 1 parameter cross-resistance Mathematical Model 1 0 0 Concentration of Drug A Single drug resistance and drug interactions predict multidrug resistance Concentration of Drug B resistance to the drug combination 0 0 Michel,Yeh, et al. – PNAS 2008

35. FUS CPR FUS ERY AMP AMI FUS CPR FUS AMI ERY AMP The mathematical model is in good agreement with the experimental data EXPERIMENT MODEL Michel,Yeh, et al. – PNAS 2008

36. Resistant to B Resistant to A Synergistic drugs kill more effectively than antagonistic drugs. But how do they impact resistance? Consider simple example with only three populations: wild type, single type resistant to drug A, and single type resistant to drug B.Independent probability distributions.

37. Resistant to B Predicted resistance MSW 1 MSW 1 MSW MSW 0 1 1 (MIC) MPC 0 0 MIC MPC 0 “effective drug” 2A:3B “effective drug” A:B 0 1 (MIC) MPC 0 “effective drug” 2A:B Some combinations of the two drugs better reduce the potential to evolve resistance Antagonism Resistant to A “effective drug” 2A:3B best “effective drug” A:B MSW Concentration of drug B “effective drug” 2A:B MSW Concentration of drug A

38. Resistant to B MSW 1 0 MIC MPC 0 “effective drug” A:B Some combinations of the two drugs better reduce the potential to evolve resistance Synergy Resistant to A best “effective drug” A:B Concentration of drug B MSW Concentration of drug A

39. Antagonistic combinations have smaller mutant selection windows: windows are scaled relative to MIC like everything else as an inset Synergy Antagonism MSW MSW 1 1 0 0 MIC MPC MIC MPC 0 0 Concentration of drug B Concentration of drug A Michel,Yeh, et al. – PNAS 2008

40. Antagonistic combinations predicted to better reduce selection for resistance Michel,Yeh, et al. – PNAS 2008

41. Suppression Antagonism Additivity Synergy Synergy The shape of equal inhibition lines in the dose-dose space defines the interaction between the drugs [B] Growth rate Growth rate [A] MIC Minimal Inhibitory Concentration

42. Directional Suppression BR AR BR AR AR - Drug A - BR + + Drug B - Drug A - + + Drug B A simple model suggests profound impact of drug interactions on selection for resistance Synergy Suppression Bacterial Fitness - - Drug A + + Drug B Hypothesis: suppressive combinations can select against resistance

43. There is very little fitness cost to resistance in a drug free environment Resistant bacteria, CFP compLB.mpg Sensitive bacteria, YFP

44. Conclusions • Synergistic combinations, currently preferred in clinical settings, may actually favor resistance • Trade-off between immediate killing efficacy and future evolution of resistance

45. Next class we will move onto papers using networks motifs for gene regulation First Homework set is due in two weeks (April 20, 2010).