The Structure, Function, and Evolution of Biological Systems Instructor: Van Savage Spring 2010 Quarter 4/13/2010 Recent papers using models of epistasis: Michel, Yeh, Chait, Moellering, Kishony Measures of epistasis 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 Cov ( w x , w y ) w xy w x w y Relative covariance ˜ Cov ( w x , w y ) BinnedCov ( w x , w y ) w xy w x w y w˜ xy w x w y 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? ….and some pathogens grow very quickly a1-phm-gro.wmv They can be killed by antibiotics… a1-phm-kil.wmv …but some bacteria can become resistant to the drug Antibiotic Resistant Bacterium Sensitive Bacterium X X Resistance confers a large fitness advantage in the presence of the drug Resistant bacteria, CFP compDOX.mpg X X Sensitive bacteria, YFP Antibiotic resistance a growing public health threat Years Main Questions I. How do drugs interact with each other, and how can we use their interactions to determine their mechanisms of action? II. How do drug interactions affect the evolution of drugresistant bacteria? III. Future Directions: What role do birds play in the transmission of drug-resistant bacteria? Multiple drugs combine to fight bacteria Drug A Drug B Two drugs can interact with each other to produce varying effects 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? Drug-Drug Network Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006 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 Drug-Drug Network Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006 Drug-Drug Network Functional Classification Cell Wall DNA Aminoglycosides Folic Acid 50S 30S Protein Synthesis Yeh, et al. – Nature Genetics 2006 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 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. How do drug interactions affect the evolution of resistance? Main result: Antagonism, typically avoided in clinical settings, better slows the emergence of resistant bacteria Some drug concentrations select for resistance Frequency of resistance wild type Mutant Selection Window 1 10-4 10-8 0 0 MIC Drug concentration MPC The Mutant Selection MPC: Window is one measure Mutant Prevention Concentration MIC: Minimal Inhibitory Concentration of the potential to evolve resistance Dong et al. 1999, Drlica 2003 In two-drug treatments, the “Mutant Selection Window” becomes an “area” of drug concentrations. 1 Multi-drug Mutant Selection Window 10-4 10-8 0 0 MIC MPC Drug concentration Dong et al. 1999, Drlica 2003 Concentration of drug Y Frequency of resistance Single Drug Concentration of drug X Michel,Yeh, et al. – PNAS 2008 Concentration of drug Y 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 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. Imaging platform delivers resistance frequencies on 2-D drug gradient Michel,Yeh, et al. – PNAS 2008 Selection for resistance strongly depends on the drug combination 102 102 MSW 103 MSW 103 10 1 10 1 ERY ERY:FUS Drug ratio FUS AMI AMI:FUS FUS Drug ratio Michel,Yeh, et al. – PNAS 2008 Another view of antibiotic interactions MICB MICB MICB Isobolograms MICA MICA MICA 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 Cx C x ,MIC Cy C y ,MIC 1 MICB MICB MICB Loewe additivity and epistatic additivity MICA MICA MICA 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. F xy Cx F x F y 1 C x ,MIC Cy 1 C y ,MIC C Cy x ~ 1 C y ,MIC C x ,MIC [B] The shape of equal inhibition lines in the dose-dose space defines the interaction between the drugs Suppression Antagonism Synergy Growth rate Growth rate [A] MIC Minimal Inhibitory Concentration FAB<<1 wild-type growth Antagonism MICB Synergy MICB Concentration of drug B A simple multiplicative model FAB = FA*FB does not work FAB=1 MICA MICA Concentration of drug A FA=1, FB=1 Multiplicative model predicts FAB=1 Michel,Yeh, et al. – PNAS 2008 There are many different resistance mechanisms • efflux pump resistant mutants see lower levels of drug • target affinity • drug degradation Concentration of drug B Resistant mutants “see” lower effective drug concentrations Rescaling wild type resistant mutant Concentration of drug A Chait, Craney, Kishony – Nature 2007 Model for single drug Can express frequency of bacteria at concentration Cx as F x (C x ) C x , MIC dF (C x ) dC x dC x F (C x ) C x , MIC ~ F ( ) F (C x ,MIC ) F (C x ,MIC ) Recognize the probability density p(C x ) dF (C x ) dC x Can also use theta/heaviside/step function or their eta function F x (C x ) C x , MIC C x ,MIC p(C x ) dC x C x Model for two drugs By analogy, F xy (C x ,MIC ,C y ,MIC ) xy p(C x ,C y )dC x dC y C y , MIC C x , MIC 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 p ind (C x ,C y ) p(C x ) p(C y ) If drugs are the same, this is extreme correlation in probability distribution. Does NOT imply additive epistasis at all. p corr (C x ,C y ) p(C x ) p(C y ) Model for two drugs Choose actual probability density to be linear combination of these two with free parameter ξ to tune model to data. p corr (C x ,C y ) p xy corr (1 ) p xy ind Measure px, py, and ηxy and 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 Single drug resistance and drug interactions predict multidrug resistance measurements Concentration of Drug B single drug resistance drug interactions 1 parameter cross-resistance Mathematical Model 0 0 resistance to the drug combination 1 0 0 Concentration of Drug A Michel,Yeh, et al. – PNAS 2008 FUS ERY AMI FUS AMP CPR ERY MODEL FUS CPR FUS EXPERIMENT The mathematical model is in good agreement with the experimental data AMP AMI Michel,Yeh, et al. – PNAS 2008 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. Resistant to B Resistant to A Some combinations of the two drugs better reduce the potential to evolve resistance Concentration of drug B Antagonism Resistant to B Resistant to A “effective drug” Predicted resistance 2A:3B best “effective drug” MSW A:B “effective drug” MSW 2A:B MSW Concentration of drug A 1 0 0 MSW MSW MSW 1MIC (MIC)MPCMPC MPC “effective “effective “effectivedrug” drug” drug”2A:3B 2A:B A:B Some combinations of the two drugs better reduce the potential to evolve resistance Concentration of drug B Synergy Resistant to B Resistant to A best “effective drug” A:B 1 MSW MSW Concentration of drug A 0 0 MIC MPC “effective drug” A:B Antagonistic combinations have smaller mutant selection windows: windows are scaled relative to MIC like everything else as an inset Concentration of drug B Synergy Antagonism MSW MSW 1 00 1 00 MIC MPC MIC MPC Concentration of drug A Michel,Yeh, et al. – PNAS 2008 Antagonistic combinations predicted to better reduce selection for resistance Michel,Yeh, et al. – PNAS 2008 [B] The shape of equal inhibition lines in the dose-dose space defines the interaction between the drugs Suppression Antagonism Synergy Growth rate Growth rate [A] MIC Minimal Inhibitory Concentration A simple model suggests profound impact of drug interactions on selection for resistance Bacterial Fitness Synergy - Suppression + + - + Directional Suppression + - - - + + Hypothesis: suppressive combinations can select against resistance There is very little fitness cost to resistance in a drug free environment Resistant bacteria, CFP compLB.mpg Sensitive bacteria, YFP Conclusions • Synergistic combinations, currently preferred in clinical settings, may actually favor resistance • Trade-off between immediate killing efficacy and future evolution of resistance Next class we will move onto papers using networks motifs for gene regulation First Homework set is due in two weeks (April 20, 2010).