1. Not All Quiet on the Biology FrontSomdeb GhoseThe Institute of Mathematical SciencesRonojoy AdhikariThe Institute of Mathematical SciencesSoma Saha and Arti DuaIndian Institute of Technology Madras

2. Not just an indecisive cat ..."For it is simply a fact of observation that theguiding principle in every cell is embodied in asingle atomic association existing only in onecopy (or sometimes two) and a fact ofobservation that it results in producing eventswhich are paragons of orderliness [...] thesituation is unprecedented, it is unknownanywhere else except in living matter."Erwin SchrdingerWhat is Life?(Cambridge University Press, 1944) 3. Sources of noiseExtrinsic IntrinsicGlobal effect Local effectRandom fluctuations inenvironmental parametersTemperature, pHFluctuations due to smallnumber of reacting molecules 4. Sources of noiseExtrinsic IntrinsicGlobal effect Local effectRandom fluctuations inenvironmental parametersTemperature, pHFluctuations due to smallnumber of reacting molecules 5. Intrinsic noiseCellular functions often involve chemical reactions between a small numberof molecules.Inherent stochasticityReactions occur due to probabilistic collisions between randomly movingmolecules. Less the number of molecules, more is the randomness.DiscretenessThe numbers of molecular species increases or decreases by integeramounts for each reaction event. 6. Intrinsic noiseCellular functions often involve chemical reactions between a small numberof molecules.Inherent stochasticityReactions occur due to probabilistic collisions between randomly movingmolecules. Less the number of molecules, more is the randomness.DiscretenessThe numbers of molecular species increases or decreases by integeramounts for each reaction event. 7. Intrinsic noiseCellular functions often involve chemical reactions between a small numberof molecules.Inherent stochasticityReactions occur due to probabilistic collisions between randomly movingmolecules. Less the number of molecules, more is the randomness.DiscretenessThe numbers of molecular species increases or decreases by integeramounts for each reaction event. 8. Stochastic gene expressionGene expressionmRNADNA ProteinTranscription Translation 9. Stochastic gene expressionGene expressionmRNADNA ProteinTranscription TranslationNoise 10. Stochastic gene expressionGene expressionmRNADNA ProteinTranscription TranslationNoise 11. Phenotypic heterogeneityGenotypeThe full hereditary information of an organism, whether expressed or not.PhenotypeThe actual observed properties of an organism, including its morphology,development, biophysical and biochemical characteristics, and behaviouraltraits.Wikipedia 12. Phenotypic heterogeneityElowitz et al, Science (2002)No intrinsic noise 13. Phenotypic heterogeneityElowitz et al, Science (2002)No intrinsic noiseWith intrinsic noise 14. Phenotypic heterogeneityFingerprints of identical twinsRaser and OShea, Science (2005) 15. Phenotypic heterogeneityFingerprints of identical twinsRainbow, on the right, and herclone, CcRaser and OShea, Science (2005) 16. Twin roles of noiseCan be exploited for positivegainsNuisance Source of variabilityImpediment to reliablebehaviour, requires regulation 17. Twin roles of noiseCan be exploited for positivegainsNuisance Source of variabilityImpediment to reliablebehaviour, requires regulation 18. Adverse effects of noiseDevelopment of embryosNoise might prevent cells from cooperating and coordinating during embryodevelopment, causing mutations and thus disease in some individuals.AgeingOlder cells show greater susceptibility to noise. For the heart, it may lead toa gradual decrease in efficiency over time.Bahar et al, Nature (2006)Pearson, Nature (2008) 19. Adverse effects of noiseDevelopment of embryosNoise might prevent cells from cooperating and coordinating during embryodevelopment, causing mutations and thus disease in some individuals.AgeingOlder cells show greater susceptibility to noise. For the heart, it may lead toa gradual decrease in efficiency over time.Bahar et al, Nature (2006)Pearson, Nature (2008) 20. Regulation of noiseA simple negative feedback loop functions as a low-pass filter that attenuateshigh-frequency noise, thus increasing stability.Negative feedbackGene expression controlProteins calledtranscription factorseither activate orrepress geneexpressionBecskei and Serrano, Nature (2000) 21. Regulation of noiseA simple negative feedback loop functions as a low-pass filter that attenuateshigh-frequency noise, thus increasing stability.Negative feedbackGene expression controlProteins calledtranscription factorseither activate orrepress geneexpressionBecskei and Serrano, Nature (2000) 22. Biochemical timekeepingAt the level of the cellCells must know when to divide and dieIf not, it could lead to cancerAt the level of the organismThey must adhere to the 24-hr circadian rhythmIf not, they run the risk of becoming a 23. Biochemical timekeepingAt the level of the cellCells must know when to divide and dieIf not, it could lead to cancerAt the level of the organismThey must adhere to the 24-hr circadian rhythmIf not, they run the risk of becoming a grad student 24. Cellular clockRepressilatorToy model of cellular clock,developed in E. coliProduces oscillations in proteinconcentration through a negativefeedback cycle.TetRcI LacIElowitz and Leibler, Nature (2000)Elowitz and Leibler, Nature (2000) 25. Cellular clockRepressilatorToy model of cellular clock,developed in E. coliProduces oscillations in proteinconcentration through a negativefeedback cycle.Not robust to noiseTetRcI LacIElowitz and Leibler, Nature (2000) 26. Noise regulation and synchronizationQuorum SensingIndividual repressilators are coupled viaexchange of signaling molecules calledautoinducers.Garcia-Ojalvo et al, PNAS (2004) 27. Noise regulation and synchronizationQuorum SensingIndividual repressilators are coupled viaexchange of signaling molecules calledautoinducers.At sufficient bacterial concentration, allrepressilators get synchronizedGarcia-Ojalvo et al, PNAS (2004) 28. Noise regulation and synchronizationQuorum SensingIndividual repressilators are coupled viaexchange of signaling molecules calledautoinducers.At sufficient bacterial concentration, allrepressilators get synchronizedGarcia-Ojalvo et al, PNAS (2004) Danino et al, Nature (2010) 29. Exploitation of noiseActivation of a positive feedback loop allows the transcription factor ComK inB. Subtilis to promote itself, resulting in higher competence (ability to take upDNA from the environment for repair and development). The positivefeedback creates a bimodal population distribution, thus increasing survivalprobability.Lowering the noise decreases the fraction of population crossing thecompetence threshold, and is thus counterproductive.Thattai and van Oudenaarden, PNAS (2001)Ozbudak et al, NatGenet (2002)Raj and van Oudenaarden, Cell (2008)Positive feedback 30. Bacterial persistenceE. coli bacteria before antibioticE. coli bacteria after antibioticBalaban et al, Science (2004) 31. Bacterial persistenceE. coli bacteria before antibioticE. coli bacteria after antibioticBalaban et al, Science (2004) 32. Eye of a fruitflyScattered pattern ofphotoreceptors in thedeveloping retina of the fruitflyDrosophila.The random switching on andoff of the spineless genecauses this distribution, wheresome photoreceptors aresensitive to blue light, whileothers are sensitive to greenlight.Wernet et al, Nature (2006) 33. A quick refresher ...Small number of molecules give rise to intrinsic noiseThis in turn causes phenotypic heterogeneity, where clones or identicaltwins have different physical characteristicsTranscriptional regulation and negative feedback loops control noise. Cellularclocks band together to overcome noise using quorum sensing.Phenotypic heterogeneity and population bimodality due to positive feedbackmechanisms allow organisms to survive or to see better 34. Enzyme kineticsEnzymes are biochemical catalysts. Their job is to ensure that criticalbiological processes such as metabolism run on time. 35. Enzyme kineticsEnzymes are biochemicalcatalysts. Their job is toensure that criticalbiological processes suchas metabolism run ontime.MechanismIn the simplest model,enzymes form complexeswith substrates, whichthen dissociate intoproducts, thusregenerating the enzymeOne enzymatic turnover 36. Deterministic mass action kineticsMichaelis-Menten equationProduct formation rates are given, in the limit ofa very large number of molecules, by the classicMichaelis-Menten (MM) rate equation 37. Deterministic mass action kineticsMichaelis-Menten equationProduct formation rates are given, in the limit ofa very large number of molecules, by the classicMichaelis-Menten (MM) rate equationA Lineweaver-Burk plot of [E0]/vvs 1/[S] will be linearLineweaver and Burk, JAmChemSoc (1934) 38. Single enzyme kineticsStochastic turnovers form a renewal process, where successive intervalsare independent and identically distributed.Xie and Lu, JBiolChem (1999)Kou et al, JPhysChemB (2005)English et al, NatChemBio (2006)A reinterpreted MM equation holdsHere is the mean of the intervalsbetween turnovers. A plot of vs1/[S] will again be linear. 39. Multiple enzyme kineticsMaster Equation Simulate using Doob-GillespieMonte Carlo algorithmka= k1[S]Actual enzyme kinetics involves finite, but small, number of enzyme andsubstrate molecules. Molecular noise thus dictates affairsSaha, SG, Dua, Adhikari,PhysRevLett (2011) 40. Nonrenewal processWaiting times are not identicallydistributed and are multiexponentialSaha, SG, Dua, Adhikari,PhysRevLett (2011) 41. Breakdown of MM equationBlue curve corresponds tosingle enzyme, where MMequation holdsSaha, SG, Dua, Adhikari,PhysRevLett (2011) 42. Breakdown of MM equationBlue curve corresponds tosingle enzyme, where MMequation holdsRed and green curves are formultiple enzymes. Here MMequation breaks down.Saha, SG, Dua, Adhikari,PhysRevLett (2011) 43. Anticorrelation and Regulation?Waiting times areanticorrelated. A longer intervalis likely to be followed by ashorter one, and vice versa.Anticorrelation reduces thevariance in the productturnovers and creates aregulatory effect, thus ensuringa uniform turnover rate atsteady state.Might be a possible mechanismfor ensuring robustness againstnoise in gene expression.Saha, SG, Dua, Adhikari,PhysRevLett (2011) 44. Anticorrelation and Regulation?Waiting times areanticorrelated. A longer intervalis likely to be followed by ashorter one, and vice versa.Anticorrelation reduces thevariance in the productturnovers and creates aregulatory effect, thus ensuringa uniform turnover rate atsteady state.Might be a possible mechanismfor ensuring robustness againstnoise in gene expression.Saha, SG, Dua, Adhikari,PhysRevLett (2011) 45. Anticorrelation and Regulation?Waiting times areanticorrelated. A longer intervalis likely to be followed by ashorter one, and vice versa.Anticorrelation reduces thevariance in the productturnovers and creates aregulatory effect, thus ensuringa uniform turnover rate atsteady state.Might be a possible mechanismfor ensuring robustness againstnoise in gene expression.Saha, SG, Dua, Adhikari,PhysRevLett (2011) 46. Can noise drive cellular clocks?Test systemWe test the effects of intrinsic noise at the population level, using a modelof epidemic spreadingOur test system is closed to the outside.It is inhabited by a small number of individuals to ensure sufficient noisestrength. 47. Can noise drive cellular clocks?Test systemWe test the effects of intrinsic noise at the population level, using a modelof epidemic spreadingOur test system is closed to the outside.It is inhabited by a small number of individuals to ensure sufficient noisestrength. 48. Can noise drive cellular clocks?Test systemWe test the effects of intrinsic noise at the population level, using a modelof epidemic spreadingOur test system is closed to the outside.It is inhabited by a small number of individuals to ensure sufficient noisestrength. 49. SIRS epidemic model 50. Deterministic analysisSystem of ordinary differential equationsHas one endemic fixed point, which caneither be a stable focus (underdamped)or a stable node (overdamped)SG, Adhikari, PhysRevE (2010) 51. Deterministic analysisSystem of ordinary differential equationsHas one endemic fixed point, which caneither be a stable focus (underdamped)or a stable node (overdamped)No sustained oscillations in thedeterministic caseSG, Adhikari, PhysRevE (2010) 52. Stochastic analysisMaster equationSimulate using DGMC algorithmSG, Adhikari, PhysRevE (2010) 53. Stochastic analysisMaster equationSimulate using DGMC algorithmNoise-induced sustainedoscillations in the stochasticcaseSG, Adhikari, PhysRevE (2010) 54. Regularity of oscillationsRegularity is maximum at intermediate noise valueNoise is essential for stable oscillationsSG, Adhikari, PhysRevE (2010) 55. Noise-operated cellular clocks?Oscillations are generated due to noise instead of inspite of noise.Noise-induced oscillations seen in a simple model, albeit at apopulation-level one.Possible applications at cellular level? 56. Thats all, folks!Thanks for listening to this noisy presentation!Ronojoy Adhikari Arti Dua