Biodiversity: periodic boundary conditions and spatiotemporal stochasticity
Assessing Stochasticity and Failure Rates in Biology and ...
10
Assessing Stochasticity and Failure Rates in Biology and Electronics Albert J. Keung, PhD ([email protected]), Assistant Professor Gregory N. Parsons, PhD ([email protected]), Alcoa Professor Chemical and Biomolecular Engineering North Carolina State University Contribution in Support of the SRC SemiSynBio Roadmap Summary Hybrid semiconductor-biological systems could provide a major transition for future information storage and computation. While largely unexplored in this context, biological systems hold intriguing potential due to their low energy usage, high storage density, and unique molecular and cellular architectures. However, biological systems are well known to exhibit significant and inherent variability in genomic sequence, gene structure, protein and RNA concentrations, synaptic responses, and other biological variables. This variability results in “noisy” or stochastic response or output at many levels, ranging from single molecule to full organism scales. This noise directly impacts the reliability and accuracy of future hybrid SemiSynBio devices. Stochastic behavior and component/device failure in semiconductor electronic systems is well known, but the relationships and potential interfaces between stochasticity in electronic and biological systems is not well developed or defined. Thus, an important starting point for SemiSynBio networks is to develop a clearer picture of how noise is considered and measured in both biological and semiconductor systems. Furthermore, the establishment of a common syntax as well as quantitative comparisons of noise in both types of systems will facilitate the integration of biology into semiconductor systems, as well as provide a quantitative roadmap to inform future research directions. I. Failure Rates Before discussing individual noise characteristics of biological and semiconductor systems, one can first compare components and devices from both categories at a practical level by defining a parameter for the “failure rate”. This parameter may then contribute to a more broadly defined overall system failure rate. Defining a failure rate provides a broader perspective of how far and in what properties biological systems need to improve to match the reliability of semiconductor systems. It also aggregates the large number of sources of noise present in individual components, like transistors or genes, into a practical metric. The diversity of communication within biological systems relative to electronic systems adds additional complexity. For example, semiconductors and synapses/ion channels are both based on electronic architectures, allowing their noise characteristics to be compared with a similar syntax. However, noise in gene expression or other biological information management processes are not as easily translated to semiconductor systems. While the biological sciences, synthetic biology, and bioengineering (excluding medical device engineering) have yet to adopt common metrics for failure rates, other engineering disciplines and industries have developed mature frameworks to quantify failure rates in products and devices. The semiconductor industry uses common terminology to refer to failure rates, including mean time between failure (MTBF in hours) and failure in time (FIT) with: 1 = 1,000,000,000 ℎ Ia. Failure rates of electronic devices and components. FIT and MTBF can be used to refer to failure rates of entire industrial plants, devices such as computers, or individual transistor or circuit components. Typically, modern multicomponent devices in the semiconductor industry have FIT numbers near 100-1000, while the FIT numbers in modern individual components are so small that, in many cases, they are no longer reported. A variety of electronic devices and their worse-case (most conservative estimate) FIT numbers were obtained from literature and are listed in Table 1 (blue shading) and plotted in Figure 1 (blue diamonds). Devices and components from a range of time periods over almost 30 years are included to indicate their quantitative range as broadly (conservatively) as possible. Cycle time is estimated from transistor or integrated circuit clock speeds, or from memory access speeds. Failure time was then calculated as MTBF = (cycle time) / (fractional failure).
Transcript of Assessing Stochasticity and Failure Rates in Biology and ...
AssessingStochasticityandFailureRatesinBiologyandElectronics
AlbertJ.Keung,PhD([email protected]),AssistantProfessorGregoryN.Parsons,PhD([email protected]),AlcoaProfessor
ChemicalandBiomolecularEngineeringNorthCarolinaStateUniversity
ContributioninSupportoftheSRCSemiSynBioRoadmapSummaryHybrid semiconductor-biological systems could provide amajor transition for future information storage andcomputation.Whilelargelyunexploredinthiscontext,biologicalsystemsholdintriguingpotentialduetotheirlow energy usage, high storage density, and uniquemolecular and cellular architectures. However, biologicalsystems are well known to exhibit significant and inherent variability in genomic sequence, gene structure,protein and RNA concentrations, synaptic responses, and other biological variables. This variability results in“noisy”or stochastic responseoroutputatmany levels, ranging fromsinglemolecule to fullorganismscales.ThisnoisedirectlyimpactsthereliabilityandaccuracyoffuturehybridSemiSynBiodevices.Stochasticbehaviorand component/device failure in semiconductor electronic systems is well known, but the relationships andpotentialinterfacesbetweenstochasticityinelectronicandbiologicalsystemsisnotwelldevelopedordefined.Thus, an important starting point for SemiSynBio networks is to develop a clearer picture of how noise isconsideredandmeasured inbothbiologicalandsemiconductorsystems.Furthermore, theestablishmentofacommon syntax as well as quantitative comparisons of noise in both types of systems will facilitate theintegrationofbiologyintosemiconductorsystems,aswellasprovideaquantitativeroadmaptoinformfutureresearchdirections.I.FailureRatesBeforediscussingindividualnoisecharacteristicsofbiologicalandsemiconductorsystems,onecanfirstcomparecomponentsanddevicesfrombothcategoriesatapracticallevelbydefiningaparameterforthe“failurerate”.Thisparametermay thencontribute toamorebroadlydefinedoverall system failure rate. Defininga failurerateprovidesabroaderperspectiveofhow farand inwhatpropertiesbiological systemsneed to improve tomatchthereliabilityofsemiconductorsystems.Italsoaggregatesthelargenumberofsourcesofnoisepresentin individual components, like transistors or genes, into a practical metric. The diversity of communicationwithin biological systems relative to electronic systems adds additional complexity. For example,semiconductors and synapses/ion channels are both based on electronic architectures, allowing their noisecharacteristics to be comparedwith a similar syntax. However, noise in geneexpressionor other biologicalinformationmanagementprocessesarenotaseasilytranslatedtosemiconductorsystems.Whilethebiologicalsciences,syntheticbiology,andbioengineering(excludingmedicaldeviceengineering)haveyet to adopt commonmetrics for failure rates, other engineering disciplines and industries have developedmatureframeworkstoquantifyfailureratesinproductsanddevices.Thesemiconductorindustryusescommonterminologytorefer to failurerates, includingmeantimebetweenfailure (MTBF inhours)andfailure in time(FIT)with:
1 𝐹𝐼𝑇 = 1,000,000,000 ℎ𝑟𝑠
𝑀𝑇𝐵𝐹
Ia. Failure ratesofelectronicdevicesand components.FITandMTBFcanbeusedtoreferto failureratesofentire industrial plants, devices such as computers, or individual transistor or circuit components. Typically,modernmulticomponentdevicesinthesemiconductorindustryhaveFITnumbersnear100-1000,whiletheFITnumbers inmodern individual components are so small that, inmany cases, they are no longer reported. Avarietyofelectronicdevicesandtheirworse-case(mostconservativeestimate)FITnumberswereobtainedfromliterature and are listed in Table 1 (blue shading) and plotted in Figure 1 (blue diamonds). Devices andcomponentsfromarangeoftimeperiodsoveralmost30yearsareincludedtoindicatetheirquantitativerangeasbroadly(conservatively)aspossible.Cycletimeisestimatedfromtransistororintegratedcircuitclockspeeds,orfrommemoryaccessspeeds.FailuretimewasthencalculatedasMTBF=(cycletime)/(fractionalfailure).
Table1.Failureratesestimatedfromliteratureforbothelectronicandbiologicalcomponentsanddevicesacrossdiverselengthscalesandchemistries.(1-29)
Figure 1. Plot of FIT vs. shortest possible device cycle time shows electronic devices areconsiderablymorereliablethanthecurrentlynascentbiologicaldevices.(1-29)
Ib.Failureratesofbiologicaldevicesandcomponents.Forcomparison,biological“devices”arealsoplottedonFigure1. Inordertocomparebiologicalandelectronicdevices,thefractionalfailuresandcycletimesforeachbiological system was estimated from literature values, andMTBF and FIT values were then derived. These“devices”and thebasis for theirestimatedparametersaredescribedbelow.For theseestimations, therearetwoimportantpointstoconsiderwhencomparingelectronicandbiologicalsystems:First, thenaturalcyclingtimesforbiologicalsystemsaretypicallymuch longerthanelectronicsystems(and isalsoanimportantreasonwhycomparingnoiseisdifficult,asdiscussedinSectionII).SinceMBTFiscalculatedas(cycletime)/(failurefraction),longercycletimesresultinlongerMBTFs(andsmallerFITvalues).AssmallerFITvalues are desirable (fewer Failures In Time), FIT estimates for biological devices are in general optimistic(conservative) relative to electronic devices, since increasing the biological cycle times to match those ofelectronicdeviceswhilekeepingthefailurefractionsconstantwouldresultinmuchgreaterbiologicalFITvalues.Toaccount for this trade-offbetweencycle timeandFIT, theestimatedcycle timesareplottedon thex-axis.Thus,devicestowardsthelowerleftoftheplothavethemostfavorablecharacteristics(shortcycletimesandfewerFailures InTime). In a sense,decreasing cycle times couldbeassociatedwith increasing computationalpower, somoving to the left on the x-axis could also be considered a surrogate of increasing computationalpower.Second, inmostcases,definingadevice“failure” is subjective; therefore, themostoptimisticestimateswereusedtocalculateFITnumbers.Forexample,fortoggleswitches,thelowestthresholdratiopossibleofthetwogeneswasusedtodefine“ON”states.Similarly, forhumanbirths,onlyspontaneous intrauterine fetaldeathsare considered in calculating FIT numbers (preterm genetic abnormalities, developmental disorders, electiveabortions,andpostnataldeathsarenotincluded).(Fig1,greentriangles)Syntheticgeneticcircuits.Thesecircuitsincludethetoggleswitch,whichiscomprisedoftwogenesthatmutuallyrepresseachother,aswellasgeneticlogicgatesandotherswitch-likegeneticcircuits.Cycletimeswereestimatedasthetimeittookforeachgeneticdevicetofullyswitchfromonestatetoanother.Forexample,ittookabout6hoursforapopulationofcellscontainingagenetictoggleswitchtoswitchstates(8,16).Sothenumberofcyclespossibleinayearis(8760hoursinayear)/(6hourspertoggleswitchcycle).Notallcells switched states, so the6hourswaswhen theproportionof cells that switched reached saturation. Thefailurefractionwasthefractionofcellsthatdidnotswitchstates.(Redcircles)Wholeorganismsand their successfulgestation resulting ina livebirth.Thecycletimewastheaveragegestationperiodforaspecies.Forexample, thegestationperiodforhumans is9months.Thefailurefractionwascalculated fromepidemiologicalestimatesas the fractionofembryos thatwereconceived in thewombbutthatdidnotresultinalivebirth.Thefailurefractionsareoptimisticestimatesasthereareprobablymany conceived embryos that aborted within the first 1-2 months without the mother’s (or researcher’s)knowledgeorthatwerenotreported.(Purplesquares)Synapticfiringorthereleaseofvesicularneurotransmittersinresponsetoanabove-thresholdpotential.Thefiringrateofsynapseswasestimatedfromexperimentsofbothindividualsynapses,collectionsofmultiple synapses on a single neuron, or multiple bundled neurons (i.e. calyx of Held). A cycle time wasconsidered the time between synaptic action potentials if a constant depolarizing threshold potential wasapplied to the neurons. To be optimistic, longer estimates of cycle times were used. If shorter cycle timeestimateshadbeenused, thedatapointswould shiftupand to the left. Failure rateswereestimatedby thepercentageoftimesasynapseorcollectionofsynapseswouldfailtofireinresponsetoapplicationofadiscreteabove-thresholdpotential.(Greycrosses)DNAdegradation,synthesis,andsequencing.ForDNADecay,thecycletimewasarbitrarilysetatone year (8760 hours). The failure rate was then calculated as the (cycle time) / (DNA half-life). This is anoptimisticestimate,asthefailureratewouldbemuchgreaterifa“failure”wasdefinedasdegradationoflessthanhalfoftheDNA.ForDNAsynthesis,thecycletimewasestimatedas1minute(conservativeestimateofthetimetoaddonebasetoagrowingDNApolymerthroughphosphoramiditechemistries)andthefailureratewas
theerror ratepermonomer.ForDNAsequencing, theerror rates foravarietyofnextgenerationsequencingtechnologieswasestimatedtobe0.01perbase,andthecycletimewasthetimetosequenceeachbase(8760hrsinayear/52billionbasesperyear).ItisinterestingtonotethatthebiologicaldevicesexhibitthetrendofincreasingFITwithdecreasingcycletime.Thissametrendhasbeenobserved forelectronicdevicesasseen inFigure2whereFITnumbers increase forelectronicdevicesastheyincreaseineithermemoryornumberoflogicarrays.However,itisimportanttonotethat with electronic devices, the increase in “failure events” per unit time is more than compensated by agreaterincreaseintotalnumberofevents.Asimilargoalshouldbesetforeachbiologicalcategory:assyntheticbiologyandbioengineereddevicesincreaseinsophisticationandcapabilities,eventspertimeshouldincreaseatagreaterratethanfailureeventspertime.
Figure2.Plotsof FITvs.DRAMsizeandFITvs. logicgates showbothexperimentaland theoreticalmodelsprojectincreasingFITwithdevicecomplexity(plotsreproducedfrom(25)).It is also important to note that aside from the examples of synaptic firing, failure rates of most biologicaldeviceshaveonlybeenmeasuredaserrorswithinapopulationofdevices,asitisexperimentallyverydifficulttorepeatedlyreuseasyntheticbiologydevice.Thisisduetoavarietyofreasonsincludingthefactthatbiologicalcells are constantly changing at the molecular scale and that most synthetic biology devices have beenengineered inmitotic (dividing)cells.Thus, itmaybemoreaccuratetocomparethefailureratesofbiologicaldevicestodefectratesincomputerchipmanufacturing.Thedefectrateoftransistorsincomputerchipsisnear1in30billion(30),stillatleast5ordersofmagnitudebetterthanthesyntheticbiology“deadmanswitch”(5)orofDNAsynthesisandsequencingerrorrates.While there is a large gap between both the manufacturing and repeated-use reliability of electronic andbiological systems, research in biological systems have only begun to address reliability engineering, leavingample room for improvements. Furthermore, while failure rates in biological systems are high, thecomputationalcomplexityandenergyefficiencyofdevicessuchasthehumanbrainispowerfulandatcertaintippingpoints,orforparticularapplications,couldbeaworthwhiletradeoffwithhigherfailurerates.II.StochasticityandNoiseWhilefailureratescanbedefinedinageneralwaythatallowsreasonablecomparisonsbetweenverydifferenttypesofcomponentsanddevices,noisehasmorecomplexoriginsandthusdiversetheoreticalunderpinnings.There are many sources of noise and theoretical treatments of stochasticity that have been extensivelyreviewed by others for both electronic (31) and biological systems (32, 33). Here we discuss one biologicalsystemthatissimilartosemiconductorsystemsaswellasmanybiologicaldevicesthatwillrequireconsiderablefutureworkandimprovementsbeforequantitativecomparisonstoelectronicsystemswillbeuseful.IIa. Similarities in the treatment and magnitudes of baseline noise fluctuations in semiconductor devices,neural synapses, and cellularmembranepotentials.Semiconductorandbioelectric (synapsesandmembranepotentials) systems exhibit a range of similar sources of baseline or resting noise, including thermal (i.e.Johnson-Nyquist) and 1/f noise. For example, thermal and 1/f noise are also known to be prominent influctuationsofcellularmembranepotentials(34).Inaddition,thesignalsandnoiseofbothtypesofsystemscan
(andareoften)measuredinacontinuousway.Forcontinuousprocesseswherelongitudinalmeasurementsaremade,onecanobtainthenoisespectraldensity(thepowerspectraldensityofnoiseatdifferentfrequencies).
𝑃𝑜𝑤𝑒𝑟 𝑠𝑝𝑒𝑐𝑡𝑟𝑎𝑙 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑆!! 𝜔 𝑜𝑓 𝑎 𝑡𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠 𝑥 𝑡 = lim!⟶!
𝐸[ 𝑥 𝜔 !]
𝑤ℎ𝑒𝑟𝑒 𝑥 𝜔 =1𝑇
𝑒!!"#𝑥(𝑡)𝑑𝑡!
!
The noise spectral density can often provide insights into the origin or mechanism of different noisecomponents. Intriguingly, noise spectral densities of semiconductor devices roughly match those obtainedthrough continuousmeasurements of synaptic activity andmembrane potentials in biological experiments infrequencydependence. Forexample, theelectronicdevicesused tomeasure synapticactivityandmembranepotentialhavetobecarefullytunedtomatchthefrequencyandnoisecharacteristicsofthebiologicalsystem,assometimes1/fflickernoiseinthemeasuringdevicecanoverwhelmthatpresentinthebiologicalsystem(Figure3) (35, 36). Furthermore, externally applied voltages during experiments are often of similar magnitude(~400mVforsemiconductordevices,~120mVforpatch-clampedvoltage-gatedionchannels).
Figure3.(Left)Noisespectraldensitiesforneuronalvoltage-gatedionchannelsreproducedfrom(36).(Right)Noise spectral densities for a transistor with or without a neuron sitting on top of the gate between thesourceanddrain(reproducedfrom(35)).IIb.ChallengesforSemiSynBiodevicesduetosignificantdiscretenoisecharacteristicsofbiologicalsystems.Amajor challenge for hybrid SemiSynBio devices is how to compare noise characteristics. While it appearsbioelectricandsemiconductordevicesmight interfaceseamlessly infuturehybridSemiSynBiodevices,astheycan be described by noise spectral densities that can be matched in magnitude and frequency (35), mostsynthetic biology devices rely on non-electrical processes including gene transcription, translation, anddegradation.Thesecellularprocesseshavemuchlongertimescalesrelativetoelectricalsignals(canbe<10-4Hzforproductionofa fully functionalproteinvs100-105Hz forelectricalprocesses). Inaddition,manybiologicalexperimentsarelimitedintheirmeasurementaccuracyandstabilityovertimecomparedtoelectronicdevices,sotheyoftenrelyonendpointmeasurementsoflargenumbersofadevice(suchasofcells)andcannotobtaincontinuousmeasurements like thoseoftenmade forelectronic systems.Finally,even in the rareexperimentsthathaveproducedlongitudinalmeasurementsofgeneexpression(37),noisespectraldensityanalysisrevealedcharacteristicfrequenciesof~10-4Hz.Even in neurons, where the electrical properties of neuronal synapses may be similar to those ofsemiconductors, the challengeof time scales is also important for discretedownstreamevents. For example,even when the threshold action potential is exceeded for a neuron, it often does not fire (release synapticvesicles). Infact, low“releaseprobabilities” intherange10-20%arecharacteristicofmostbiologicalsynapses(38).OtherexamplesofnoiseindiscreteneuronaleventsincludevariationsinthetimedelaybetweenanactionpotentialfiringandaCa2+spikeandpostsynapticcurrentfluctuationsinresponsetoapresynapticsignal.Given this challenge of comparing electronic and biological noise, and the general lack of frequency sweptexperimentaldataforbiologicaldevices,hereweutilizeanoisemetricotherthanthenoisespectraldensity.Fordiscretemeasurementswhereeithermanydevicescompletedanevent,orofasingledevicecompletedseveral
limited number of discrete events, the noise coefficient, 𝜂 = !!, can be used. It is the ratio of the standard
deviationofasignaltothemeanofthatsignal,wherethesignalcouldbeavoltage,geneexpression level,orsome other experimentally accessible parameter. Relatedly, the Fano factor (𝜎!/𝜇) is often also used torepresent noise strength. Figure 4 estimates noise coefficients, many of which approach 1, for a diverserepresentativesampleofelectronicandbiologicalprocesses.Formostbiologicalprocesses,onlyendpointdatawereavailable tocalculate thestandarddeviations (SD)andmeans, thus the frequencyspectraof theirnoisewereunavailable.Forbestcomparisontothesebiologicaldevices1/fflickernoisewasquantifiedfromthenoisespectradensityfunctionsforthelowestfrequenciespossible,as1/fflickernoisedominatesinmagnitudeoverthermalandother sourcesofnoise inmanyelectronicdevices. Thus, theestimatednoise coefficients for theelectronic devices (transistors, bottom four samples of Figure 4) are themost conservative (yielding highestnoise coefficients) that we could estimate. As seen in Figure 4, while spontaneous and continuousmembrane/synaptic fluctuations are comparable to fluctuations in transistors, noise coefficients for non-electricalbiomolecularprocessesrelatedtogeneexpression,andforotherdiscretebiologicalevents,aremuchgreater.
Figure4.Noisecoefficientsforavarietyofdifferentbiologicalprocessesandmeasurementtechniqueswereestimatedfromliterature(35,39-55).Considerationsforthedesignoffuturehybridsystems.Stateoftheartbiologicaldevicesaswellasnaturalbiologicalsystemsingeneralexhibithigherfailureratesandnoisecomparedtosemiconductorsystemsandcomponents.However, therearesomebiologicalcomponentsthat approach the performance of semiconductor components, and if composed in new ways, could beinterfacedwithsemiconductorsystems.Forexample,whenconsideringbaseline/resting fluctuations insignal,membranepotentialsholdpromisecomparedtoelectronicsystems,whilenon-electricalbiomolecularprocessesare far inferior. In contrast, when considering failure rates of device manufacturing or of repeated device
cycling, no biological process, electrical or otherwise, are within even several orders of magnitude of thereliabilityofelectronic systems.However,noiseandhigh failure rates innaturalbiological systemsmayservemany beneficial functions including robustness to catastrophic failure, minimization of energy usage, andadaptability/plasticity (34, 56). Additional measurements and estimations of parameters such as metabolicenergyusage,energyneededtostoreinformationinbiologicalsystems,andratiosofoverallresourceusagetoinformation/computational density will be needed to determine the true tradeoffs of using biology incomputation and information storage. Simple estimations suggest energy efficiency alone may be enoughmotivationtopursuedevelopmentofhybridSemiSynBiosystems.Forexample,thehumanbrainiscomposedof1011neuronsusingatotalpowerofapproximately20Wforapowerusagedensityof2-10W/neuron.Incontrast,a computer uses about 200 W with approximately 109 transistors, yielding a power usage density of 2-7
W/transistor.Withoutevenconsideringthefactthateachneuronhasmultiplesynapses,ifthe“manufacturing”andfailureratesofneuronalsystemscouldbeimproved,theenergysavingscouldbesubstantial.References1. AuslanderS,AuslanderD,MullerM,WielandM,FusseneggerM.2012.Programmablesingle-
cellmammalianbiocomputers.Nature487:123-127.2. Beehner J,OnderdonkD,AlbertsS,AltmannJ.2006.Theecologyofconceptionandpregnancy
failureinwildbaboons.BehavioralEcologydoi:10.1093/beheco/arl006.3. BonnetJ,SubsoontornP,EndyD.2012.Rewritabledigitaldatastorageinlivecellsviaengineered
controlofrecombinationdirectionality.ProcNatlAcadSciUSA109:8884-8889.4. BonnetJ,YinP,OrtizME,SubsoontornP,EndyD.2013.Amplifyinggeneticlogicgates.Science
340:599-603.5. ChanCT,Lee JW,CameronDE,BashorCJ,Collins JJ.2016.'Deadman'and'Passcode'microbial
killswitchesforbacterialcontainment.NatChemBiol12:82-86.6. Chen G, Harata NC, Tsien RW. 2004. Paired-pulse depression of unitary quantal amplitude at
singlehippocampalsynapses.ProcNatlAcadSciUSA101:1063-1068.7. EnglitzB,TolnaiS,TypltM,JostJ,RubsamenR.2009.Reliabilityofsynaptictransmissionatthe
synapsesofHeldinvivounderacousticstimulation.PLoSOne4:e7014.8. GardnerTS,CantorCR,CollinsJJ.2000.ConstructionofagenetictoggleswitchinEscherichiacoli.
Nature403:339-342.9. Grass RN, Heckel R, PudduM, Paunescu D, StarkWJ. 2015.Robust Chemical Preservationof
Digital Information on DNA in Silica with Error-Correcting Codes. Angewandte Chemie-InternationalEdition54:2552-2555.
10. Green AA, Silver PA, Collins JJ, Yin P. 2014.Toehold switches: de-novo-designed regulators ofgeneexpression.Cell159:925-939.
11. GregoryE,MacDormanM,Martin J.2014.Trends in fetalandperinatalmortality intheUnitedStates,2006-2012.NCHSDataBrief.
12. Hardingham NR, Larkman AU. 1998. Rapid report: the reliability of excitatory synaptictransmission in slices of rat visual cortex in vitro is temperature dependent. J Physiol507 ( Pt1):249-256.
13. HengenKB,LamboME,VanHooserSD,KatzDB,TurrigianoGG.2013.Firingratehomeostasisinvisualcortexoffreelybehavingrodents.Neuron80:335-342.
14. HermannJ,PeckaM,vonGersdorffH,GrotheB,KlugA.2007.SynaptictransmissionatthecalyxofHeldunderinvivolikeactivitylevels.JNeurophysiol98:807-820.
15. Kotula JW, Kerns SJ, Shaket LA, Siraj L, Collins JJ, Way JC, Silver PA. 2014. Programmablebacteriadetectandrecordanenvironmentalsignalinthemammaliangut.ProcNatlAcadSciUSA111:4838-4843.
16. LeeJW,GyorgyA,CameronDE,PyensonN,ChoiKR,WayJC,SilverPA,DelVecchioD,CollinsJJ.2016.CreatingSingle-CopyGeneticCircuits.MolCell63:329-336.
17. LennieP.2003.Thecostofcorticalcomputation.CurrBiol13:493-497.18. Macia J,ManzoniR, CondeN,UrriosA, deNadal E, SoleR,Posas F.2016.Implementationof
ComplexBiologicalLogicCircuitsUsingSpatiallyDistributedMulticellularConsortia.PLoSComputBiol12:e1004685.
19. Markram H,Wang Y, TsodyksM. 1998.Differential signaling via the same axon of neocorticalpyramidal neurons. Proceedings of the National Academy of Sciences of the United States ofAmerica95:5323-5328.
20. Mizuseki K, Diba K, Pastalkova E, Buzsaki G. 2011. Hippocampal CA1 pyramidal cells formfunctionallydistinctsublayers.NatNeurosci14:1174-1181.
21. Nakamura T. 2008.Terrestrialneutron-induced soft errors in advancedmemorydevices.WorldScientific,Hackensack,NJ.
22. OertnerTG,SabatiniBL,NimchinskyEA,SvobodaK.2002.Facilitationatsinglesynapsesprobedwithopticalquantalanalysis.NatNeurosci5:657-664.
23. RossMG,RussC,CostelloM,HollingerA,LennonNJ,HegartyR,NusbaumC, JaffeDB.2013.Characterizingandmeasuringbiasinsequencedata.GenomeBiol14:R51.
24. SeagateTechnologyL.2009.BarracudaLPSeriesSATAProductManual.25. Shiono N, Arai E, Mutoh S. 2013. Historical overview of semiconductor device reliability for
telecommunication networks-field data, prediction model of device failure rate, and wear-outfailureanalysesatNTT.NTTTechnicalReview11.
26. SiutiP,YazbekJ,LuTK.2013.Syntheticcircuitsintegratinglogicandmemoryinlivingcells.NatBiotechnol31:448-452.
27. Thomson AM, Bannister AP. 1999. Release-independent depression at pyramidal inputs ontospecificcelltargets:dualrecordingsinslicesofratcortex.JournalofPhysiology-London519:57-70.
28. Thomson AM, West DC, Deuchars J. 1995. Properties of Single Axon Excitatory PostsynapticPotentialsElicitedinSpinyInterneuronsbyAction-PotentialsinPyramidalNeuronsinSlicesofRatNeocortex.Neuroscience69:727-738.
29. Ziegler JF,NelsonME,Shell JD,PetersonRJ,GelderloosCJ,MuhlfeldHP,MontroseCJ.1998.Cosmic ray soft error rates of 16-Mb DRAM memory chips. Ieee Journal of Solid-State Circuits33:246-252.
30. Anonymous.2009.InternationalTechnologyRoadmapforSemiconductors.31. Konczakowska A, Wilamowski B. 2011. Noise in Semiconductor Devices. Fundamentals of
IndustrialElectronicsChapter11.32. TsimringLS.2014.Noiseinbiology.RepProgPhys77:026601.33. KaernM,ElstonTC,BlakeWJ,CollinsJJ.2005.Stochasticityingeneexpression:fromtheoriesto
phenotypes.NatRevGenet6:451-464.34. WhiteJA,RubinsteinJT,KayAR.2000.Channelnoiseinneurons.TrendsNeurosci23:131-137.35. Voelker M, Fromherz P. 2006. Nyquist noise of cell adhesion detected in a neuron-silicon
transistor.PhysRevLett96:228102.36. AdairRK.2003.Noiseandstochasticresonanceinvoltage-gatedionchannels.ProcNatlAcadSciU
SA100:12099-12104.37. Cox CD, McCollum JM, Austin DW, AllenMS, Dar RD, SimpsonML. 2006. Frequency domain
analysisofnoiseinsimplegenecircuits.Chaos16:026102.38. Branco T, Staras K. 2009. Theprobability of neurotransmitter release: variability and feedback
controlatsinglesynapses.NatRevNeurosci10:373-383.39. ArriagaEA.2009.Determiningbiologicalnoiseviasinglecellanalysis.AnalBioanalChem393:73-
80.40. Deneux T, Kaszas A, Szalay G, Katona G, Lakner T, Grinvald A, Rozsa B, Vanzetta I. 2016.
Accurate spike estimation from noisy calcium signals for ultrafast three-dimensional imaging oflargeneuronalpopulationsinvivo.NatCommun7:12190.
41. Dorval AD, Jr., White JA. 2005. Channel noise is essential for perithreshold oscillations inentorhinalstellateneurons.JNeurosci25:10025-10028.
42. Elowitz MB, Levine AJ, Siggia ED, Swain PS. 2002. Stochastic gene expression in a single cell.Science297:1183-1186.
43. Finkenstadt B, Woodcock D, Komorowski M, Harper C, Davis J, White M, Rand D. 2013.QUANTIFYING INTRINSICANDEXTRINSICNOISE INGENETRANSCRIPTIONUSINGTHELINEARNOISE APPROXIMATION: AN APPLICATION TO SINGLE CELL DATA. The Annals of AppliedStatistics7.
44. Hensel Z, Feng H, Han B, Hatem C,Wang J, Xiao J.2012. Stochastic expressiondynamicsof atranscriptionfactorrevealedbysingle-moleculenoiseanalysis.NatStructMolBiol19:797-802.
45. Neher E, Sakaba T. 2001. Estimating transmitter release rates from postsynaptic currentfluctuations.JNeurosci21:9638-9654.
46. NewmanJR,GhaemmaghamiS,IhmelsJ,BreslowDK,NobleM,DeRisiJL,WeissmanJS.2006.Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise. Nature441:840-846.
47. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A. 2002. Regulation ofnoiseintheexpressionofasinglegene.NatGenet31:69-73.
48. ReiterM,KirchnerB,MullerH,HolzhauerC,MannW,PfafflMW.2011.Quantificationnoiseinsinglecellexperiments.NucleicAcidsRes39:e124.
49. RosenfeldN,Young JW,AlonU,SwainPS,ElowitzMB.2005.Generegulationatthesingle-celllevel.Science307:1962-1965.
50. Volfson D, Marciniak J, BlakeWJ, Ostroff N, Tsimring LS, Hasty J. 2006. Origins of extrinsicvariabilityineukaryoticgeneexpression.Nature439:861-864.
51. KleinpenningTGM,BareikisV,KatiliusR.1995.Low-frequencynoiseinBJT'sandHBT's.NoiseinPhysicalSystemsand1/fFluctuations.
52. Costa D, Harris JS. 1992. Low-FrequencyNoiseProperties ofN-P-NAlgaasGaasHeterojunctionBipolar-Transistors.IeeeTransactionsonElectronDevices39:2383-2394.
53. CostaD,TuttMN,KhatibzadehA,PavlidisD.1994.Tradeoffbetween1/FNoiseandMicrowavePerformance in Algaas/Gaas Heterojunction Bipolar-Transistors. Ieee Transactions on ElectronDevices41:1347-1350.
54. Plana R, Graffeuil J, Delage SL, BlanckH, DifortepoissonMA, Brylinski C, Chartier E.1992.Low-Frequency Noise in Self-Aligned Gainp/Gaas Heterojunction Bipolar-Transistor. ElectronicsLetters28:2354-2356.
55. Kleinpenning TGM, Holden AJ. 1993. 1/F Noise in N-P-N Gaas/Algaas Heterojunction Bipolar-Transistors - Impactof IntrinsicTransistorandParasiticSeriesResistances. IeeeTransactionsonElectronDevices40:1148-1153.
56. McDonnell MD, Ward LM. 2011. The benefits of noise in neural systems: bridging theory andexperiment.NatRevNeurosci12:415-426.
