Hierarchical modelling of automated imaging data

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1 Darren Wilkinson School of Mathematics & Statistics, Newcastle University, UK Theory of Big Data 2 UCL, London 6th 8th January, 2016

2 Overview Background: Budding yeast as a model for genetics High-throughput robotic genetic experiments Image analysis and data processing (Stochastic) modelling of growth curves Hierarchical modelling of genetic interaction Joint work with Jonathan Heydari, Keith Newman, Conor Lawless and David Lydall (and others in the Lydall lab )

3 Saccharomyces cerevisiae Budding yeast biology and genetics Synthetic genetic array Telomeres HTP yeast SGA robotic screens Saccharomyces cerevisiae, often known as budding yeast, and sometimes as brewer s yeast or baker s yeast, is a single-celled eukaryotic organism Eukaryotic cells contain a nucleus (and typically other organelles, such as mitochondria) It is useful as a model for higher eukaryotes, having a great deal of biological function conserved with humans It is the most heavily studied and well-characterised model organism in biology (eg. first fully sequenced eukaryote)

4 Synthetic Genetic Array (SGA) Budding yeast biology and genetics Synthetic genetic array Telomeres HTP yeast SGA robotic screens Possible to obtain a library of around 4,500 mutant strains, each of which has one of the non-essential genes silenced through insertion of a (kanmx) antibiotic resistance cassette and tagged with a unique DNA barcode These strains (stored frozen in 96-well plates) can be manipulated by robots in 96-well plates (8 12), or on solid agar in 96, 384 or 1536-spot format Synthetic Genetic Array (SGA) is a clever genetic procedure using robots to systematically introduce an additional mutation into each strain in the library by starting from a specially constructed query strain containing the new mutation

5 Telomeres Yeast Budding yeast biology and genetics Synthetic genetic array Telomeres HTP yeast SGA robotic screens The ends of linear chromosomes require special protection in order not to be targeted by DNA damage repair machinery (bacteria often avoid this problem by having just one chromosome arranged in a single loop) Telomeres are the ends of the chromosomal DNA (which have a special sequence), bound with special telomere-capping proteins that protect the telomeres CDC13 is an essential telomere-capping protein in yeast cdc13-1 is a point-mutation of cdc13, encoding a temperature-sensitive protein which functions similarly to wild-type CDC13 below around 25 C, and leads to telomere-uncapping above this temperature

6 Basic structure of an experiment Budding yeast biology and genetics Synthetic genetic array Telomeres HTP yeast SGA robotic screens 1 Introduce a mutation (such as cdc13-1) into an SGA query strain, and then use SGA technology (and a robot) to cross this strain with the single deletion library in order to obtain a new library of double mutants 2 Inoculate the strains into liquid media, grow up to saturation then spot back on to solid agar 4 times 3 Incubate the 4 different copies at different temperatures (treatments), and image the plates multiple times to see how quickly the different strains are growing 4 Repeat steps 2 and 3 four times (to get some idea of experimental variation) 5 Repeat steps 2 to 4 with a control library that does not include the query mutation

7 Budding yeast biology and genetics Synthetic genetic array Telomeres HTP yeast SGA robotic screens Some numbers relating to an experiment Initial SGA work (introducing mutations into the query and the library) takes around 1 month of calendar time, and several days of robot time The inoculation, spotting and imaging of the 8 repeats takes 1 month of calendar time, and around 2 weeks of robot time The experiment uses around 3,000 of consumables (plastics and media) The library is distributed across well plates or 18 solid agar plates (in 384 format, or 1536 in quadruplicate) If each plate is imaged 30 times, there will be around 35k high-resolution photographs of plates in 384 format, corresponding to around 13 million colony growth measurements (400k time series) This is big data!

8 pipeline pipeline Image processing (from images to colony size measurements) Fitness modelling (from colony size growth curves to strain fitness measures) (from strain fitness measures to identification of genetically interacting strains, ranked by effect size) Possible to carry out three stages separately, but benefits to joint modelling through borrowed strength and proper propagation of uncertainty. Not practical to integrate image processing step into the joint model, but possible to jointly model second two stages.

9 Yeast pipeline Automated image analysis (Colonyzer)

10 pipeline Growth curve A B Normalised cell density (AU) his3δ htz1δ Time since inoculation (h)

11 pipeline We want something between a simple smoothing of the data and a detailed model of yeast cell growth and division Logistic growth models are ideal simple semi-mechanistic models with interpretable parameters related to strain fitness Basic deterministic model: dx dt = rx(1 x/k), subject to initial condition x = P at t = 0 r is the growth rate and K is the carrying capacity Analytic solution: x(t) = KP e rt K + P (e rt 1)

12 Statistical model Yeast pipeline Model observational measurements {Y t1, Y t2,...} with Y ti = x ti + ε ti Can fit to observed data y ti using non-linear least squares or MCMC Can fit all (400k) time courses simultaneously in a large hierarchical model which effectively borrows strength, especially across repeats, but also across genes

13 Growth curve model Yeast pipeline l m n ŷ lmn y lmn Time Point Repeat K lm r lm orf τ K l τ K l ν l K o l r o l σ K,o σ τ,k σ r,o σ τ,r σ ν Population K p τ K,p r p τ r,p P ν p

14 Colony fitness Yeast pipeline The results of model fitting are estimates (or posterior distributions) of r and K for each yeast colony, and also the corresponding gene level parameters Both r and K are indicative of colony fitness keep separate where possible Often useful to have a scalar measure of fitness many possibilities, including rk, r log K, or MDR MDP, where MDR is the maximal doubling rate and MDP is the maximal doubling potential Statistical summaries can be fed in as data to the next level of analysis (or, ultimately, modelled jointly as a giant hierarchical model)

15 Epistasis Yeast pipeline From Wikipedia: Epistasis is the interaction between genes. Epistasis takes place when the action of one gene is modified by one or several other genes, which are sometimes called modifier genes. The gene whose phenotype is expressed is said to be epistatic, while the phenotype altered or suppressed is said to be hypostatic. Epistasis and genetic interaction refer to the same phenomenon; however, epistasis is widely used in population genetics and refers especially to the statistical properties of the phenomenon.

16 Multiplicative model Yeast pipeline Consider two genes with alleles a/a and b/b with a and b representing wild type (note that A and B could potentially represent knock-outs of a and b) Four genotypes: aa, Ab, ab, AB. Use [ ] to denote some quantitative phenotypic measure (eg. fitness ) for each genotype Multiplicative model of genetic independence: [AB] [ab] = [Ab] [ab] no epistasis [AB] [ab] > [Ab] [ab] synergistic epistasis [AB] [ab] < [Ab] [ab] antagonistic epistasis Perhaps simpler if re-written in terms of relative fitness: [AB] [ab] = [Ab] [ab] [ab] [ab]

17 pipeline Genetic independence and HTP data Suppose that we have scaled our data so that it is consistent with a multiplicative model what do we expect to see? The independence model [AB] [ab] = [Ab] [ab] translates to [query : abc ] [wt] = [query] [abc ] In other words [query : abc ] = [query] [wt] [abc ] That is, the double-mutant differs from the single-deletion by a constant multiplicative factor that is independent of the particular single-deletion ie. a scatter-plot of double against single will show them all lying along a straight line

18 Statistical modelling Yeast pipeline Assume that F clm is the fitness measurement for repeat m of gene deletion l in condition c (c = 1 for the single deletion and c = 2 for the corresponding double-mutant) Model: F clm N( ˆF cl, 1/ν cl ) log ˆF cl = α c + Z l + δ l γ cl δ l Bern(p) δ l is a variable selection indicator of genetic interaction Then usual Bayesian hierarchical stuff...

19 Genetic interaction model pipeline c α c l n ˆF clm F clm Repeat σ γ c γ cl ν cl Condition orf Z l δ l Z p σz ν p σ ν Population

20 pipeline Genetic interaction results VPS8 BUD14 KIN3 MUM2 UBC4 CHK1 RIF1 :::MRC1 MRC1 MAK31 PTC6 RPN4 RPL13A YDL109C YDL118W YDL119C RPP1B RPL35B RPL35A ARX1 MTC5 SAN1 RAD9 SWM1 YDR269C IPK1 SAC7 RPL27B RPL37B MAK10 NOP16 TMA20 YER119C A SCS2 FTR1 RAD24 BMH1 BUD27 RPO41 UBP6 RPL2A PIB2 RPL24A DBP3 RPL9A ARO2 TOS3 ARO8 YGL217C UPF3 RPL11B PPT1 PHB2 RPL8A SSF1 NMD2 EST3 YIL055C FYV10 DPH1 MPH1 PET130 TMA22 GEF1 MRT4 ELM1 HAP4 ZRT3 LST4 DPH2 DOA1 MEH1 UTH1 BAS1 RIC1 ERG3 YLR111W SRN2 RPL37A EST1 YLR261C TAL1 SUR4 REH1 VIP1 RIF2 OGG1 VPS9 GTR1 NAM7 ECM5 YMR206W YKU70 YNL011C RPL16B ESBP6 RAD50 MCK1 KRE1 YNR005C STI1 EXO1 SHE4 STD1 CKA2 HIS3 RAD17 HAT1 PNG1 DDC1 YPR044C TKL1 CLB2 VPS4 EDE1 YBL104C PAT1 CYK3 EBS1 RPP2B BST1 LRP1 YIL057C MNI1 FKH1 VPS51 YPT6 RPL6B YML010C B RPL42A MNT4 RTC1 RIM1 DIE2 COX23 CST6 JJJ3 RPL43A LTE1 SLA1 ARA1 UFD2 RVS167 POT1 CCW12 SUB1 YMR057C FET3 NPT1 CLB5 HMT1 YDL012C PHO2 RPL24B YPS6 IRC21 YPL080C ELP3 MNI2 RPL8B CKB2 NUP2 HSP26 GUP1 AIR1 SNX4 YJR154W CDC73 MFT1 QCR9 THP2 RPL16A HPR5 DID2 STM1 PGM2 MRE11 CCC2 UFD4 RPL36A MET18 LDB19 PHO13 OCA6 PPH3 VID28 RAD23 SKI8RPL34A BNR1 YMR193C A PET122 VPS35 POL32 YLR402W RPL29 DBF2 HGH1 ELP2 BUD28 PPQ1 GPH1 AVT5 MDM34 CTP1 BEM2 RMD11 TEL1 CRD1 CRP1 UPS1 LIA1 COX12 ICT1 GUF1 YMR153C A MSS18 SYS1 DPH5 COX7 RPL4A RRD1 UBX4 OAC1 YPL062W NAT1 DPB4 SIM1 HCM1 RHR2 YER093C A GPD2 VPS21 :::RTT103 KAP122 SER2 KEX1 XBP1 BCK1 VPS24 PFK26 VAM10 AYR1 YIL161W TNA1 CBP4 HSP104 VPS60 YGL218W COQ10 YDR271C CLG1 DYN3 ALD6 CAP2 SIW14 NAP1 YNL226W SRB2 YLR218C YLR290C MON1 YPR050C EOS1 OST3 YDL176W PUS7 IMG2 GZF3 FKH2 YKE4 TRP1 VRP1 DCC1 IRA2 TIP41 BUB2 RPL26A SLT2 YLR338W DPB3 FEN1 FCY2 RPS4A RPL43B IKI3 NUP53 PUF6 FUS3 SKI2 NPR1 RPL21B UBX7 YGR259C MCX1 YKR035C ZWF1 PUF4 ARO1 ARP1 NUP133 YJL185C YOR251C VID24 RNR3 YPT7 PTC2 AEP2 PER1 SAS4 YBR266C CBF1 DRS2 YLR143W OST4 GIM3 ALG3 PTC1 ELP4 CKB1 YML013C A DYN1 YBL083C STP1 PSD1 TRM44 ARC18 YDR262W ALG12 RPL40B SAS5 BMH2 MAK3 KTI12 YGL042C JNM1 CAT5 GDH1 YTA7 TEF4 CTF4 YKR074W VPS1 ELG1 NRG2 KNS1 VPS5 GPA2 FPS1 PEX32 VID30 VPS17 YBR277C MCM16 YBL059W PHO80 BEM4 EMI5 SBP1 OTU2 LSM6 RPL23A VPS38 UBP3 GID8 DBR1 RPL17B SWF1 MNE1 YMR074C VHS2 SPT2 SWI4 FIT2 CYT2 JJJ1 CBT1 PAC1 SKI7 MBP1 RPL33B PAN2 YNL120C NPL4 EAF3 YOR309C SFH5 CSN12 IMP2' SHE1 FMP35 YDL050C YBR144C PBP2 YLR184W YGL149W RPL9B INP52 YGL057C NTO1 QCR2 RTF1 DOT1 OMS1 VAM7 CYT1 EMI1 NBP2 VAC14 RAV1 YLR407W RPP1A CAC2 MRPL1 LAC1 HPT1 XRS2 YJL206C KEX2 MDM38 MMM1 ERG24 ACE2 ALD3 CTK1 VAM3 RPE1 OYE2 ERJ5 RVS161 PKR1 ERG6 OCA4 YBR028C GOS1 MRN1 HAP5 MGR2 SAS2 AAH1 CYC2 CHL1 TOM70 RSM25 RBS1 TMA19 SWC5 UBA4 HSE1 ELP6 MTC3 HAP2 UBP2 HSP12 YAP1 SET2 APQ12 APT1 PMS1 BFA1 YUR1 LEU3 VAM6 YJL120W GRS1 HAP3 ASC1 TOP1 DIP5 YNR029C UME1 ALG9 RMD5 SIR3 BTS1 YDR203W TPS3 LDB18 ERD1 ALG6 URM1 PHO87 DSK2 GET1 CKA1 MLH1 YPR098C DEP1 YPR039W GEM1 YDR266C REI1 RNH202 AKL1 MET16 YDR049W YJL211C PEX8 PHB1 MDM10 YLR217W LRG1 YBR025C EFT2 YBR246W SNF1 YDR149C BRE5 PEX15 PAN3 PAH1 FYV1 YHL005C MIR1 VTS1 RPL22A YPL102C IRC3 PUF3 YDR348C TOM7 THR4 PEX2 YAP1801 PEX13 PMP3 MNN11 QCR6 SYT1 YLR091W YPR084W YGL024W BUL1 ALG5 PPZ1 KAR9 HSP82 TCM62 CPS1 CCZ1 AZF1 SYF2 YML090W OCA5 YDR537C CYM1 ATP10 URE2 KRE11 YBL071C NBA1 YPL035C PEP8 RGS2 PTP3 YOR052C BNA2 YBR232C YKL121W NCS2 YBR226C DEG1 CSM3 TOM6 MMS22 SPE2 YMR310C HIR3 RTT109 YBR099C MIS1 ASR1 RTC4 IMP2 RAD27 YPR004C Fitness (F) of double mutants at 27 C (doublings / day) 2 double mutants at 27 C (doublings / day) 2 Fitness (F) of orfδ ura3δ orfδ cdc13-1

21 pipeline Joint modelling of growth curves and genetic interaction We can integrate together the hierarchical growth curve model and the genetic interaction model into a combined joint model This has usual advantages of properly borrowing strength, proper propagation of uncertainty, etc. Also very convenient to avoid requiring a scalar measure of fitness If y clmn is the colony size at time point n in repeat m of gene l in condition c, then y clmn N(ŷ clmn, 1/ν cl ) ŷ clmn = X(t clmn ; K clm, r clm, P ) log K clm N(α c + K o l + δ l γ cl, 1/τ K cl ) log r clm N(β c + r o l + δ lω cl, 1/τ r cl )

22 Joint model Yeast pipeline c l m n ŷclmn y clmn Time Point σ γ c γ cl K clm r clm Repeat α c Condition σ ω c ω cl β c ν cl τ K l τ r l orf K o l δ l r o l σ K,o σ τ,k σ r,o σ τ,r σ ν Population K p r p τ K,p τ r,p P ν p

23 pipeline Joint model results VPS8 LTE1 BUD14 KIN3 SLA1 FUS3 EDE1 YBL059W ALG3 YBL083C RPL23A TEL1 AVT5 YBL104C YBR025C RPL4A HMT1 MUM2 AKL1 HSP26 UBC4 VID24 CCZ1 ARA1 PEX32 RPS9B MCX1 YBR266C UBX7 CHK1 RIF1 YBR277C DPB3 SNF5 CTP1 SGF29 :::MRC1 MRC1 MAK31 RIM1 FEN1 BUD31 HCM1 PAT1 PTC6 PTC1 YDL012C RPN4 NAT1 MBP1 RPP1A RPL13A PHO2 YDL109C CYK3 YDL118W YDL119C RPP1B RPL35B CRD1 YDL176W UFD2 RPL35A OST4 PHO13 TRP1 OCA6 PPH3 VPS41 ARX1 DPB4 ARO1 MTC5 SAN1 SAS4 EBS1 RAD9 SWM1 YDR262W YDR269C CCC2 YDR271C :::RTT103 IPK1 MSN5 RPP2B EFT2 RVS167 SAC7 HPT1 DOT1 STP1 RPL27B VPS60 PUF6 RPL37B EMI1 RAD23 MAK10 NOP16 TMA20 FCY2 RPL34A PTC2 YER093C A SWI4 YER119C A SCS2 FTR1 PET122 BEM2 RAD24 BMH1 BUD27 BST1 STE2 RPO41 UBP6 RPL2A RPL29 PUF4 KAP122 CKB1 PIB2 YGL024W RPL24A YGL042C DBP3 GUP1 MON1 RPL9A ARO2 YGL149W KEM1 TOS3 ARO8 KEX1 VAM7 SKI8 CLG1 YGL217C YGL218W MDM34 UPF3 RPL11B DBF2 PCP1 PPT1 RPL24B QCR9 HGH1 ELP2 DIE2 PHB2 YGR259C TNA1 YTA7 OTU2 OPI1 RMD11 RPL8A SLT2 SSF1 NMD2 LRP1 COX23 ARP1 THP2 EST3 VID28 YKE4 CAP2 CST6 RHR2 YIL055C YIL057C AIR1 FYV10 XBP1 DPH1 PFK26 MNI1 SIM1 AYR1 MET18 FKH1 RPL16A RRD1 IMP2' BNR1 POT1 YIL161W MPH1 YPS6 SYS1 PET130 SNX4 HPR5 BCK1 GSH1 GZF3 YJL120W VPS35 RPL17B YJL185C YJL211C TMA22 GEF1 POL32 CBF1 LIA1 CSN12 GRR1 RPL43B JJJ3 CPA2 RPS4A YJR154W MRT4 UFD4 VPS24 ELM1 TEF4 HAP4 KTI12 OAC1 ZRT3 LST4 DPH2 DOA1 MEH1 VPS51 YKR035C DID2 UTH1 NAP1 NUP133 RPL40B BAS1 KNS1 HSP104 FPS1 RPL8B COX12 RIC1 ERG3 RPL22A BUD28 ICT1 CCW12 YLR111W SRN2 YLR143W STM1 DPH5 RPL37A UPS1 YLR218C EST1 YLR261C YPT6 GUF1 NUP2 VRP1 YLR338W RPL26A TAL1 SUR4 IKI3 REH1 SKI2 YLR402W VIP1 CDC73 RPL6B RIF2 YPT7 ERG6 YML010C B YML013C A YMD8 OGG1 MFT1 VPS9 GTR1 SUB1 CSM3 BUB2 YMR057C FET3 UBX4 IRC21 NAM7 PGM2 PKR1 YMR153C A ALD3 ECM5 YMR193C A RPL36A YMR206W MRE11 COX7 AEP2 YKU70 JNM1 DYN3 YNL011C SIW14 FKH2 RPL16B EOS1 YNL120C ESBP6 RPL42A PSD1 YNL226W ZWF1 RAD50 ERG24 MCK1 KRE1 YNR005C CSE2 MNT4 PHO80 COQ10 GSH2 GPD2 EMI5 IRA2 RTC1 STI1 EXO1 SHE4 CKB2 STD1 CKA2 VAM10 VPS5 OST3 VPS21 CAT5 VPS17 ELG1 HIS3 NPT1 SAS5 RPL33B PUS7 PAC1 YOR309C RPL20B LDB19 RAD17 GDH1 HAT1 TRM44 ALD6 YPL062W BTS1 RPL21B YPL080C ELP3 PNG1 BEM4 PPQ1 MRN1 DDC1 YPL205C HSP82 NTO1 TIP41 RPL43A YPR044C MNI2 MCM16 SPE3 TKL1 CLB2 CLB5 MSS18 GPH1 VPS4 YBR226C PBP2 YDL050C BMH2 SWF1 YDR266C IES5 UBP3 CBP4 CRP1 RNR3 RPE1 SFH5 RAV1 CTK1 VPS1 PEX13 VPS38 ARC18 VAC14 YLR407W PPZ1 CAC2 YMR310C ALG12 MDM12 SKI7 YOR251C MNE1 OMS1 KRE28 TRP5 YGL057C VID30 SBP1 UBA4 YJL206C CYT2 YKR074W LDB18 YLR290C TPS3 PMS1 HAP5 ALG5 QCR2 DRS2 HAP3 YBR144C RMD5 RNH202 SSD1 OCA5 GOS1 VHS2 DBR1 ASC1 NUP53 RPL9B JJJ1 YPL102C RVS161 NCS6 SER2 YMR074C UBP2 EAF3 REI1 PER1 IMG2 OYE2 CBT1 YAP1 YKU80 SAS2 AAH1 ALG9 YDR203W RPL14A BCH2 MDM38 AKR2 YOR052C DCC1 ERD1 GET1 MMM1 YNR029C YPR050C GEM1 NBP2 CPS1 GID8 NPR1 YNR020C CTF4 FMP35 OCA4 PEX8 PEP8 YUR1 RPS1B FIT2 MRPL1 GPA2 MTC3 SET2 YLL029W TOM7 ALG6 MGR2 SLX9 YLR091W YDR049W PMP3 YAP1801 YNL109W VAM3 MIS1 HSE1 CYT1 RTF1 SPT2 ACE2 IMP2 SPE2 AHA1 YDR537C PAN2 CPR7 LEU3 SIN4 LEO1 DYN1 ATP10 BUL1 :::GAL11 HSP12 DSK2 MAK3 SRB2 MOG1 MDM10 RBS1 BNA2 ELP4 PHO87 LRG1 YLR184W PAN3 LRE1 ARC1 PAH1 AZF1 NMD4 ERJ5 YKL121W PEX15 LSM1 NRG2 YDR348C IOC3 HAP2 POC4 VAM6 DCW1 SPE1 YOR131C YBR028C APT1 BRE5 IBD2 PTH1 RSM25 YPR039W GRS1 LHP1 YOR008C A TOP1 KRE11 MET16 PEX2 TOM70 RGA1 VPS30 GIM3 CYC2 VTS1 MDL1PKH3 MLH1 LAC1 RPS24A STE4 PEX14 FYV1 MKS1 KEX2 TMA16 CHL1 PUF3 YDR029W RTC4 TLG2 TMA19 CYM1 BUB3 YBR232C ARL3 HCR1 STB5 MNN11 MID2 RRN10 FKS1 OCA1 MMS2 URE2 YML108W ARP8 APL4 BFA1 LSM6 SFL1 APL1 APC9 SNF1 NCS2 DEG1 TPM1 RTG2 IES2 RHO5 MIR1 TCM62 FMP36 PEX10 SSA1 TGS1 YAL004W UBC13 DIP5 MFB1 MVB12 ICE2 BUD19 PHB1 ROT2 YBR285W SIF2 YML102C A MFA1 PEX6 YPR098C XRS2 TOM6 IRC3 DEP1 SHE1 MGA2 YLR217W LAS21 CUE3 YML053C ISU2 INP52 PTP3 ASH1 QCR6 NIF3 NBA1 YPL041C COX8 ALG8 NFI1 MRPS9 TOS1 IOC4 RPL41B YDR467C RAD27 ARL1 TSA1 YPR097W BUB1 RAX2 FIS1 MMS22 TPS1 GDS1 RSM28 UME1 CKA1 PDE2 RCE1 ASM4 VIK1 YPS7 CWH43 VPS27 MEP3 ABP1 SWC5 STE50 RPS27A ELF1 YPL035C VPS75 MSC6 :::GUK1 YNL198C SKG3 SER1 VPS53 YNL171C PEX12 YNL105W YDR506C KAR9 YPR004C YBR224W RIT1 CHS3 YOR082C RBL2 PHO88 RNH203 VPS29 CTF18 PET494 YBL071C IXR1 PRS5 IRC15 ILV6 APE2 GGA2 YCF1 YML090W YBR246W YLR118C SYC1 YPR096C MSH2 RTG1 MET3 DIA2 OCA2 STB1 YIL166C SPO14 SWA2 YER077C SRL1 YPL105C GIS4 ADE1 YBR134W YDR149C YBR099C OST5 EAF6 LEM3 NPL4 YAF9 GAS1 ASR1 YJL215C YLR282C RPP2A YHL005C SOH1 NHP10 YMR144W RTC6 AHP1 RNH201 YPL225W PSR2 THR4 WWM1 BUD13 URM1 JSN1 KES1 YPR084W MMS1 ELP6 DCR2 YPR148C OSH3 SNC2 SKI3 MPA43 PEX5 JID1 YGR242W PET127 PIN4 COX5B YGL235W YGL046W CWH41 IOC2 AUA1 COX5A YDL041W YKL158W INP53 STE11 ADY4 KIP2 RGS2 BEM3 MLH2 YAL058C A YPR090W YOL079W CHZ1 OPI10 RPS30B YCR051W YLR334C APP1 SCD6 COG7 PRE9 YLR404W PAM17 YSA1 RPA14 PEX4 NRM1 ERF2 YML119W CCS1 REX4 RHO2 RFM1 FYV12 GCV2 AAD3 CTI6 HMX1 PRM4 YOR022C ATG27 ITR1 SKT5 HOS2 SCS7 YIL064W ARF1 SYT1 ARR1 RPS23B YNR004W YHL044W APL3 YBR238C GTR2 MAD1 VTC4 CSR2 KAR3 RTG3 SYF2 SPO11 PUS4 PRX1 MRP49 INP2 YDL071C NDL1 ZRT1 SRF6 YIA6 HUL5 OM45 FMP25 YER078C APS2 COG8 GIS3 MCR1 SLM1 GIM4 TFP1 NUP60 PBY1 SBA1 PMT2 IRC8 YPL183C RTT102 RPL19A YER066W RAD52 SEM1 YNL140C SHE9 ECM22 BSP1 ALB1 YOL153C YGR226C MLS1 KEL1 SRB8 MGR1 MNN2 BUG1 SIR4 ERV14 FSF1 YMC2 PIH1 AGA1 PEX25 YKL077W UBA3 NCE102 VPS13 YNG1 HST2 YHM2 ENT2 THR1 YDR445C PEX30 YGL132W YPT32 BIK1 POM34 ATH1 YLR434C MED1 MET31 ATP18 HPC2 LYS20 RPS14A HOM2 SRF4 SSK1 YER084W IMD4 SSH1 PEX3 YIL102C PCT1 PHO86 BUD21 ATG5 MMR1 double mutants at 27 C (doublings / day) 2 Fitness (F) of double mutants at 27 C (doublings / day) 2 Fitness (F) of orfδ ura3δ orfδ cdc13-1

24 Summary References Big data issues Understanding conflict between model and data in big data contexts does more data demand more complex models? Model simplifications and improvements to MCMC (block updates and proposals, reparameterisations, GVS, etc.) Basic parallelisation strategies (parallel chains, parallellelised single chain) Investigation of data parallel strategies (consensus Monte Carlo, etc.) Novel representations and implementations of Bayesian hierarchical models using functional programming languages

25 Summary References Summary Modern bioscience is generating large, complex data sets which require sophisticated modelling in order to answer questions of scientific interest Big data forces trade-offs between statistical accuracy and computational tractability Stochastic dynamic models are much more flexible than deterministic models, but come at a computational cost the LNA can sometimes represent an excellent compromise Notions of genetic interaction translate directly to statistical models of interaction Big hierarchical variable selection models are useful in genomics, but can be computationally challenging

26 Summary References Funding acknowledgements Major funders of this work: BBSRC MRC Wellcome Trust Cancer Research UK

27 References Yeast Summary References Addinall, S. G., Holstein, E., Lawless, C., Yu, M., Chapman, K., Taschuk, M., Young, A., Ciesiolka, A., Lister, A., Wipat, A., Wilkinson, D. J., Lydall, D. A. (2011) Quantitative fitness analysis shows that NMD proteins and many other protein complexes suppress or enhance distinct telomere cap defects. PLoS Genetics, 7:e Heydari, J. J., Lawless, C., Lydall, D. A., Wilkinson, D. J. (2016) Bayesian hierarchical modelling for inferring genetic interactions in yeast, Journal of the Royal Statistical Society, Series C, early view. Heydari, J. J., Lawless, C., Lydall, D. A., Wilkinson, D. J. (2014) Fast Bayesian parameter estimation for stochastic logistic growth models, BioSystems, 122: Lawless, C., Wilkinson, D. J., Addinall, S. G., Lydall, D. A. (2010) Colonyzer: automated quantification of characteristics of microorganism colonies growing on solid agar, BMC Bioinformatics, 11:287. Wilkinson, D. J. (2009) Stochastic modelling for quantitative description of heterogeneous biological systems, Nature Reviews Genetics. 10(2): Wilkinson, D. J. (2011) Stochastic Modelling for Systems Biology, second edition. Chapman & Hall/CRC Press.