D. Combinatorial transcriptional control. Complex eukaryotic promoter

Transcription

1 D. Combinatorial transcriptional control Complex bacterial s with multiple inputs: Complex eukaryotic [Davidson et al] 1

2 Mechanisms of complex transcriptional control? specific, complex protein-protein interaction but different TFs can work together to implement different functions combinatorial control favors simpler, less specific interaction alternative: regulated recruitment [Ptashne & Gann 97] simple, glue-like interaction between TFs/RNAP arrange DNA binding sites/strengths to accomplish desired control functions but how to implement? and what are the limitations? Theory of Combinatorial Transcription Control Statistical Mechanics [Buchler et al, PNAS 03] 2

3 Theory of Combinatorial Transcription Control ω A-B ω B-p ω A2,C1 K A1 K B1 K A2 K C1 K p 1 O B1 2 O C1 ωc-p [Buchler et al, PNAS 03] quantitative description: via changes in regulatory sequences alone occupation of site j: σ j = {0,1} TF-operator interaction: K j = exp(-βδg j ) = 1 ~ 1000 nm TF-TF and TF-RNAP interaction: ω i,j = exp(-βe ij ) = {0, 1, 10 ~ 100} regulated recruitment [M. Ptashne] long-distance interaction possible via DNA looping activity ~ equilibrium occupation prob P [TF j ] è thermodynamic model N ( ) σ j Z = [TF j ] / K j i ω { } i, j formally programmable = neural network molecular (Boltzmann Boltzmann machine) machine! What kind of control functions P ([TF j ]) are implementable via the appropriate choices of {K j, ω i,j }? σ i j=1 i< j ( ) σ p σ i σ j [Shea & Ackers, 85] 1. non-interacting ω A-p ~20 ω R-p =0 K A K p K R O R simple activation: W off = 1 + [A] K A W on = [RNAp] + ω A p [A] [RNAp] K p K A K p P W on = [RNAp] 1 + ω [A] / K A p A W off K p 1+ [A] / K A (for typical weak s) simple repression: P [RNAp] K p co-regulation 1 1+ [R] / K R multiplicative P 1+ ω [A] / K A p A 1 1+ [A] / K A 1+ [R] / K R [example: lac (details later)] 3

4 2. Synergistic activation ω A ω B RNAp can simultaneously contact two TFs (e.g., and Fnr) K A 1 O B K B K p statistical weight W for each configuration {σ A, σ B, σ p }, with q X = [X]/K X W off W on W (0,0,0) = 1 W (1,0,0) = q A W (0,1,0) = q B W (1,1,0) = q A q B W (0,0,1) = q p W (1,0,1) = ω A q A q p W (0,1,1) = ω B q B q p W (1,1,1) = ω 3 q A q B q p consider ω 3 ω A ω B P ([A],[B]) W on W off logic A AND B q p 1 + ω A q A 1 + q A 1 + ω B q B 1 + q B 3. Competitive (or independent ) activation P O B P ([A],[B]) q p 1+ ω A q A + ω B q B 1 + q A + q B 4. Cooperative activation [A] logic A OR B [B] ω AB ω Bp K A O B K B K p could work as AND or OR by choosing K A, K B 4

5 5. Cooperative repression P logic NAND O B [A] [B] note: direct interaction between A and B not necessary (cf collaborative competition ) 6. Competitive repression logic NOR O B More complex control function, e.g., XOR? A/B lo/lo AND OR NAND XOR EQ cannot be implemented by overlapping A and B sites lo/hi hi/lo hi/hi [cf: linear perceptron (Minsky 69)] XOR(A,B) = (A OR B) AND NOT(A AND B) Gene cascade problems: need a gene for each intermediate result multiple rounds of gene expression: noise + delay synchronization difficult amplification nontrivial 5

6 More complex control function, e.g., XOR? A/B lo/lo AND OR NAND XOR EQ cannot be implemented by overlapping A and B sites lo/hi hi/lo hi/hi [cf: linear perceptron (Minsky 69)] XOR(A,B) = (A OR B) AND NOT(A AND B) Allosteric or co-factor mediated problem: need dedicated component lose combinatorial control e.g., can t implement AND elsewhere XOR O B More complex control function, e.g., XOR? A/B lo/lo AND OR NAND XOR EQ cannot be implemented by overlapping A and B sites lo/hi hi/lo hi/hi [cf: linear perceptron (Minsky 69)] XOR(A,B) = (A OR B) AND NOT(A AND B) Regulated recruitment integrates OR and NAND into a single regulatory region no need for special proteins XOR modular and evolvable 1 O B1 2 O B2 OR NAND 6

7 More complex control function, e.g., XOR? P P x [A] [B] P [A] [B] XOR 1 O B1 2 O B2 OR NAND [A] [B] More complex control function, e.g., XOR? è alternative implementations exist, e.g., p1 p2 1 O B2 1 O B2 A & (Not B) B & (Not A) gene expression P p1 ([A],[B]) + P p2 [A],[B] P ( ) XOR [A] [B] 7

8 XOR in bacteria? NtrC~P glnhpq glnhp1 glnhp2 : senses carbon shortage NtrC~P: senses nitrogen shortage function of glnhpq gene product: Glutamine transporter Glutamine (C 5 H 10 N 2 O 3 ) use as carbon source under carbon shortage use as nitrogen source under nitrogen shortage è need quantitative characterization of such s è design of synthetic s using exogenous regulators EQ gate? strong need multiple ways of repression A/B EQ A (low) B (high) or A (high) B (low) lo/lo lo/hi hi/lo hi/hi à possible solution: interaction at a distance e.g., DNA-looping via dimers (AraC, GalR, MelR, ) heterodimers: [A. Hochschild et al] à competitive binding awkward due to limited size (dead end) 8

9 E.g., distal repression by heterodimer pair R and R allow control by TF R R R R site A site R site R (weak) (weak) Implementation of EQ gate: Effective cascade w/o new genes! A/B EQ A1 R B1 B2 R A2 A & NOT B A1 B & NOT A R B1 B2 R A2 NOT A & NOT B A & B R R default c) default P 1 10 [A] [A] lo/lo lo/hi hi/lo hi/hi [B] [C] Generalized control architecture w/ multiple TF s Output = [ OR OR ] & NOT[ & & ] & NOT[ & & ] phenotype: dominant repression Conjunctive Normal Form Output = [ & & ] OR [ & & ] OR [ & & ] phenotype: enhancer autonomy Disjunctive Normal Form à all logic functions reducible to minimal CNF or DNF à schemata for constructing arbitrary regulatory logic functions (programmable molecular computer!) 9

10 Molecular computer Neural network TF concentration (n) TF binding sites (j) activity (P) binding strength (K j ) input neurons output firing threshold ω TF-TF interaction (ω i,j ) synapse K single node of GRN is already a network! symmetric interaction hidden units (cofactors) Molecular Boltzmann machine! learning çèevolution of regulatory sequences Summarize: A large variety of control functions P([TF j ]) may be implementable via appropriate choices of {K j, ω i,j }, i.e., via regulatory sequences alone = programmable molecular computer è synthesize desired transcriptional logic gates è breed regulatory sequences to implement desired control functions Potential application: cell-specific gene expression profiling gene 1 gene 2 gene 3 cell A cell B cell C cell X à cell type discrimination: use multiple traits à cell X revealed by a reporter gene driven by designed regulatory sequences à cell X eliminated by activating apoptosis à targeted delivery not required ( ~ smart bomb! ) 10

11 Ingredients for complex transcription control programmable protein-dna interaction weak, glue-like interaction between nearby proteins long-distance activation/repression insulation of gene regulatory control Eukaryotes: generic cooperative interaction mediated by nucleosomes [Polach & Widom, 96] physical attraction not necessary formalism as phenomenological model short-range quenching [Arnosti, Levine] distal repression via recruitment of chromatin modification agents insulating elements: crucial for minimizing cross talk similar ingredients but superior implementation platform E. Quantitative characterization of the lac lac of E. coli: best-studied system of molecular biology all molecular components characterized many mutants studied in vivo most parameters measured in vitro exemplary model system of combinatorial gene regulation involves activation, repression, and DNA looping Quantitative confrontation of model and experiment è applicability of the thermodynamic description of tsx control? è can the in vivo behavior of a system be understood in terms of its parts? 11

12 Review: regulation of the lac-operon of E. coli Physiology: lac-operon: utilization of lactose repressed by the Lac Repressor (encoded by ) repression alleviated by allo-lactose (by-product of lactose metabolism) or the synthetic inducer activated by the global regulator ; requires the inducer synthesized endogenously by Adenylate Cyclase (encoded by cyaa) activity of repressed by glucose uptake Function: expression LY in the presence of lactose AND absence of glucose glucose qualitative behavior: glucose expression low high low low high high high low Review: regulation of the lac-operon of E. coli Function: expression LY in the presence of lactose AND absence of glucose glucose qualitative behavior: glucose expression low high low low high high high low molecular ingredients: O R3 O R1 specific protein-dna binding protein-protein interaction protein-mediated DNA looping è theory: quantitative prediction of gene regulation by LacI, - è expt: characterize LacZ activity for different levels of regulatory proteins -- control protein levels by varying the inducers ( and ) 12

13 Quantitative characterization glucose :gfp on plasmid 3x 10x Previous expt: [Setty et al, PNAS, 2003] Grow cells in medium with glucose,, -- use glucose to suppress synthesis -- control -level extracellularly inconsistent with behavior of mutants: Δ: > 1000x; Δcrp > 50x è possible problems: complex links between extracellular and intracellular inducer conc. theory 100x 1000x Quantitative characterization of mutants glucose weak dependence: glucose-mediated repression of activity may be incomplete è delete cyaa gene (encoding ) è find ~100x change in LacZ activity è Hill coeff 2 incompatible w/ biochem and thermodynamic model of tsx control activity 1 + ω A p [A] / K A 1 + [A] / K A CRP 2 + CRP 2 : [] [A] = [CRP 2 ] total K + [] slope 2 100x in vitro biochem irrelevant? other effects exerted by CRP-? 13

14 Quantitative characterization of mutants slope 1 glucose slope 2 weak dependence: glucose-mediated repression of activity may be incomplete è delete cyaa gene (encoding ) è find ~100x change in LacZ activity è Hill coeff 2 incompatible w/ biochem and thermodynamic model of tsx control 100x activity 1 + ω A p [A] / K A 1 + [A] / K A CRP 2 + CRP 2 : [] [A] = [CRP 2 ] total K + [] in vitro biochem irrelevant? other effects exerted by CRP-? è degraded by PDE (cpda) è effect of cpda deletion? è Hill coeff 1, agrees with model è role of PDE: no known phenotype [insulation of ext?] è mechanism of cooperativity? Quantitative characterization of mutants dependence: cyaa- cells with []=0 è very cooperative! (Hill coeff 4) LacI forms tetramer (dimer of dimers) strong coupling within each dimer and weak coupling between dimers slope 2 slope 4 100x è suggest Hill coeff = 2 (widely cited in literature) other effect: despite its permeability, uptake increased by LacY; large coop. from +ve feedback? è delete Hill coeff 2 è constitutive expression of LacY only shifted dependence great, but Hill coeff = 2 is one of the many pseudo-facts regarding Lac 14

15 Quantitative characterization of mutants dependence: cyaa- cells with []=0 è very cooperative! LacI forms tetramer (dimer of dimers) strong coupling within each dimer and weak coupling between dimers LacI 4 - binding non-cooperative LacI 4 + LacI 4 : weakly cooperative in the presence of operator DNA (Hill coeff = 1.4 ~ 1.6) [Matthews lab, 85] è uninduced dimer needed for specific binding to Lac operators O R3 O R1 K R auxiliary Lac operators stabilize LacI-O1 binding via DNA looping [Muller-Hill] active repressors simple repression 2 [LacI [R] = 4 ] total 1 + [] / K 1 tsx activity 1 + [R] / K R ( ) 2 Quantitative characterization of mutants dependence: cyaa- cells with []=0 è very cooperative! LacI forms tetramer (dimer of dimers) strong coupling within each dimer and weak coupling between dimers LacI 4 - binding non-cooperative LacI 4 + LacI 4 : weakly cooperative in the presence of operator DNA (Hill coeff = 1.4 ~ 1.6) [Matthews lab, 85] è uninduced dimer needed for specific binding to Lac operators O R3 O R1 auxiliary Lac operators stabilize LacI-O1 binding via DNA looping [Muller-Hill] è increase fold-repression from f = 2[LacI 4 ]/K R to f (1+L 0 ) but value of L 0 not known independently active 2 [LacI [R] = 4 ] total repressors 1 + [] / K simple 1 tsx activity repression 1 + [R] / K R include DNA looping in model ( ) 2 L [R] [R] + 0 [LacI 4 ] total ( 1 + [] / K ) 4 L 0 : local increase of [LacI] due to looping 15

16 Quantitative characterization of mutants looping model w/ L 0 12, 2[LacI 4 ]/K R = x slope 3 slope 2 240x O R3 O R1 auxiliary Lac operators stabilize LacI-O1 binding via DNA looping [Muller-Hill] è increase fold-repression from f = 2[LacI 4 ]/K R to f (1+L 0 ) but value of L 0 not known independently è single parameter L 0 fits both fold-repression and slope active 2 [LacI [R] = 4 ] total repressors 1 + [] / K simple 1 tsx activity repression 1 + [R] / K R include DNA looping in model ( ) 2 L [R] [R] + 0 [LacI 4 ] total ( 1 + [] / K ) 4 L 0 : local increase of [LacI] due to looping Quantitative characterization of mutants looping model w/ L 0 12, 2[LacI 4 ]/K R = x slope 3 slope 2 240x è single parameter L 0 fits both fold-repression and slope O R3 O R1 L auxiliary Lac operators stabilize LacI-O1 binding via DNA looping [Muller-Hill] è increase fold-repression from f = 2[LacI 4 ]/K R to f (1+L 0 ) but value of L 0 not known independently 16

17 Quantitative characterization of mutants looping model w/ L 0 12, 2[LacI 4 ]/K R = x slope 3 slope 2 240x è single parameter L 0 fits both fold-repression and slope O R3 O R1 L -dependence of DNA looping Ω 8 Fried et al, 84; Balaeff et al, 04 in vitro study found coop. factor Ω = 4 ~12 Direct probe of DNA looping in vivo Use dimeric LacI mutant remove auxiliary operators è cooperativity in response requires DNA looping (Lac tetramer + auxiliary ops) [Oehler & Muller-Hill, 06] data well-fitted by DNA looping model Hill coeff = 1.5 Hill coeff = 2.5 è -LacI-operator interaction same as in vitro 17

18 back to physiology lactose glucose LacY -, cyaa-, cpdalactose glucose expression low high low low high high high low glycerol glucose only ~3x decrease from glucose to glycerol small fraction of dynamic range; (operating in saturation of -CRP) 10x change possible by reducing K crp è repression by glucose not the intended function? Summary theory E. coli MG1655 (cyaa-,cpda-,-) main findings for the lac : enhances DNA looping abrupt response despite non-cooperative LacI- interaction; è suggests physiological role of - as enhancer of repression mechanism of -LacI interaction? coop response due to PDE; physiological function? mechanism? general lessons for quantitative systems biology: hidden interaction and pseudo-facts abound even for the best studied system quantitative description of in vivo biology is possible need solid, qualitative knowledge of the components (e.g., Hill coeff) (in vitro results surprisingly robust in this regard) (semi) quantitative characterization generates spectrum of phenotypes è provides clues for identifying unknown components and mechanisms è provides phenomenological description of for high-level studies 18