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The lac repressor-operator system: Swimming in Data Collaborators: Mitch Lewis , Bob Daber, Leslie Milk, Matt Sochor, Chuck Bell, Steve Stayrook Thermodynamics of Allostery Kinetics of Allostery: Induced Fit or Landscape Shift? Large Scale Analysis of base sequence specificity/affinity

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the lac repressor operator system swimming in data
The lac repressor-operator system:Swimming in Data
  • Collaborators:
  • Mitch Lewis, Bob Daber, Leslie Milk, Matt Sochor, Chuck Bell, Steve Stayrook
  • Thermodynamics of Allostery
  • Kinetics of Allostery: Induced Fit or Landscape Shift?
  • Large Scale Analysis of base sequence specificity/affinity
slide2

Repressor has two conformations

R: Active form, binds DNA tightly, Inducer weakly

R*: Induced form, binds DNA weakly, Inducer tightly

slide6

Symmetrized O1 operator

G4

T5

G6

Q18

R22

Y17

Position L87654321.12345678R

Base TTGTGAGC.GCTCACAA

Residue RQY YQR

/ | \

aa number 22 18 17

slide7

How does the lac genetic switch work?

Mechanism of allostery

Thermodynamics

Kinetics

The origin of base sequence specific recognition of DNA by proteins

Prototype for gene therapy

Design of Tools for DNA manipulation

Cronin, et al lac operator-repressor system is functional in the mouse Genes & Dev. 2001. 15: 1506-1517

slide8

in-vivo system for evolution and functional characterization of lac repressor

(Lewis Lab)

Expression/Assay System

Two plasmid system: one contains a Lac repressor gene other contains the GFPmut3.1 gene controlled by the Lac promoter and a given operator.

FACS used to screen and separate phenotypes by GFP fluorescence.

Directed evolution:

Randomize plasmid sequence corresponding to given aa positions in repressor

Screen for given phenotype

Engineered heterodimer:

Permits assymmetric DNA recognition domains

to target non-symmetric Operator Sequences

Knockout one inducer site: Probe allosteric mechanism

slide9

E. Coli with GFPmut3.1 reporter and repressor plasmid

Fluorescence quantified by plate reader

Fractional GFP expression relative to that with no repressor plasmid

Induced by IPTG

slide10

MWC model for Allostery

KRR*: Repressor conformational equilibrium (Induced/active)

KIR*, KIR: Inducer binding affinities for induced, active repressor

KR*O, KRO: Operator DNA binding affinities for induced, active repressor

slide11

MWC model for Allostery

O/(O+RO)-> Transcription (mRNA) -> Translation (GFP level)

Fractional GFP expression with no inducer

Fractional GFP expression at saturation (n=1 inducer site)

(n=2 inducer sites)

slide12

Repressor Conformation Equilibrium [R*]/[R] = 2

Inducer Binding Affinity Ratio KIR*/KIR = 15

In Vivo Repressor Concentration [R]KRO = 150

Inducer-Repressor Binding Affinity KD,IR* = 4uM

All constants are obtained in vivo, without doing a single binding measurement!

slide13

KRR*=2 in ‘wrong’ direction. DG 0

This explains why Xtal structures of lac with and without IPTG bound are so similar

But why is Repressor conformational equilibrium so weak?

DG to drive conformational change available from inducer binding is about 1.6 kcal/mole, or about 3.2kcal/mole total, a fairly modest amount

slide14

Cell achieves effective repression in spite of weak equilibrium by setting [R] at 150-fold excess

Lac Switch has evolved to combine effective switchability given modest driving force from inducer binding, balancing the conflicting requirements of repression and induction

slide15

Comparison of Allostery in lac and Hb

Lac Hb

# of ligands 2 4

Binding Ratio 15-20 30

Conf. Equilibrium 2 1/1000

Hill # 1.2 >3

Comparison of equilibrium constants with previous in vitro studies

slide16

‘Classic’ view of ligand induced conformational change of a protein

Ligand L binds, induces conformational change A->B (induced fit)

B is of higher free energy than A

L binds to B tighter than to A, so now LB has lower free energy than A or LA

B

A

L

DG

slide17

‘New’ view of ligand induced conformational change of a protein

Protein exists in an ensemble of conformations A, B, C….. Higher energy forms less populated. L binds to and ‘selects’ one of the higher energy conformers, lowering its free energy so it becomes the dominant form

This is the population selection model, aka the protein landscape model, the protein ensemble model

B

L

A

DG

slide18

…applied to the Lac-Operon system

RO

R+O

I

I

RIO

RI+O

Low inducer, R binds O tightly

slide19

…applied to the Lac-Operon system

R+O

RO

I

I

RI+O

RIO

High inducer, R dissociates from O

slide20

Population selection route?

R+O

RO

RI+O

RIO

Induced fit route?

…applied to the Lac-Operon system

This can only be determined by kinetics, not equilibria.

Lac is one of the few systems where there is enough kinetic data to definitively discriminate

slide21

…applied to the Lac-Operon system

2x109 /M/s

RO

R+O

I

I

0.08 /s

5x104 /M/s

0.2 /s

5 /s

5x104 /M/s

40 /s

RIO

RI+O

2x109 /M/s

Association rates depend on concentration

In cell, [R] = 1nM

[I] varies

slide22

…applied to the Lac-Operon system

Time constants for various steps at I = 1uM

0.5 s

RO

R+O

I

I

12 s

20 s

5 s

0.2 s

20 s

25 ms

RIO

RI+O

0.5 s

slide23

…applied to the Lac-Operon system

Time constants for various steps at I = 10uM

0.5 s

RO

R+O

I

I

12 s

2 s

5 s

0.2 s

2 s

25 ms

RIO

RI+O

0.5 s

slide24

…applied to the Lac-Operon system

Time constants for various steps at I = 100uM

0.5 s

RO

R+O

I

I

12 s

0.2 s

5 s

0.2 s

0.2 s

25 ms

RIO

RI+O

0.5 s

slide25

PS route

R+O

RO

RIO

RI+O

Flux at 1uM IPTG

(below induction midpoint)

RO→R+O

RO+I→RIO

RIO→RI+O

slide26

R+O

RO

RIO

RI+O

IF route

Flux at 10uM IPTG

near midpoint

RO+I→RIO

RIO→RI+O

RO→R+O

slide27

R+O

RO

RIO

RI+O

IF route

slide28

Repressor is leaky-This is functionally important, since in vivo inducer is metabolic product of enzymes repressed by lac

  • Leakiness is directly related to repressor-operator affinity, KRO

Changes in leakiness, as measured by GFP levels, due to mutation/base changes → R-O affinity changes

slide29

Screening for functional Repressor-Operator Sequence Pairs

Functional Rules for Lac Repressor-Operator Associations and Implications for Protein-DNA Interactions

Milk, Daber and Lewis,Protein Science (2010) Vol 19.

A library of Lac mutants, fully randomized at positions 17, 18 and 22 screened against 64 symmetric Lac operator variants.

Functional repressors sequenced, purified and assayed with the corresponding operators.

Lower GFP expression = Tighter binding. Increase in GFP by IPTG = Inducibility.

GFP levels in absence of inducer (leakness) used to calculate change in Repressor-Operator affinity relative to wild type (YQR-GTG).

Changes in affinity occur due to localized sequence changes in 3 aa’s or 3 bp’s within the framework of the rest of the lac-operator

slide30

Base sequences recognized by a given aa triplet sequence

AA    Bases                            AA    Bases               

AAN   TGA   TTA                        HNR   GTG               

AAR   GAG   GGA   GTA                  HQN   TTT               

ACR   GAA   GCA                        HQR   GTG               

AGN   TGA   TTA                        HSN   TGG   TTT            

AGR   GAA   GGA   GGG   GTA   GTG      HSR   GAG   GAT   GGG   GTG      

AIR   GGT                              HTA   CTT               

AKN   TAC                              HTK   CTT               

AKR   GAC                              HTN   TTG   TTT            

AMR   GAT   GGT   GTG                  HTR   GTA   GTG            

ANR   GTG                              HVR   GTA               

APR   GAA                              HYR   GTG               

AQR   GAT   GGG   GTG                  IAA   CTA               

ASA   CGA   CGT                        IAF   CTA               

ASL   TAG                              IAG   CTA               

ASN   TGA   TGG   TGT                  IAN   TGA   TTA            

ASR   GCA   GGG   GGT                  IAR   GAA   GTA            

ASS   CGA                              IAY   CTA   TTA            

...

CAN   TTA                              IGR   GAA   GGA   GTG   TAA      

CMR   GGT   GTG                        IKR   GAC               

CQR   GTG                              IMR   GAG               

CSR   GGG   GGT                        INR   GTG               

CTR   GAA   GGA   GGT                  IQR   GTG               

DAR   GTA                              ISL   CGA               

EAR   GTA                              ISR   GAA   GCA            

EMR   GTG                              ITR   GAA   GCA   GTG         

ESR   GGG                              IWK   CTA               

FAR   GAA                              KAN   TGG               

FKR   GAC                              KAR   GAG   GGG            

FMR   GTG                              KGR   GTG               

GAN   TTA                              KMR   GGG   GTG            

GAR   GAA   GCA   GGA   GTA            KNR   GGG               

GCR   GAA                              ...    ...        

GGR   GTG                              YQR   GTG  (Wild Type)     

GKR   GAC                              YTR   GTG            

196 Different AA sequences

26 Different Base sequence

slide31

AA sequences recognized by a given Base triplet sequence

AGG CGA CGG CGT CTA CTT GAA GAC GAG GAT GCA GGA GGC GGG GGT GTA GTG TAA TAC TAG TGA TGG TGT TTA TTG TTT

KSL ASA KSA ASA IAA HTA ACR AKR AAR AMR ACR AAR GSR AGR AIR AAR AGR IGR AKN ASL AAN ASN ASN AAN HTN HMN

    ASS KSC KSA IAF HTK AGR FKR HAR AQR ASR AGR     AQR AMR AGR AMR PAN PKN HGN AGN HGN KSN AGN     HQN

    ATA KSL PSA IAG     APR GKR HCR HSR GAR ATR     ASR ASR ATR ANR PSN     KSL ASN HSN PSN CAN     HSN

    ISL KSM TSA IAY     AVR IKR HGR PAR GSR AVR     CSR ATR DAR AQR         PAN ATN KAN TSN GAN     HTN

    PSA KSY     ICK     CTR MKR HSR PMR GTR CTR     ESR AVR EAR CMR         PSN IAN KSA     HAN      

    PTA KTA     ICN     FAR NKR IMR SMR ISR GAR     GSR CMR GAR CQR         RSL LGN KSC     IAN      

    SSA KTD     ICY     GAR PKR KAR TMR ITR GSR     HGR CSR GTR EMR             PAN KSF     IAY      

    STA KTM     IWK     GCR SKR PAR     PCR GTR     HSR CTR HTR FMR             PSN KSG     IGN      

        KTN     TAA     GTR TKR PQR     PGR IGR     KAR GSR HVR GGR             PTN KSH     SAH      

                TAY     HAR     RAR     PSR NTR     KMR GTR IAR GMR             TGH KSL     SAN      

                        IAR     RSR     SAR PVR     KNR KQR LAR GNR             TGN KSM     SAY      

                        IGR     SSR     SCR SGR     KSR KSR MAR GQR             KSS         SGN      

                        ISR             SSR STR     KTR KTR PAR GTR             KSY         STN      

                        ITR             STR TTR     NSR PIR PTR HAR             KTN         TAH      

                        LAR             TAR         NTR PVR QAR HCR             PSN         TAN      

                        MAR             TTR         PSR SMR SAR HGR             RSL         TAY      

                        MTR                         PTR SSR SCR HNR             RSN         TGN      

                        PCR                         QSR STR SGR HQR             SSN         VAN      

                        PVR                         RAR TMR STR HSR                         YAN      

                        QAR                         RGR TSR TAR HTR                         

                        SAR                         RQR TTR TCR HYR                         

                        SCR                         RSR VMR TGR IGR                         

                        SGR                         RTR VTR TTR INR                         

                        TAR                         SGR     VAR IQR                         

                        TSR                         SSR     VYR ITR                         

                        TTR                         STR         KGR                         

                        VAR                         TGR         KMR                         

                                                    TSR         KQR                         

                                                    TTR         LMR                         

                                                    VSR         ...                         

>300 aa-base pair combinations now screened. Now we have a Thermodynamic

Model for Induction, all 300+ affinities can be extracted from the leakiness…

slide32

AGG CGA CGG CGT CTA CTT GAA GAC GAG GAT GCA GGA GGC GGG GGT GTA GTG TAA TAC TAG TGA TGG TGT TTA TTG TTTAGG CGA CGG CGT CTA CTT GAA GAC GAG GAT GCA GGA GGC GGG GGT GTA GTG TAA TAC TAG TGA TGG TGT TTA TTG TTT

Relative

Affinity

slide33

Origin of sequence specific Protein-DNA Recognition I.

Given:

196 variants of Lac differing in aa sequence in the recognition helix, each of which bind specifically to different subsets of 26 DNA base pair sequences, for a total of 331 aa-bp complexes with known affinity.

Extract as much sequence level information about specificity as possible to infer sequence recognition ‘rules’.

Can take a ‘bioinformatics’ approach

slide34

Analysis of aa-bp sequence pair recognition by clustering

AA’s

Bases

Bipartite Graph partitioning

slide35

Origin of sequence specific Protein-DNA Recognition II

Given: 331 (and counting) amino-acid, base sequence variants and their relative affinities

Identify the structural basis for sequence specific protein-DNA recognition using a conformational analysis approach, i.e. by searching through protein and base sequence/conformation space to generate Lac-DNA structural models that explain, and ultimately predict, which amino-acid sequences recognize which base sequences.

What structural features determine high affinity, and/or sequence specificity? Can we predict, and so design, repressor sequences that will bind given lac-operator sequences, and more generally, bind any base sequence of the same length?

EVOLVE: Searches in both protein and DNA sequence space, with full amino-acid, base rotamer exploration, torsional minimization.

Simultaneously generations conformers for bound, unbound states, evaluates energy difference.

slide37

Analysis of 75 or 331 amino acid base pair variants so far

EVOLVE energy difference vs. Measured Affinity difference.

Correlation coefficient = 0.66

Not bad: without full rotamer exploration (depth first), no solvent, and no binding entropy yet