A rigid-base model for DNA structure prediction. O. Gonzalez

Transcription

1 A rigid-base model for DNA structure prediction O. Gonzalez

2 Introduction Objective. To develop a model to predict the structure and flexibility of standard, B-form DNA from its sequence.

3 Introduction Objective. To develop a model to predict the structure and flexibility of standard, B-form DNA from its sequence. Idealized structure proposed by Watson and Crick, 953. AT GC CG CG T A

4 Introduction Objective. To develop a model to predict the structure and flexibility of standard, B-form DNA from its sequence. Idealized structure proposed by Watson and Crick, 953. AT GC CG CG T A Actual structure depends strongly on sequence, circa 98.

5 Introduction Objective. To develop a model to predict the structure and flexibility of standard, B-form DNA from its sequence. Idealized structure proposed by Watson and Crick, 953. AT GC CG CG T A Actual structure depends strongly on sequence, circa 98. Background. 3 years of history; lack of data hindered progress; recent construction of large MD dataset is making it accessible.

6 Ascona B-DNA Consortium Contributing labs. D. Beveridge (Wesleyan) T. Bishop (Tulane) D. Case (Rutgers) T. Cheatham (Utah) B. Jayaram (Delhi) F. Lankas (Prague) C. Laughton (Nottingham) R. Lavery (Lyon) J. Maddocks (Lausanne) M. Orozco (Barcelona) R. Osman (Mt. Sinai) A. Perez (Barcelona) H. Sklenar (Berlin) J. Sponer (Brno) M. Young (Berkeley) MD dataset. (consortiumlocal) over 5 different DNA oligomers (-8 bp each) all 36 unique tetramer sub-sequences represented all unique dimer end-sequences represented standard simulation protocol w/amber program all simulations w/explicit water and counterions 5- ns simulation time for each oligomer

7 Basic problem Under fixed solvent conditions, we seek a model to predict the ground-state structure and flexibility of any given DNA oligomer. ground state fluctuations (measure of flexibility) ρ DNA config space w R N ρ(w) = Z e βu(w) w configuration coordinates ρ(w) probability density function U(w) free energy Z, β constants

8 Rigid-base representation We consider a model in which each base is modeled as a separate rigid body; side-chains are not considered explicitly. X X X X X X X X 3 n 3 n X { T, A, C, G }, a =... n a A = T, T = A, C = G, G = C G C G C A T A T

9 Configuration coordinates An oligomer with n basepairs has 6n intra-basepair and 6(n ) inter-basepair degrees of freedom; a total of N = n 6. X X X3 Xn y z y z y3 z3 X shear buckle X X3 stretch propeller stagger opening zn y Xn n ya R6 intra The oligomer coord vector is shift tilt slide roll rise twist za R6 inter w = (y, z,..., zn, yn ) RN.

10 Free energy Motivated by observed data, we consider a model in which the free energy is quadratic. X X X X X X X S = X X 3 n 3 n 3 n X X X ρ µ K w R N ρ(w) = Z e βu(w), U(w) = (w µ) K(w µ) µ = µ(s) R N ground-state configuration K = K(S) R N N ground-state stiffness We seek explicit approximations to the functions µ(s) and K(S).

11 Sample data: coordinate marginals S=GCTATATATATATATAGC GC CT TA AT TA AT TA AT TA AT TA AT TA AT TA AG GC Tilt.8.6 Roll Twist.4. 4

12 Sample data: ground-state configuration S=GCTATATATATATATAGC shear stretch stagger 3 shift slide rise.. G C T A T A T A T A T A T A T A G C G C T A T A T A T A T A T A T A G C buckle propeller opening.5.5 tilt roll twist.5 G C T A T A T A T A T A T A T A G C.5 G C T A T A T A T A T A T A T A G C

13 Sample data: ground-state configuration S=GCTATTTATATATATAGC.3.. shear stretch stagger 4 3 shift slide rise.. G C T A T T T A T A T A T A T A G C G C T A T T T A T A T A T A T A G C tilt roll twist.5 buckle propeller opening G C T A T T T A T A T A T A T A G C.5.5 G C T A T T T A T A T A T A T A G C

14 Sample data: ground-state stiffness S=GCGATCGATCGATCGAGC 5 4 tilt roll twist 3 G C G A T C G A T C G A T C G A G C

15 A monomer/dimer based model We consider a model based on two types of interaction energies. monomer interaction energy X y X w m = y R 6 U m = (w m µ X m) K X m (w m µ X m) µ X m R 6, K X m R 6 6 X {T, A, C, G} dimer interaction energy X Y y z y X Y w d = (y, z, y ) R 8 U d = (w d µ XY d ) Kd XY (w d µ XY d ) µ XY d R 8, K XY d R 8 8 X, Y {T, A, C, G}

16 A monomer/dimer based model By summing the monomer/dimer contributions along an oligomer, we obtain the energy U(w) = (w µ) K(w µ) C µ = µ(s, P), K = K(S, P), C = C(S, P), where S is the oligomer sequence and P is the model parameter set Km X, σm X := Km X µ X m, X {T, A, C, G} P = Kd XY, σd XY := Kd XY µ XY d, X, Y {T, A, C, G}.

17 A monomer/dimer based model The ground-state configuration µ(s, P) and stiffness K(S, P) are determined by S = X X X n and P = {Km X, σm, X Kd XY, σd XY }. K: = n n n n n n n 6x6 monomers 8x8 dimers NxN oligomer σ: = 3 4 n n n n 4 4 n n n 6x monomers 8x dimers Nx oligomer µ: µ(s, P) = K(S, P) σ(s, P)

18 Data for parameter estimation To estimate the parameter set P, we used a database of MD-observed probability densities ρ (j) o (w) for sequences S (j), j =,..., J. ρ (j) o (j) o µ K (j) o w R N (j) ρ (j) o (w) = Z (j) e βuo (w) (j) U o (j) (w) = (w µ(j) o ) K o (j) (w µ (j) o )

19 Functional for parameter estimation A best-fit parameter set P can be obtained by minimizing the objective functional F(P) = J j= D(ρ(S (j), P), ρ (j) o ), where D is the Kullback-Leibler divergence (pre-distance) [ ] ρ (w) D(ρ, ρ o ) = ρ (w) ln dw. ρ o (w) For Gaussians, D(ρ, ρ o ) = [ ( ) ] det K Ko : K o (µ µ o ) K o (µ µ o ) ln I : I. det K

20 Results A best-fit parameter set P was obtained from the MD dataset via numerical minimization of the Kullback-Leibler functional. The parameter set P allows us to predict the ground-state configuration µ(s, P) and stiffness K(S, P) for any sequence S.

21 MD vs Model: ground-state configuration S=GCTATATATATATATAGC shear stretch stagger 3 shift slide rise.. G C T A T A T A T A T A T A T A G C G C T A T A T A T A T A T A T A G C buckle propeller opening.5.5 tilt roll twist.5 G C T A T A T A T A T A T A T A G C.5 G C T A T A T A T A T A T A T A G C

22 MD vs Model: ground-state configuration S=GCTATTTATATATATAGC.3.. shear stretch stagger 4 3 shift slide rise.. G C T A T T T A T A T A T A T A G C G C T A T T T A T A T A T A T A G C tilt roll twist.5 buckle propeller opening G C T A T T T A T A T A T A T A G C.5.5 G C T A T T T A T A T A T A T A G C

23 MD vs Model: ground-state stiffness S=GCGATCGATCGATCGAGC G 8 G A A 4 4 MD G 5 4 A 6 G tilt roll twist A Model 6 3 G C G A T C G A T C G A T C G A G C

24 Summary A model to predict the ground-state configuration and flexibility of B-form DNA from its sequence has been developed. The model can resolve sequence-effects both within and between oligomers. The model was parametrized using MD and its predictive capabilities have been tested against MD. The model provides a way to quantify the intrinsic pre-stress or frustration in DNA. The model suggests non-local dependence of ground-state on sequence is due to pre-stress.

25 Thank You