Conformational Free-Energy Differences by Confinement Simulations

Transcription

1 Conformational Free-Energy Differences by Confinement Simulations Marco Cecchini Laboratoire d Ingeniérie des Fonctions Moléculaires (ISIS) UMR 76 - Université de Strasbourg mcecchini@unistra.fr HPC days - Strasbourg, Jan 214

2 Outline Conformational Free Energy Confinement approach: theory and methodology Test-case application: the β-hairpin of protein G Numerical validation of the predictions Free-energy components analysis Perspective: Energy storage in myosin Cecchini et al., J Phys Chem B (29)

3 Free-Energy Landscape Conformational Free Energy HH TR!G [kcal/mol] FS [FS] 2 [HH] [FS] 3 [TR] Rao Caflisch, J Mol Biol (24) Free-energy basins correspond to unique molecular states Conformational free energy (G) is a measure of structural stability Conformational free-energy differences (ΔG) determine the relative populations of microstates

4 the Confinement Approach A AA A * G AB G NMA A B B BB B * G AB = AA BB + G NMA A B

5 Confinement: Theory Thermodynamic Integration 1 G = U(X, λ)/ λ Energy Function U(X, λ) = U ff (X) λ k f λ dλ kf has to be large X X 2 A B AA BB A * B * G NMA A B Confinement Free-Energy = 1 kf X X 2 2 k dk = 1 2 kf X k dk Atomic Fluctuations X k = 2 U cons k k or better X k = N RMSD 2 k Tyka et al., J Phys Chem B (26)

6 Confinement: the idea 1 A1 B2 1 k 1 k 2 k 3 k f χ k 1 1 X k = N RMSD 2 k kf.1 1e-5 1e G A =G A AA Confinement G [kcal/mol] B A = 1 2 kf kf k [kcal/mol A 2 ] X k dk

7 Confinement: Normal Mode Analysis A B AA BB A * B * G NMA A B Classical Partition Function Z = exp ( E /k B T ) i Absolute Free Energy k B T hν i harmonic oscillator G A = k B T log Z A confined = k B T log Z B states G B Free-Energy Difference (ΔG NMA ) G NMA A B = E B E A k B T i ln ( ωi A ω i B ) NMA leg enthalpic contribution entropic contribution G NM = H NM T S NM E from energy minimization ωi from Hessian diagonalization

8 Test case: the β-hairpin of protein Krivov Karplus, PNAS (24) 2 3

9 Confinement Simulation Setup free-energy basins 1 and 2 of the β-hairpin of protein G 23 MD simulations per confinement with harmonic restraints ranging from to 82. kcal/mol/a 2 1 ns sampling per run (2.3 μs per confinement) the reference was a deeply minimized conformation MD Setup: Langevin dynamics (γ=1. ps K, best-fit harmonic restraint, EEF1implicit solvation model, time step of 2 fs with SHAKE a Cα-RMSD cutoff of 2. A from the reference was used to define the boundaries of the free-energy basins

10 1 Confinement Simulations A1 B2 Results: Confinement Legs 1 A B χ k 1 Confinement G [kcal/mol] 1 kf.1 1e-5 1e X k = N RMSD 2 k A1 B2 = 1 2 kf kf X k dk Max strength of 82 kcal/mol/a 2 A B AA BB A * G NMA A B B * k [kcal/mol A 2 ]

11 A B Results: NMA Leg Energy [kcal/mol] Normal Mode Analysis H T S G Max strength of 82 kcal/mol/a 2 A AA A * 2.16 G NMA A B -1 kf k [kcal/mol A 2 ] B BB B * ΔGAB = = 1.88 kcal/mol

12 A B Results: Conformational ΔG!G AB [kcal/mol] !G [kcal/mol] Confinement Result A B 1.88 ±.13 ΔGAB = 1.88 ±.13 kcal/mol 1e k f [kcal/mol/a 2 ]

13 Numerical validation by equilibrium MD 5 independent MD 36 K (each 4 μs) total sampling of 2 μs a Cα-RMSD cutoff of 2. A from the reference to define the boundaries of the free-energy basins round-trip decomposition of the individual MD runs (184 roundtrips sampled in total) boot-strapping analysis of the roundtrips to estimate the free-energy difference along with its statistical error forward 1 2 backward G 12 = k B T log(# 2 /# 1 ) σ N = 1 M M i=1 ( ) 2 G i G

14 confinement approach is ~5 times more efficient than CTMD Results: Numerical Validation.12 N=184.6 y = 1.73 # x -.2 number of roundtrips.1.5 Probability !!G [Kcal/mol] !G /"N ΔG12 = 1.86 ±.12 kcal/mol ΔG12 = 1.88 ±.13 kcal/mol from 2 µs CTMD from 4 µs confinement MD

15 Take Home Messages the confinement approach is a useful method to compute the free-energy difference between conformers of a biomolecule it allows for predictions of mutational effects through free-energy components analyses it may ultimately open up to a microscopic interpretation of the free energy

16 Transformation of chemical energy into mechanical work Molecular Motors: Myosin Muscle Contraction (MyoII) Vale & Milligan, Science (2)

17 Energy Storage in Myosin Málnási-Csimadia et al., Biochemistry (21)

18 Acknowledgments Prof. Martin Karplus Dr. Sergei Krivov Dr. Martin Spichty ISIS (Strasbourg) Laboratoire d Ingeniérie des Fonctions Moléculaires