Thermodynamical Stability of Biomolecular Systems: Insights from Molecular Dynamics Free Energy Simulations and Continuum Electrostatics Georgios Archontis Department of Physics, University of Cyprus

Overview Relative Binding Strength to Glycogen Phosphorylase of Catalytic-site inhibitors, by MDFE calculations. Dinucleotide inhibitor binding to Ribonuclease A by MD/PB calculations. A continuum electrostatics/linear response method to calculate pKa shifts in proteins.

Relative Strength of Binding of Ligands in the Catalytic Site of Glycogen Phosphorylase, by MDFE calculations

P P Gpa, activeGpb, inactive Gpb, activeGpa, inactive Kinase Phosphatase GlucoseGlucose-6-PAMP Regulation of Glycogen Phosphorylase (simplified)

Interactions of Glucose with Catalytic Site

Interactions of Hydantoin with Catalytic Site

The Simulation System R R = H HYDAN R = CH 3 MHYDAN R = NH 2 NHYDAN Ligand Structure

Technical Details Dual topology. Linear Dependence of Hamiltonian on λ. Fitting of van der Waals Free Energy Derivatives to a power law ~λ -3/4 at end points.

Summary of Free Energy Runs Run # DGvwelec Protein H  M Average8.6 ± 2.0 Solution H  M Average4.85 ± 0.05 ΔΔG3.75Exp: 3.6

Summary of Free Energy Runs Run # DGvwelec Protein H  N H  H’  N Average1.65 ± 0.95 Solution H  N Average0.65 ± 0.15 ΔΔG1.0Exp: 2.3

Left: Interaction of the HYDAN ring with the catalytic site residues, observed in the simulations. D283 N284 E88 G134 W200 W176 N1 H377 Right: Typical MD snapshot of the M-HYDAN: GP complex. W176 is most of the time displaced by ~1 A and interacts with E88. Interactions of GP with HYDAN/MHYDAN H377 G134 E88 W176 W200 D283 N284 N1 M-HYDAN

D283 W176 E88 G134 N284 H377 N-HYDAN N1 Right: Typical MD snapshot of the N-HYDAN:GP complex. As in M-Hydan, W176 is most of the time displaced by ~1 A and interacts with E88. Interactions of GP with N-HYDAN

Van der Waals Free Energy derivatives H  M H M λ=0.06 Log(dF/dλ)

a) H  M b) H  N Components: vw elec vw elec Runs: D W W N G Sum: a) H  M: Residue D283 opposes the creation of the M methyl group, due to steric interference and loss of electrostatic interactions, as shown by the large vw and elec components. Water W176 also opposes the transformation, mainly due to steric repulsion. Other, more distant residues favor the M state mainly due to improved dispersion interactions. b) H  N: Replacement of the HYDAN proton by the NH2 group introduces steric interference mainly with D283 and W176. Electrostatic interactions are improved, but mainly with distant residues. Residue Free Energy Decomposition of  G  ( in protein )

Superposition of MD structures of the various ligands in the GP Catalytic site

Free Energy Profile for W176 (Asp283  Glu88) D283 E88 HYDAN MHYDAN HYDAN MHYDAN

Conclusions The experimental relative binding order of hydantoin inhibitors is reproduced by MDFE calculations. Interactions between HYDAN and GP or water residues in the catalytic site are optimal. Introduction of CH3 or NH2 causes steric interference, that mostly accounts for the reduced binding strength of M- and NHYDAN relative to the best inhibitor (HYDAN).

Free Energies of Binding between Ribonuclease A and dinucleotide inhibitors, evaluated by MD/PB schemes

Recognition Subsites in the RNAse A Active Site

Putative catalysis mechanism by RNAseA Raines & co/rs, Biochem. 40:4949 (2001)

RNAse inhibitors considered in this work dUppA (deoxyuridine-3-pyropho- sphate (P->5) adenosine) pdUppAp (5΄-phospho-3΄- deoxyuridine 3-pyrophosphate (P->5) adenosine 3-phosphate) PD PB PA PG PB PA

Typical interactions between pdUppAp and surrounding protein residues, observed in the MD simulations PD PB PA PG HIS12 HIS119 GLN11 LYS7

Typical interactions between dUppA and surrounding protein residues, observed in the MD simulations PBPA HIS12 HIS119 LYS7 GLN11

RNAse complex with pdUppAp

In a standard PB binding calculation, the protein and ligand are assumed to have the same conformation in the biomolecul- ar complex (left) and in the infinitely separated, solvated states (right). The binding free energy is obtained by  G * bind = G * pl – G * p – G * l + G * p + G * l G * pl Standard scheme to calculate Binding Free Energies by PB P* L* P* L*

Binding Free Energies evaluated by the standard scheme (a, b). L i g a n d ε prot pdUppAp (c) dUppA (c) Diff (d) (a) Experimental K m values are 27 nM (dpUppAp) and 11.3 μM (dUppA), corresponding to a ΔΔG = 3.6 Kcal/mol. (b) All energies in Kcal/mol; (c) Binding energies averaged over 200 structures taken from a 4-ns simulation. (d) Binding free energy relative to the RNAse:pdUppAp complex. At values of ε prot used typically in PB binding calculations ( ), dUppA is predicted to bind more weakly by Kcal/mol.

Expanded scheme to calculate Binding Free Energies by PB Upon dissociation, the system is allowed to relax to equilibrium structures of the separated states. (step 2). + PL  G bind =  G * bind +  G P* L* P* L*  G * bind G2G2

Thermodynamic cycle used to calculate PB binding energies in the expanded scheme Infinite Homogeneous Medium (ε solv =ε prot =ε) ΔG bind = = P*:L1*P* + L1*P + L1 P* + L1*P + L Standard scheme Solution (ε solv =80; ε prot =ε).

Binding Free Energies evaluated by the expanded scheme (a). L i g a n d ε prot pdUppAp (b) dUppA (b) Diff (c) (a) Experimental K m values are 27 nM (pdUppAp) and 11.3 μM (dUppA), corresponding to a ΔΔG = 3.6 Kcal/mol. (b) Binding energies averaged over 200 structures taken from a 4-ns simulation; (c) Binding free energy relative to the RNAse:pdUppAp complex. At values of ε prot used typically in PB binding calculations ( ), dUppA is predicted to bind more weakly by 1.5 – 3.6 Kcal/mol.

Conclusions PB/MD calculations, averaged over multi- ns trajectories can predict correctly the order of binding of dinucleotide inhibitors to RNAse. Accuracy is improved when the relaxation of protein and ligands after dissociation is included.

A method to calculate pKa shifts in proteins. Calculations with Continuum Electrostatics and Linear Response

Thermodynamic Cycle for pKa shift P-RHP-R - + H + R - + H + RH (1) (2) ΔΔG = ΔG 1 – ΔG 2 pK a, prot – pK a, model = 1/(2.303 k B T)*ΔΔG

Calculation of Ionization Free Energies Two-step Procedure to Calculate Charge Insertion Free Energies (Marcus, 1956) I : Insert q with environment fixed: ΔG x, stat = q V x  q II: Allow environment to relax: ΔG x, stat = ½ q V x, q  q q q I II “Reactant” State “Product” State  G static  G relax

Static Free Energy ΔG x, stat = q V x  q (Average Interaction Energy between q and rest of the system, at equilibrium state x) Relaxation Free Energy ΔG x, stat = ½ q V x, q  q (Born self-energy of inserted charge)

q q I II  G reac, static  G reac, relax ΔG = ΔG reac, stat + ΔG reac, relax (1) q II I ΔG’ = -ΔG = ΔG prod, stat + ΔG prod, relax (2)  G prod, relax  G prod, static

2ΔG = (ΔG reac, stat - ΔG prod, stat ) + (ΔG reac, relax - ΔG prod, relax ) = q(V reac, stat - V prod, stat ) ΔG = ΔG reac, stat + ΔG reac, relax (1) -ΔG = ΔG prod, stat + ΔG prod, relax (2) ( Linear Response ) = 0 ΔG = q/2 (V reac, stat - V prod, stat ) =1/2 (ΔG reac, stat - ΔG prod, stat ) Average Electrostatic Energy over reactant and product

Application Thioredoxin Asp26 (pKa = 7.5; ΔΔG exp = 4.8) Thioredoxin Asp20 (pKa = 4.0; ΔΔG exp = 0) RNAse A Asp14 (pKa = 2.0; ΔΔG exp = -2.7)

A. Αsp26 (Thioredoxin) # of waters ΔΔG 0 1 MDFE (CHARMM) ½(ASPH+ASP) ¼ (ASPH+2*Mid+ASP) Exp: 4.8 B. Asp14 (Rnase A) ½(ASPH+ASP) ¼ (ASPH+2*Mid+ASP) -3.8 Exp: -2.7 Averages over structures, spanning ~ 4-6 ns Protein dielectric constant ε = 1

Static Step Free Energies A. Αsp26 (Thioredoxin) # of explicit waters State 0 1 ASPH ASP Midpoint ½(ASPH+ASP) ¼ (ASPH+2*Mid+ASP) B. Model Compound ASPH 6.0 ASP(-) Midpoint ½(ASPH+ASP) ¼ (ASPH+2*Mid+ASP) -66.5

C. Αsp20 (Thioredoxin) ΔΔG MDFE (CHARMM) ½ ( reac + prod ) Midpoint 5.9 ¼ (reac + 2*midpoint + prod) 5.7 Exp: 0.0 Continuum Assumption. Equilibrium structures consistent with MD force-field.

Conclusions PKa shifts can be calculated with a continuum electrostatics/LR method. Averaging over end-states accounts for structural reorganization upon titration. Optimal Protein dielectric constant for static calculation ε ~1. Relaxation Free Energies require a different dielectric constant (optimal values, ε ~2-6).

Acknowledgements Glycogen Phosphorylase –Dr. Qian Xie (MDFE, University of Cyprus). –Dr. Nikos Oikonomakos (x-ray, NHRF, Greece). Ribonuclease A –Dr. Demetres Leonidas (x-ray, NHRF, Greece). pKa work –Thomas Simonson (MDFE/CHARMM, Ecole Polytechnique). University of Cyprus ($).