1. Free energy with controlled uncertainty 2. The modes of ligand binding to DNA

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1 1. Free energy with controlled uncertainty 2. The modes of ligand binding to DNA Tomáš Kubař Institute of Organic Chemistry and Biochemistry Praha, Czech Republic

2 Thermodynamic Integration Alchemical change of an atom/group Force-field parameters for both initial and final state Coupling parameter λ introduced mixing of the initial (λ=0) and final (λ=1) states: H λ = 1 λ H λ=0 λ H λ=1 Simulation for a number of λ values from 0 to 1; then, for every λ: dg de dv λ = λ dλ dλ dλ λ Finally, numerical integration gives the free-energy difference (delta G) of the initial and final state

3 Usual simulation protocol In every lambda point a simulation with separated equilibration period and production phase, both of fixed length Only the production phase used to calculate dg/dλ The uncertainty of dg/dλ may be evaluated but not controlled for every lambda value dv/dλ values discarded calculated mean value of dv/dλ dg dλ = dv dλ

4 Reverse cumulative averaging No preset length of equilibration nor data collection phase The simulation proceeds in blocks of fixed length (2000 steps) When a block finishes, the longest equilibrium region is identified starting from the end of simulation the region where the dv/dλ values come from a normal distribution (on a preset confidence level) Shapiro Wilk normality test adopted from the R project (GPL) Standard error of the mean <dv/dλ> is calculated in the equilibrium region IF error > threshold THEN continue with current λ ELSE record dg/dλ = <dv/dλ> and proceed to the next λ dv/dλ values discarded JCP 2004, 120, 2618 calculated mean value of dv/dλ and its error

5 Fragment of the.mdp file... free-energy-method = ti_rca init_lambda = 0.0 delta_lambda = 0.05 lambda_points = 21 target_error = Number of windows The threshold to be fulfilled in every window (kj/mol) Also, the upper bound of uncertainty of total G.

6

7 Application I DNA intercalation Ethidium DNA binding drug, a strong carcinogen Binding free energy difference of ethidium and its derivatives CEJ 2006, 12, 280

8 Application I DNA intercalation Thermodynamic cycle DNA ETD A DNA EPP 1 2 Free ETD B Free EPP G = G(2) G(1) = G(B) G(A) Results: kcal/mol value error G(A) G(B) G sampling (ns) exptl: +1.6 kcal/mol

9 Application II Thermostable protein and its mutants Rubredoxine a globular protein, which survives temperatures over 100 C containts a distinct hydrophobic core mutation of a bulky amino acid in the core makes melting temperature drop Folding free energy difference of RB and the mutants Results may be compared with a calorimetric experiment CEJ 2007, submitted

10 Application II Thermostable protein and its mutants Thermodynamic cycle Denat-PHE A Denat-ALA Folded-PHE Folded-ALA G = G(2) G(1) = G(B) G(A) Studied mutations: Protein T m ( C) F48A F48G WT (F29A) F29G F29I 1 2 B WT > 100 F48A 63.0 F48G 62.5 F29I 55.5 F29G 47.5 G (kcal/mol) ± ± ± ± 1.1

11 Application II Thermostable protein and its mutants Differential scanning calorimetry experiment

12 Modes of ligand binding to DNA The most important non-covalent binding modes: intercalation minor-groove binding What do they have in common? What are the points they differ in? (apart from the obvious the structure and deformation of DNA)

13 The molecular systems and force field DNA two decanucleotides (CGTATATACG) 2 AT rich (CGCGCGCGCG) 2 CG rich The ligand ellipticin and its derivatives (9-hydroxy polar, both forms protonated on N2) Force field AMBER parm99 + parmbsc0 For every complex a 50ns simulation at 300 K, 1 atm

14 Look at the trajectory Intercalative complexes all stable, the ligand remains in the binding site Minor-groove complexes any molecule with AT-rich stable all molecules with GC-rich - unstable the ligand leaves the minor groove; either flows away from the DNA or gets stacked at the end of the double helix First conclusions sequence preference intercalative mode none or weak minor-groove binding strong preference for AT-rich We should look for an explanation later on

15 The interaction energy The measure of inherent attraction between molecules, without any external influence (environment) energygrps in.mdp Eint Intercalation Minor groove kcal/mol elli 9oh elli 9oh AT neutral rich proton GC neutral rich proton No significant difference found except between neutral and protonated (charged)

16 Dynamics of the complex The desired quantity is entropy (as component of free energy) How: trajectory > covariance matrix of atomic fluctuations > eigenvalues > normal-mode vibration frequency > entropy (following Schlitter or Karplus) Using g_covar Entropy depends on the length of simulation upon which the covariance matrix was constructed We involve the smallest possible number of atoms in the calculation only the heavy atoms of DNA bases and ligand

17 Conformational entropy intercalative complexes favored by T S 30 kcal/mol where is the difference in flexibility localized?

18 Dynamics of the complex A look at the dynamic behavior of individual nucleotides: C G T A T A T A C G G C A T A T A T G C The change in flexibility of DNA is localized in a few nucleotide residues

19 Why no MiG binding to GC-rich? The reason must be sought in the DNA itself, not the ligand MiG width is the same in AT-rich and GC-rich (not shown) Interaction energy of bases with water in bare DNA? kcal/mol AT-rich 44 GC-rich 63 This may be the explanation. The (any) ligand cannot probably compete with water in the binding to DNA bases. (Happy) End

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