Interaction Between Positively Charged Amino Acids and Halide Anions

Introduction Interaction of halides with amino acids Conclusion

Interaction between positively charged amino acids and halide anions

Mgr. Jan Heyda1,2 Doc. Mgr. Pavel Jungwirth, CSc.1

1Institute of Organic Chemistry and Biochemistry, Academy of Science v.v.i., CR 2Section of Mathematical Modeling, MFF, Charles University in Prague

Young investigator forum 07.04.2008

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Hofmeister series

In 1888, Franz Hofmeister ordered ions according to their ability to salt proteins in/out

↑ Surface tension ↓ Surface tension ↑ Protein stability ↓ Protein stability Harder to make cavity Easier to make cavity Salting out (aggregate) Salting in (solubilize) ↓ Solubility of proteins ↑ Solubility of proteins ↓ Protein denaturation ↑ Protein denaturation

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Hofmeister series

In 1888, Franz Hofmeister ordered ions according to their ability to salt proteins in/out

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Hofmeister series

In 1888, Franz Hofmeister ordered ions according to their ability to salt proteins in/out

these series are widely used, but ...... understanding at the atomic level is still missing

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Hofmeister series

In 1888, Franz Hofmeister ordered ions according to their ability to salt proteins in/out

these series are widely used, but ...... understanding at the atomic level is still missing

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Main Goals

To understand the order of halide anions in the Hofmeister series Ordering of halide anions’ (F−, Cl−, Br−, I−) attraction to basic amino acids – Lysine, Arginine, Histidine Qualitative and quantitative analysis of the trajectories Reliability of used interaction potential for more general projects (proteins) Anionic speciﬁcity ⇒ speciﬁc interaction sites

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Classical MD in canonical ensemble [N,p,T]

Molecular dynamics gives us a description on the atomic level We study the system in thermodynamic equilibrium to obtain statistically averaged data Verlet algorithm is used for propagating Newton’s equations of motion Used interaction potential plays a key role in our simulations

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Governing equations and deﬁnition of interaction potential

pi r˙i = mi ˙ pi = Fi = −∇ri V (ri ) intra inter V (ri ) = V (ri ) + V (ri )

stretch ki 0 2 bend li 0 2 Vi = 2 (bi − bi ) Vi = 2 (θi − θi )

2 dihe vi 0 coulomb e zi zj V = 1 + cos(ni ωi − ω ) V = i 2 i ij 4π0 rij 12 6 LJ σij σij polar V = 4ij − V = µ · E = αi E · E ij rij rij i i

pi r˙i = mi ˙ pi = Fi = −∇ri V (ri ) intra inter V (ri ) = V (ri ) + V (ri )

stretch ki 0 2 bend li 0 2 Vi = 2 (bi − bi ) Vi = 2 (θi − θi )

2 dihe vi 0 coulomb e zi zj V = 1 + cos(ni ωi − ω ) V = i 2 i ij 4π0 rij 12 6 LJ σij σij polar V = 4ij − V = µ · E = αi E · E ij rij rij i i

pi r˙i = mi ˙ pi = Fi = −∇ri V (ri ) intra inter V (ri ) = V (ri ) + V (ri )

stretch ki 0 2 bend li 0 2 Vi = 2 (bi − bi ) Vi = 2 (θi − θi )

2 dihe vi 0 coulomb e zi zj V = 1 + cos(ni ωi − ω ) V = i 2 i ij 4π0 rij 12 6 LJ σij σij polar V = 4ij − V = µ · E = αi E · E ij rij rij i i

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Outline

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Jan Heyda Halides and amino acids interaction Introduction Motivation Interaction of halides with amino acids Methodology Conclusion Analysis Thermodynamic analysis

Ergodic theorem The average of a quantity (i.e. X) over time is equal to its average over an ensemble.

A trajectory is used to sample the phase space Results of our analysis are: Density maps ρ(x, y, z) Radial distribution function g(r) Z Z 1 2π π ρ(r) g(r) = 2 ρ(r, ϕ, θ)sin(θ)dϕ dθ = 4πr 2 0 − π ρ0 2 Contacts are given by the cumulative sums N(R) Z R N(R) = 4πr 2 g(r) dr 0

Jan Heyda Halides and amino acids interaction Arginine Introduction Lysine Interaction of halides with amino acids Protonated histidine (charged form) Conclusion Deprotonated histidine (neutral form) Amino acids and halides

arginine; guanidinium+

lysine; amonium+

histidine; imidazolium+

arginine; guanidinium+

lysine; amonium+

histidine; imidazolium

All simulations were run with AMBER8 package Simulation box of approximate dimensions 31.7 A˚ x 31.7 A˚ x 31.7 A˚ with periodic boundary conditions was introduced Each box has ≈ 600 (SPCE or POL3) water molecules, 1 amino acid − + molecule, 4 anions X (equal to ≈ 0.5 M). Three potassium cations K are added to obtain electroneutrality In cases of anionic mixtures, 4 atoms of each anion were included and 7 potassium cations K+ were added to obtain electroneutrality Cutoff for long range electrostatic interaction – 7.5 A˚ Minimalization of potential energy (to prevent overlaps) Heating procedure (T=0 K −→ 300 K, isochoric) Pressure procedure (isothermal) Equilibration time of 500 ps, [N,p,T] ensemble Production run: ≈ 50 ns in nonpolarizable, ≈ 20 ns in polarizable simulations, [N,p,T] ensemble

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

− − + F , I , K , H2O

vizualization of nearest periodic images

Arginine without polarizability (% of simulation time) Anion Arginine Guanidinium F− 34 34 Cl− 10 9 Br− 7 6 I− 10 6

Arginine with polarizability (% of simulation time) Anion Arginine Guanidinium F− 17 16 Cl− 8 6 Br− 8 7 I− 8 5

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Lysin without polarizability (% of simulation time) Anion Lysin Amonium F− 17 17 Cl− 10 8 Br− 8 6 I− 13 7

Lysin with polarizability (% of simulation time) Anion Lysin Amonium F− 8 6 Cl− 7 5 Br− 8 5 I− 11 5

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Protonated histidine (not pol.) (% of simulation time) Anion Histidine Imidazolium F− 24 23 Cl− 7 5 Br− 6 3 I− 11 4‘

Protonated histidine (with pol.) (% of simulation time) Anion Histidine Imidazolium F− 11 8 Cl− 8 6 Br− 6 4 I− 10 3

1 Introduction Motivation Methodology Analysis

2 Interaction of halides with amino acids Arginine Lysine Protonated histidine (charged form) Deprotonated histidine (neutral form)

3 Conclusion

Deprotonated histidine (not pol.) (% of simulation time) Anion Histidine Imidazole F− 2 2 Cl− 3 1 Br− 5 2 I− 8 3

Deprotonated histidine (with pol.) (% of simulation time) Anion Histidine Imidazole F− 5 2 Cl− 3 2 Br− 5 2 I− 7 2

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Conclusion

Statistically converged results for interaction between halide anions and positively charged amino acids were obtained Small (harder) anions bind strongly to positively charged parts of amino acids – ion pairing behavior Bigger (softer) anions also interact with the hydrophobic parts of amino acids There is qualitatively the same effect in both polarizable and nonpolarizable cases, quantitatively weaker for the polarizable case The effects follow Hofmeister ordering

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Future outlook

Amino acids are the basic building blocks of proteins Ions mediate protein-protein interactions, but it’s unclear how To interpret behavior of proteins in salt solutions, understanding of ion-protein interactions is necessary

Jan Heyda Halides and amino acids interaction Thank You!

Introduction Interaction of halides with amino acids Conclusion

Thanks to my colleagues doc. Mgr. Pavel Jungwirth, CSc. RNDr. Lubosˇ Vrbka, PhD. RNDr. Robert Vacha´ Mikael Lund, PhD.

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion

Thanks to my colleagues doc. Mgr. Pavel Jungwirth, CSc. RNDr. Lubosˇ Vrbka, PhD. RNDr. Robert Vacha´ Mikael Lund, PhD.

Thank You!

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion

F. Hofmeister, Naunym-Schmiedebergs Archiv Exp. Pathol. Pharmakol., 23 (1888) 247; English translation: W. Kunz, J. Henle, B. W. Ninham Curr. Opin. Colloid Interface Sci. 9 (2004) 19 http://www.lsbu.ac.uk/water/hofmeist.html

P. Jungwirth, D. J. Tobias, J. Phys. Chem. B 105 (2001) 10468

P. G. Kusalik and I. M. Svishchev, Science 265 (1994) 1219

J. W. Caldwell and P. A. Kollman, J. Phys. Chem. 99 (1995) 6208

M. Lund, P. Jungwirth, C. E. Woodward, Phys. Rev. Lett. submitted J. Heyda, T. Hrobarik,´ P. Jungwirth, J. Am. Chem. Soc. submitted

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Verlet algorithm

derived from forward and backward step in Newton’s equation

r(t + δt) = 2r(t) − r(t − δt) + δt2a(t) r(t + δt) − r(t − δt) v(t) = 2δt equivalent alternative is Leap-Frog algorithm time reversible, symplectic computationaly cheap – gradients (95% of computional time) are calculated only once in every time-step robust (time step, stability)

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Gear’s algorithm

predictor-corrector method of 4th order 1 1 r p(t + δt) = r(t) + δtv(t) + δt2a(t) + δt3b(t) 2 6 1 v p(t + δt) = v(t) + δta(t) + δt2b(t) 2 ap(t + δt) = a(t) + δtb(t) bp(t + δt) = b(t) finally ∆a(t + δt) = ac(t + δt) − ap(t + δt) is defined and all r c, v c, ac, and bc are calculated not time reversible, not symplectic more precise then Verlet, but only for sufficiently short time step

More precise algorithms (i.e. Runge-Kutta) are not usually used because of multiple calculation of forces in every step.

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Theoretical background of thermostats Berendsen thermostat

by the use of equipartition theorem scales the velocities 3 1 X N k T = m v 2 2 B 2 i i i 1 ∆t T 2 λ = 1 + − 1 τT T0

v new = λ v old

λ is velocity scaling parameter, τT is the ”rise time” of the thermostat, T0 targeted temperature

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Theoretical background of thermostats Stochastic NVT thermostats

Andersen thermostat each step, prescribed number of particles is randomly selected, and their velocities are drawn from a Gaussian distribution at the prescribed temperature:

3/2 2 β − βp P(p) = exp 2m 2πm 1 where β = kT Langevin thermostat – new degree of freedom (friction)

m ¨r i = −∇i V − m Γ r˙i + W i (t) 0 0 hW i (t), W j (t )i = δi,j δ(t − t ) 6 kB m T Γ −1 Γ is a friction coefﬁcient (τ ) and W i (t) is stochastic random force, uncorrelated in time and across particles

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Conﬁguration space exploration by anions

Averaged length of contact (100ns trajectories for ARG) av. length [ps] number F− 210 162 Cl− 28 325 Br− 18 310 I− 17 317

interruption time for contact with guanidinium was 100ps

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Spacetime information – trajectory

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Basic MD parameters – ions

Table: MD parameters for halide anions and potassium cation are adopted from the publication [3].

−1 3 Name Atomic weight rm [A]˚ [kcal·mol ] α [A˚ ] Fluoride 19 1.758 0.20 0.974 Chloride 35.45 2.435 0.10 3.690 Bromide 79.90 2.638 0.10 4.530 Iodide 127.45 2.89 0.10 6.90 Potassium 39.10 1.771 0.10 0.83

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Basic MD parameters – solvent

Table: MD parameters for water models – SPCE1 and POL32.

−1 3 Name Weight Charge [e] rm [A]˚ [kcal·mol ] α [A˚ ] SPCE1model Oxygen 16 -0.8476 1.7766 0.1554 0 Hydrogen 1 0.4238 0 0 0 POL32model Oxygen 16 -0.73 1.798 0.156 0.528 Hydrogen 1 0.365 0 0 0.170

1 from publication [4] 2 from publication [5]

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Results for arginine in binary mixture

Strength of ﬂuoride attraction is independent on presence of other ions. The effect of different salts is roughly additive at present concentration.

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Density proﬁles for water oxygens

Jan Heyda Halides and amino acids interaction Introduction Interaction of halides with amino acids Conclusion Interaction sites – charge distribution

Atom Charge [e] HE 0.3456 HH11 0.4478 HH12 0.4478 HH21 0.4478 HH22 0.4478 HZ1 0.3400 HZ2 0.3400 HZ3 0.3400 HD1 0.3866 HE2 0.3911 HD1 0.3649 H 0.2747

Jan Heyda Halides and amino acids interaction