Determination of protein reduced electrostatic models from smoothed molecular electrostatic potentials

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Determination of protein reduced electrostatic models from smoothed molecular

electrostatic potentials

Leherte, Laurence; Vercauteren, Daniel

Publication date:

2009

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Peer reviewed version

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Leherte, L & Vercauteren, D 2009, 'Determination of protein reduced electrostatic models from smoothed

molecular electrostatic potentials', Faraday Discussion 144: Multiscale Modelling of Soft Matter, Universite de

Groningen, Pays-Bas, 20/07/09.

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Determination of protein reduced electrostatic models from smoothed molecular

electrostatic potentials

Laurence Leherte, Daniel P. Vercauteren

Laboratoire de Physico-Chimie Informatique, Groupe de Chimie Physique Théorique et Structurale,

University of Namur - Belgium (FUNDP)

1. Location of “CG” points

A hierarchical merging algorithm, based on the idea of Leung et al. [10], is used to locate local maxima and minima in a MEP function V, as a function of the degree of smoothing t:

1. At scale t= 0, each atom of a molecular structure is considered as a local maximum or minimum of V. All atoms are thus considered as the starting points of the merging procedure.

2. As t increases from 0.0 to a given maximal value, each point moves continuously along a gradient path to reach a location in the 3D space where:

On a practical point of view, this consists in following the trajectory of the points within the MEP function calculated at taccording to Equation:

2. Molecular electrostatic potential

3. Determination of CG charges

This is achieved through the program QFIT [12] to get “CG” point charges fitted from an unsmoothed MEP grid, considering the following constraints: the total molecular charge and dipole.

)

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V

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V

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R

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,

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Unsmoothed Smoothed[11]

4. Determination of backbone “CG” charges

a) Construction of Gly15in an extended conformation (Ω = 180°, Φ = -139°, Ψ

= 135°) using SMMP05 [13], a Monte Carlo/Simulated Annealing program. b) Application of the hierarchical merging/clustering algorithm

t= 0.0 bohr2_{, isoMEP:}_-0.1_,_0.1_e-_/bohr

q

+

MEP extrema = “CG” point

q

-6. Application to potassium ion channel KcsA (1bl8.pdb)

• Positioning of “CG” points through QUATFIT, a superposition algorithm [16], using the above templates and the PDB structure of KcsA

• Extra (+) and (–) charges on terminal N and O 1492-point model (total charge = +4 e-₎

• reduced model 1492 point charges µX= 1255.2 µy= 496.1 µz= 183.6 D rmsdV= 7.6 kcal/mol rmsdµ= 45.5 D

• When the model is based on only one “CG” for each AA backbone, the two-minima region does not show up, and the zero-potential is displaced (blue curve). • Reduced point charge-based profile looks similar to the all-atom one, except for a « damping » effect (redvs. black curve).

• all-atom model 5888 atoms µ_X= 1237.7 µ_y= 496.1 µ_z= 141.5 D IsoMEP: -0.1, 0.1e-_/bohr -350 -300 -250 -200 -150 -100 -50 0 50 -15 -10 -5 0 5 10 15 20 25 30 Distance vs . K403 (A) P E M ( k c a l/ m o l) MEP profile along channel axis ED maxima (t = 1.40 bohr2) MEP extrema (t = 1.35 bohr2)

All-atom Amber [9]

Introduction

The design of coarse grain (CG) models [1] and their corresponding potential functions [2] for protein computational studies is currently an active field of research, especially in solving long-scale dynamics problems such as protein folding, protein-protein docking, … For example, to eliminate fast degrees of freedom, it has been shown that one can rely on CG representations only, or on mixtures of CG and more detailed descriptions [3,4] in order to significantly increase the time step in molecular dynamics (MD) simulations. Among the parameters involved in CG potentials, the electrostatic interactions are of major importance [5] since they govern local and global properties such as their stability [6], their flexibility [7], …

In this poster, we present an approach to design and evaluate reduced point charge models obtained from smoothed molecular electrostatic potentials (MEP). In a previous approach [8], electron density (ED)-based “CG” were determined through a merging/clustering procedure of atom trajectories generated in progressively smoothed ED distribution functions. In the present work, atoms are clustered according to their trajectories defined in a smoothed MEP function, more particularly the Amber potential reported in [9]. A fitting algorithm is applied to evaluate “CG”

charges.

5. Determination of “CG” charges of amino acid side chains

c) Charge fittingvs.unsmoothed MEP as a function oft:

a) Construction of Gly7-AA-Gly7 in an extended conformation (Ω = 180°, Φ = -139°, Ψ = 135°) with various AA rotamers [14] using SMMP05 [13]. Examples:

Conformation χ1 (°) χ2 (°) χ3 (°) χ4 (°) Occurrence (%) Arg g-, t, g-, g- 300 180 300 300 9.5 g-, t, g-, t 300 180 300 180 11.9 g-, t, g+, t 300 180 60 180 12.2 g-, t, t, t 300 180 180 180 12.2 Asn t, Nt 180 0 11.1 t, Og- 180 300 21.3 t, Og+ 180 60 23.6

b) Use of “CG” points obtained att= 1.35 bohr2 _{(see sections 1 and 2)}

c) “CG” charge fitting with additional constraints: Gly15charges (see section 3) except

for the points located on the central AA. Examples:

Arg -.202 .314 .280 .316 .281 Arg -.202 .314 .280 .316 .281 Glu -.273 .192 -.458 -.458 _Glu -.273 .192 -.458 -.458 Asn -.220 .261 .103 .069 -.232 Asn -.220 .261 .103 .069 -.232 Thr -.251 .283 -.157 .123 Thr -.251 .283 -.157 .123 Charge separation

polar spheres in MARTINI [15]:

Charges not located on atoms

1.4 1.5 1.6 1.7 1.8 1.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 t (bohr2₎ M in . O b je c ti v e F u n c ti o n

Best fit achieved att= 1.35 bohr2_,_q₊_{= 0.208,}_q_-_{= -0.208 e}

-Phe -.237 .266 -.166 .033 .048 .032 .027 Phe -.237 .266 -.166 .033 .048 .032 .027 Ile -.284 .229 .068 -.012 _Ile -.284 .229 .068 -.012 References

[1]Tozzini, Curr. Opin. Struct. Biol. 2005, 15, 144 [2]Nielsen et al. J. Phys.: Condens. Matter 2004, 16, R481 [3]

Neriet al. Phys. Rev. Lett. 2005, 95, 218102/1 [4]Colombo et al. Theor. Chem. Acc. 2006, 116, 75 [5]Vizcarraet al. Curr. Opin. Chem. Biol. 2005, 9, 622 [6]Stigteret al. Proc. Natl. Acad. Sci. USA 1991, 88, 4176 [7]Kumaret al. IBM. J. Res. & Dev. 2001, 45, 499 [8]Leherteet al. in The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Matta & Boyd, Eds.; Wiley-VCH, 2007, 285 [9]Duanet al. Comput. Chem. 2003, 24, 1999 [10]Leunget al. IEEE T. Pattern Anal. 2000, 22, 1396 [11]Amara & Straub, Phys. Rev. B 53 (1996) 13857[12]

Borodin et al. Force Field Fitting Toolkit; University of Utah; www.eng.utah.edu/~gdsmith/fff.html[13]Eisenmenger

et al. Comp. Phys. Comm. 2006, 174, 422; www.smmp05.net[14]Simms et al. Prot. Eng. Design & Selection 2008, 21, 369; www.dynameomics.org[15]Monticelliet al., J. Chem. Theory Comput. 2008, 4, 819 [16] Heisterberg, Technical report, Ohio Supercomputer Center. Translation from FORTRAN to C and Input/Output by Labanowski, Ohio Supercomputer Center, 1990 [17]Baker et al. http://apbs.sourceforge.net/

7. Conclusions, on-going work

• A “CG” model built from a smoothed MEP

• seems to be a more significant electrostatic model than a description based on AA centers-of-mass, for simulating electrostatic effects close to the protein a more complete CG model would involve distinct steric and electrostatic centers

• can be derived for any set of point charges (Amber99, Gromos43A1 also set) • Transferability has to be confirmed (in progress)