Protein crystal’s shape and polymorphism prediction within the limits resulting from the exploratio

Protein crystal’s shape and polymorphism prediction within the limits resulting from the exploratio

BioSystems94(2008)233–241

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Protein crystal’s shape and polymorphism prediction within the limits resulting from the exploratio

BioSystems

j o u r n a l h o m e p a g e:w w w.e l s e v i e r.c o m/l o c a t e/b i o s y s t e m

Protein crystal’s shape and polymorphism prediction within the limits resulting from the exploratio

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Protein crystal’s shape and polymorphism prediction within the limits resulting from the exploration of the Miyazawa–Jernigan matrix

Jacek Siódmiak

Department of Modeling of Physicochemical Processes,Institute of Mathematics and Physics,University of Technology and Life Sciences,Kaliskiego7,85-796Bydgoszcz,Poland

a r t i c l e i n f o

Article history:

Received24April2008 Accepted30May2008

Keywords:

Protein crystal

Coarse-graining

Unit cell

Polymorphism

HP-type model

Miyazawa–Jernigan matrix

PACS:

61.50.Ks

81.10.Aj

87.15.kp

87.15.nt a b s t r a c t

A computer study of the prediction of the protein crystal’s shape and polymorphism of crystal’s struc-tures within the limits resulting from the exploration of the Miyazawa–Jernigan matrix is presented.In this study,a coarse-graining procedure was applied to prepare a two-dimensional growth unit,where instead of full atom representation of the protein a two-type(hydrophobic–hydrophilic,HP)aminoacidal repre-sentation was used.The interaction energies between hydrophobic(E HH)aminoacids were chosen from the well-known HP-type models(E HH∈[−4,−3,−2.3,−1]),whereas interaction energies between hydropho-bic and hydrophilic aminoacids(E HP)as well as interaction energies between hydrophilic aminoacids(E PP) were chosen from the range:<−1,1>,but not all values from this range fulfiled limitations resulting from the exploration of the Miyazawa–Jernigan matrix.Exploring every positively vetted combinations of energy interactions a polymorphism of the unit cell was observed what led to the fact that different final crystal’s shapes were obtained.

©2008Elsevier Ireland Ltd.All rights reserved.

1.Introduction

Nowadays physical computation becomes a useful tool/method in soft-matter physics,especially in protein science(Dima and Thirumalai,2002).Since1958whenfirst protein(myoglobin)crys-tal structures was solved by Max Perutz and Sir John Kendrew (Kendrew et al.,1958),protein crystallization is still a great chal-lenge both for experimentalists and theoreticians and still rests upon the trial and error“method”rather than on the theoretical prediction of the results of the crystallization process.In the age of the laboratory robots the trial and error method stays the fastest method of the protein crystallization and the performance/cost ratio is relatively high enough(Stevens,2000).The difficulty follow-ing from the fact that proteins under influence of some components of the solution(even water)can change their conformation(shape) what entails,e.g.charge distribution changes with a changeability of physicochemical conditions of the environment in which they are immersed.In the case of protein solution the most important parameters which have the strongest influence on physicochemi-cal conditions and crystallization processes are:pH of the solution, electrolyte concentration(ionic strength),temperature and proper E-mail address:siedem@utp.edu.pl.concentration of some precipitants(Gilliland and Ladner,1996; George et al.,1997;Bonnete et al.,1999;Chernov,2003;George and Wilson,1994;Rosenberger,1996;Velev et al.,1998).

As an indirect physicochemical-parameter dependent deter-minant of crystallization can be treated the value of the second virial coefficient,B22,which is a measure of intermolecular attrac-tion(interaction energy U<0)or repulsion(U>0)averaged over various spatial(and temporal)mutual positions of(spherical) molecules separated by the distance r(Chernov,1997).In general, B22depends on the temperature.The data for a number of pro-teins,including lysozyme,suggest that crystallization takes place only in solvents which provide a moderately negative virial coef-ficient within the approximate narrow range:−8×104≤B22≤−2×104mol ml/g2(George and Wilson,1994).At higher positive

B22no crystallization occurs while lower B22is correlated with amorphous precipitation rather than with crystallization.Velev et al.(1998)clearly show that B22strongly depends on pH and elec-trolyte concentration I.

Practically,taking all physicochemical parameters of the solu-tion(e.g.,protein concentration,pH,ionic strength,precipitants concentration,and temperature)and some characteristic proper-ties of a given macromolecule(primary,secondary,and tertiary structure,number of chains,nativity)into consideration it is impos-sible to predict in which conditions,especially new,protein will be crystallized or only unorderly aggregated.There is a very nar-

0303-2647/$–see front matter©2008Elsevier Ireland Ltd.All rights reserved. doi:10.1016/j.biosystems.2008.05.032

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