Can We Learn Anything from Simple Mechanical Models of Globular Proteins? Peter Marfey and Lee Klein Department of Biological Sciences, SUNY-Albany, Albany, NY 12222
The study of protein flexibility using simple mechanical models made of readily available materials has been neglected because of the availability of more modern methods such as computer modelling techniques. These techniques are very sophisticated, expensive, and generally not available to researchers without large amounts of research funds (I, 2). We believe that considerable amount of information about molecular flexibility (compressibility) can be obtained by careful study of mechanical models, provided that these models incorporate all the known features of molecular structure (disulfide bonds, a-helices, 8-structure, random structure). An excellent example of the usefulness of mechanical models in the study of molecular properties is provided by the work of Lindman (3-6) who constructed macro-models
of simple asymmetric molecules and used them for the study of rotationof plane-polarized radio waves. In this way he was able to arrive at quantitative law6 governing roration quite similar to those governing rotation of plane-polarized light 1,). optically artive nlolecules in solution. With vrotcin models made of flexible roooer . wire (see the figure), o n e can study such a phenomenon as m&ecular comoressibilit~and determine alone which axis a maximum or m-inimum cbmpressibi~it~ is achieved. This kind of information is useful in considering the orientation of a orotein in condensed media such as bioiogical membrane, the preferential orientation of a protein subunit in a molecular complex, or the behavior i f enzymes under high hydrostatic pressure. We have constructed a coouer . wire model of ese white ---~lysozyme (Figure), that was based on information derived from X-ray diffraction (7) and have measured the motion of different molecular segments when a stress was applied along one of three axes passing through residues 37 and 96, residues 48 and 125, and residues 84 and 110. The magnitude of stress and the resultant displacements of the model are recorded in the tahle. One can see from the results that the model is least compressible along the 37-96 residue axis. It required 20 g of stress to achieve displacements comparable to those obtained with 10 g and 5 g stresses along the other two axes. With a 20-g stress the greatest displacements were observed for the 10-30 and 60-110 amino acid residue segments and the smallest displacement for the 1-10 and 30-50 residue segments. The 1 0 3 0 segment contains mostly a-helices, whereas the 60-110 segment is partly a-helical and partly antiparallel pleated sheet. &
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Movements In Egg White Lysoryme Model Resulting trom Appiled Mechanical Stress*
Z.7 Sequence sagmem
Acopper wire (gauge 18) model of egg white lysoryme. The lengthof the wlre per amino acid residue was 1 cm, which corresponds to a distance of 3.62 A. which is a distance between two consecutive a-carbon atoms in a fully extended polypeptide chain. The regions containing 0-helices and &shuclures are represented by spiral segments and by pleated segments of the wire. respe~lively.The four disulfide bridges are represented by straiFt wire segments of a length correspondingto approximately 6 A (2 X 1.54 A (C-C bond) 2 X 1.81 A (C-S bond) 1.99 A (S-S band): dihedral angle CrS-S-Co. 90': angle S-SGg, 105'). The residue positions defining thethree orthogonal axes (37-96,48-125, and 84-110)alang which stresses wereappiiedtothe model are maned by armws.
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Approximate displacement (In mm) along the axes passing through r e s l d m : 37-96 48-125 84-110
m e anessapplied alongmesxls peaaingmroughrerid- 37-98 was 20g, along me axis of residues 48-125. 10 g, and along me axis 8C110.5 g. medlsqlaamemo of me mDdel segments nneomding to me sequence ssoegmems in IFwere mesnursd with a divider and a rum. m e u r p p wire mdei war svniclently elastic to allow of stress. me m-ursd restaatlm of the cdgin.4 segment poanion upon re-i divlaawnts reprerent only polypeplide backbane and do not Incapwale wssible urmrlbuli~n'lof me amino acm aide chains.
Volume 63 Number 11 November 1986
975
Application of a 10-g stress along the axis passing through residues 48 and 125 produced largest dis~lacementsfor the 1-30 and 100-129 segments. ~ h e s segments e contain the Nand C-terminal ends of the lysozyme and are made up of a helical and random parts. The smallest displacements are observed for the 40-60 and 80-90 residue segments. The former consists mostly of &structure, whereas the latter is partly a-helical and partly random structure. When a 5-g stress was applied along the 8P110 residue axis, the largest displacements were observed for the 1-30, 40-70. 80-90. and 120-129 residue segments. The smallest displacement was found for the 90-160 segment. This segment contains half-cvstine 94 which forms a disulfide bond with the half-cystin; 76. Because of this, the 70-80 region was also characterized by having a relatively small displacement. On the basis of these results we can say that compressibili ~ of y the lyso7yme model is lnrgest dong the 84-1 10 residue axis. Does t his result hn\.i*any s~ynificancewhen ronsidering rornpressihilitv of a real lyso7yme molerule in solutim? \Ye brlirre that it has. The lysurymr molecule has a shape of a nrdates~heroidwith thedimensions annroximatelv 15 X 30 k 30 A. it contains a cleft that divides the molecule roughly
976
Journal of Chemical Education
into two halves. One half contains the two ends of the molecule and is folded around a central core of hydrophobic residues. The other half. which contains the central ort ti on of the chain (residues 40-85), including &structural region, is characterized by numerous hydrophilie residues lining the outer surface and the cleft surface (7). Our model predicts that the observed larae com~ressibilitvalona- the 84-110 residue axis may correspond to widening and narrowing of the lvsozvme . . cleft. This kind of deformation in lgsozyme cwld he re;iponsil,le fur the increase of its enzymatic activity PIQSSIIIL. 18. 9) as e\,idenced by rhe u n d i ~high - hydrostatic . negative value of the transition state activation volume (AV = -10 to -28 cm3 mol-I) observed in the pH range 6.2 to 8.7 and at 35 ' C . Literature Cited
