Review Sheet for BIOC 565 at UA
Review Sheet for BIOC 565 at UA
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A molecular mechanism for osmolyteinduced protein stability Timothy 0 Stieet D Wayne Bolen39 and George D Rosequot T c lenkins Department of ElophylThe lohns Hopkins university lenkins Hall 3400 North Charles street Baltimore MD mix and 39Department of Human Elologlal chemistry university ofTexa Medical Branch 30i university Boulevard 5 i54 Medical Research Building Galveston TX 775554052 Communicated by Carl Frlederl Washington University School of Medicine St Louis MO luly 25 2006 reeled for reView lune 22 2006 Osmolytes are small organic compounds that affect protein stabil ity and are ubiquitous in living systems In the equilibrium protein folding reaction unfolded U native N protecting osmolytes push the equi rium toward N whereas denaturing osmolytes push the equi brium toward U As yet there is no universal molecular theory that can explain the mechanism by which os molytes interact with the protein to affect protein stability Here we lay the groundwork for such a theory starting with a key observation the transfer free energy of protein backbone from water to a waterosmolyte solution Ag is negatively correlated with an osmolyte39s fractional polarsurface area Agnmeasures the degree to which an osmolyte stabilizes a protein Consequently a straightforward interpretation of this correlation implies that the interaction between the protein backbone and osmolyte polar groups is more favorable than the corresponding interaction with nonpolargroups Such an interpretation immediatelysuggests the existence of a universal mechanism involving osmolyte backbone and water We test this idea by using it to construct a quantitative solvation model in which backbonesolvent interaction energy is a function of interactant polarity and the number of energetically equivalent ways of realizing a given interaction is a function of interactant surface area Using this model calculated Agr values show a strong correlation with measured values R 099 In addition the model correctly predicts that protectingdenaturing osmolytes will be preferentially excludedaccumulated around the protein backbone Taken together these modelbased results ra tionalize the dominant interactions observed in experimental stud ies of osmolyteinduced protein stabilization and denaturation organic osm olytes l osmolyte mechanism l protein folding he equilibrium protein folding reaction unfolded U native N is not an ordinary chemical reaction because no covalent bonds are made or broken in the interconversion between N and U Instead protein denaturationrenaturation is just a reequilibration between the unfolded and folded popula tions under changed solvent conditions Accordingly a thermor dynamic descriptionofprotein folding can be framed in terms of solvent interactions with the unfolded and native states 173 Osmolytes are small organic compounds that exert a dramatic influence on the protein folding reaction againwithout making or breaking covalent bonds Protecting osmolytes push the folding equilibrium toward N whereas denaturing osmolytes push the equilibrium toward U Both types ofosmolytes are of utmost significance Protecting osmolytes are ubiquitous in nature where they play a vital role in stabilizing intracellular proteins against a wide variety of adverse environmental con ditions 477 Altematively urea a denaturing osmolyte found naturally in mammalian kidney has been a key reagent through out the long history of solvent denaturation studies 3 8710 The solution thermodynamics of proteinosmolyte mixtures has been well characterized in the literature 3 11719 In the emerging view 12 17 protecting osmolytes raise the free energy of the unfolded state favoring the folded population whereas denaturing osmolytes lower the free energy of the unfolded state favoring the unfolded population Accordingly Wwwpria olggldollo l073pna 0s0szasl03 protectingdenaturing osmolytes interact unfavorablyfavorably with the unfolded state resulting in preferential depletion accumulation ofosmolyte proximate to the protein surface Such osmolyterinduced behavior has been well characterized in there modynamic terms but thermodynamics is a descriptive science deliberately devoid of mechanism As yet there is no universal theory that can account for the mechanism by which osmolytes interact with the protein to affect stability What specific molecular interactions in a proteirkosmolyter water solution stabilizedestabilize the unfolded state of pro teins An important clue comes from recent work showing that the osmolyte effect operates predominantly on the protein backbone a component common to all residues 11713 This conclusionwas reached by measuring transfer free energies Ag of backbone models from water to 1 M osmolyte solutions Althougr side chains do play a role it is primarily the backbone transfer free energy that determines the extent to which osr molytes either stabilize ie Ag gt 0 or destabilize 39 Agu lt 0 the protein relative to an equivalent aqueous solution Thus the backbone Ag value isthe key metric for evaluating the relative denaturingstabilizing strength of different osr molytes The thermodynamic reference state for this metric is given by interactions of the peptide backbone unit with solvent water When that backbone unit is transferred from water to an aqueous osmolyte solution the very presence of a molecule that experiences backbone interactions which differ from corre sponding interactions with water either raises for a protecting osmolyte or lowers for a denaturing osmolyte the Ag value relative to this reference state Furthermore given the well defined nature of the two solvent systems the resultant Agu will arise solely from differences between backboneWater and back bonewaterosmolyte interactions Any molecular interpretation ofosmolyte interactions must be consistent with this experimen tal reality We demonstrate that Agu values for a wide variety of 0s molytes are negatively correlated with their fractional polar surface area SA 33335 The correlation suggests that polar and nonpolar osmolyte surfaces interact with the protein backbone at different energies and that the extent of interaction is related to interactant SA Specific instances in the literature are in known agreement with this plausible idea For example the polar molecule urea that has long been known to interact favorably with the amide backbone of proteins 20 21 Also in a related correlation Record and colleagues 18 noted that Agu for glycine betaine is proportional to polar SA To quantify our Table 1 Solvent accessible surface areas and AgtIr values of osmolytes Osmolyte SA A SA A SAC A 25A A Agtr calmol TMAO 00 432 1684 2116 89 2 Betaine 36 827 1667 2530 65 3 Sucrose 00 3369 1373 4742 56 i 6 Trehalose 00 3406 1452 4858 54 8 Sarcosine 245 433 1416 2094 50 i 2 Sorbitol 00 2336 978 3314 43 7 Proline 245 889 1335 2469 40 i 8 Glycerol 00 1427 841 2268 22 8 Urea 1118 514 116 1748 41 i 2 Guanidine 1678 00 116 1794 59 The 10 osmolytes listed in Fig 1 TOsmolyte surface areas in A2 with partial positive negative and neutral charge are indicated by SA SA and SAO respectively Total surface area in A2 sum of SA SA and SAO Agtr is the free energy change that accompanies the transfer of a backbone unit from water to a 1 M osmolyte solution Uncertainty in Agtr values is based on two independent measurement techniques 11 Value for guanidine was provided by S Sarker personal communication tant polarity and the interaction degeneracy ie the number of energetically equivalent ways of realizing the interaction de pends on the corresponding interactant SAs Our goal is to learn Whether this minimal model polar interactions in a statistical mechanical framework is sufficient to account for the diversity of experimental phenomena associated With protecting and denaturing osmolytes Results Calculations described below were performed by using xray structures of eight stabilizing osmolytes trimethylamine N oxide TMAO betaine sarcosine proline trehalose sucrose glyc erol and sorbitol a destabilizing osmolyte urea and a related denaturant guanidine The Agtr values for these 10 compounds have been measured by two independent methods in all cases except guanidine 11 Table 1 Comparisons between osmolyte structures and the associated water to osmolyte Agtr values Fig 1 indicate no evident correlation With either the total osmolyte SA or its polar SA For example TMAO and urea Fig 1 a and j have similar total SAs but opposite effects on protein stability Likewise sucrose Fig 16 an intermediate stabilizer has greater polar SA than either TMAO a strong stabilizer or urea a strong denaturant However there is a clear correlation R 088 between Agtr and f Ozr lzj fface for these osmolytes Fig 2 Specifically as f gg glzuiface increases the osmolyte interaction With the protein backbone becomes increasingly favorable ie their Agtr value decreases This correlation suggests that the interaction be tween the protein backbone and osmolyte polar groups is more favorable than the corresponding interaction With nonpolar A B C D Stabilizing A930 Fig 1 groups Furthermore the correlation suggests that the proba bility of interaction scales With interactant SA A Model for Solvent Interactions with the Protein Backbone Given the chemical heterogeneity of these osmolytes What accounts for the observed correlation between f gg g lzgiface and Ag The most direct explanation would be the existence of a universal inter action mechanism Accordingly we propose a quantitative model for solvent water and osmolyte interactions With back bone polar groups the amide nitrogen bearing a partial positive charge and the carbonyl oxygen bearing a partial negative charge Three types of proteinsolvent interactions were defined for these two backbone groups favorable unfavorable and neutral having energies of 1 1 and 0 kcalmol respectively Favorable interactions occur between polar groups With oppo site charges unfavorable interactions are between polar groups With like charges and neutral interactions involve nonpolar groups as illustrated for TMAO in Fig 3 The backbone amide nitrogen is assigned to have one solvent interaction site Whereas the larger carbonyl oxygen With its two lone pair electrons is assigned to have two such sites However the overall results do not change appreciably if both backbone groups are treated equivalently discussed below Solventsolvent and backbone backbone interactions are not included in the model A degeneracy term was included to quantify the number of ways of realizing a given backbonesolvent interaction in terms of the area of its available participating interactant surfaces see Methods To implement this contribution polar and nonpolar SAs were calculated for each osmolyte With polar surface further subdivided into contributions from groups With partial positive nitrogen and negative oxygen charges Table 1 E F G H J K Q30gampamp Neutral 4950 Destabilizing 4950 Molecular structures of osmolytes Protecting osmolytes are TMAO betaine sucrose trehalose sarcosine sorbitol proline and glycerol A H and denaturants are urea and guanidine J K Compounds are ordered by their measured Agtr values see Table 1 shown in spacefilling representations and colorcoded by atom type oxygen red nitrogen blue and carbon green Water polarity is represented by its surface electrostatic potential I Upper using a color saturation scale that runs from 007 red to 011 blue eA white indicates neutral potential The water surface is partitioned into discrete positive red negative blue and neutral white surfaces I Lower using electrostatic potential cutoffs described in Methods 13998 wwwpnasorgcgidoi101073pnas0606236103 Street et al 9 i I l I I I TMAO I Betaine Sucrose A 7 it Trehalose E I I Sarcoeine 1r 1 P Sorbitol 2 50 39 T i 4 P roline v Glycerol 3 I I Urea e at Guanldine 0 lt1 0 D 0 L 3 D 03 I 50 I I a I l I I I O 02 04 06 08 1 osmolyte f polar surface Fig2 The polar fraction of osmolyte surface correlates with measured Agtr values Fractional polar SA fgi r lz ace is plotted against Agtr values from Table 1 for the 10 osmolytes in Fig 1The linear regression line solid line has a negative slope with a correlation coefficient of 088 indicating that back boneosmolyte interactions become increasingly favorable as osmolytes be come increasingly polar To treat water and osmolytes in a consistent manner it was also necessary to subdivide a water molecule into polar and nonpolar regions Although the decomposition of osmolyte surfaces into polar and nonpolar components is uncomplicated Fig 3 Illustrating TMAObackbone interactions Interactions between an osmolyte such as TMAO upper molecule and the protein backbone lower structure can be favorable neutral or unfavorable Favorable interactions are between groups of opposite charge A neutral interactions involve at least one nonpolar group B and unfavorable interactions are between groups of like charge C Atoms are colorcoded as in Fig 1 A large fraction ofthe TMAO surface is nonpolar affording more opportunities Le a higher degeneracy for this osmolyte to realize neutral interactions than either favorable or unfavorable interactions Street et al a similar decomposition of water requires a method to evaluate its surface charge distribution To this end an ab initio calcula tion of the water electrostatic potential and electron density was performed as described in Methods When this potential is mapped onto a spacefilling model 22 distinct regions of positive blue negative red and neutral white charge are apparent Fig 1139 top structure After applying polar and nonpolar cutoff values see Methods the water surface is found to have approximately equal regions of positive negative neutral charge 37 33 and 29 respectively Fig 1139 lower struc ture Although the precise decomposition depends on the chosen electron density and the electrostatic potential threshold data not shown our overall results are quite insensitive to this decomposition as discussed below Consequently the total water GSA of 30 A2 the area of a watersized sphere of radius w15 A was subdivided into three equalarea regions of 10 A2 each Comparisons Between ModelBased and Measured AgtIr Values The model was tested by using it to calculate Agtr values and comparing them to experimentally measured values For 1 M osmolyte concentrations the calculated and measured Agtr val ues are in good agreement Fig 4A with a correlation coeffi cient of 099 a substantial improvement from the corresponding correlation with f gg g lggifm r 088 Although the slope of the linear regression line is less than unity slope 081 a slope of 1 with a correlation coefficient of 098 can be obtained if interaction energies are set to 15 15 and 0 kcalmol for favorable unfavorable and neutral interactions respectively As a further test Agtr values were calculated at osmolyte concentrations beyond 1 M Fig 4B solid lines these values compare favorably with the corresponding experimental values for sarcosine urea and guanidine Fig 4B symbols those osmolytes for which measurements beyond 1 M are available 13 The success of the model in predicting Agtr values for a diversity of compounds across a range of concentrations is consistent with our hypothesis that interactions between the protein backbone and osmolytes are dominated by their SA and outergroup polarity Moreover this conclusion is insensitive to substantial changes in model parameters as discussed below How Robust Are the Calculated AgtIr Values Our model has two adjustable parameters the polar and nonpolar SAs associated with water and the interaction energy between solvent and the protein backbone To assess the sensitivity of calculated Agtr values to these parameters both were varied extensively and AgtI values were recalculated Positive negative and neutral water SAs were simultaneously randomized within a 5 to 15 A2 interval with solvent interaction energies fixed at their original values The resulting Agtr values remain in good agreement with the measured values Fig 6 which is published as supporting information on the PNAS web site w90 of the calculated Agtr values have correlation coefficients with measured values that exceed 080 In another test interaction energies were assigned random values in the range 05 5 kcalmol multiplied by 1 for favor able interactions with neutral interaction energy and the polar and nonpolar water SAs held fixed at their original values The correlation with measured Agtr values was recalculated for each new value Fig 7 which is published as supporting information on the PNAS web site and again modelbased and measured Agtr values were found to be in good agreement all correlation coefficients exceed 080 As a final test the correlation between modelbased and measured Agtr values was recalculated under the alternative assumption that the backbone carbonyl oxygen provides only one solvent interaction site not two Water surface decomposition PNAS September192006 vol103 no 38 13999 BIOPHYSICS A 100 I I I I I I I B 400 TMAO 139 O Betaine A l Sucrose 39 6 x Trehalose E Sarcosine 50 p Sorbitol U 4 Proline 3 V Glycerol c b I Urea g CD ale GuanIdIne lt1 TU E o 3 3 03 8 lt1 00 a 1 E 50 t 200 I I I I 50 0 50 100 3000 f 39 39 39 39 39 39 39 539 39 g 7 Calculated Ag1r calmol Fig 4 3 4 Osmolyte M Comparison between calculated and measured Agtr values for osmolytes A Agtr values calculated from the model are plotted against experimentally determined values from Table 1 Good agreement is apparent The linear regression line solid line is given by Ag easured 081 Ag flcmated 32 with correlation coefficient 099 Data points corresponding to the 10 osmolytes in Fig 1 are annotated in Inset B Calculated Agtr values on higher osmolyte concentrations gt1 M are plotted against available experimental data for sarcosine indigo triangles urea green squares and guanidine orange asterisks Solid lines were drawn from modelbased Agtr values extended beyond 1 M osmolyte concentrations and interaction energies were held fixed at their original values Still modelbased and measured Agtr values remain highly correlated Fig 8 Which is published as supporting information on the PNAS web site although the correlation coefficient is reduced to 086 Preferential Osmolyte Interactions with the Protein Backbone Char acteristically stabilizingdestabilizing osmolytes are preferen tially excludedaccumulated at the protein surface respectively 14 15 23 To test this aspect of the model the local concen tration of osmolytes at backbone interaction sites was calculated for a 1 M osmolyte solution see Methods As shown in Fig 5 stabilizing osmolytes are preferentially excluded from backbone polar groups Whereas denaturing osmolytes are preferentially accumulated there In the model the molecular basis of these preferential interactions is rooted in solventbackbone interac tions Stabilizing osmolytes such as T MAO are preferentially excluded from the backbone because water is more likely than T MAO to interact favorably With backbone polar groups Con 100 I I I I I TMAO O Betaine 7 Sucrose T x Trehalose 2 A Sarcosine g I Sorbitol 50 T Z 4 Proline E 4 v Glycerol 3 J I Urea E 91 Guanidine b 0 lt1 3 o 5 en c5 c1 2 I 50 aIe I I I l O 05 1 15 2 Local osmolyte concentration M Fig 5 Protectingdenaturing osmolytes are preferentially depleted accumulated at the protein backbone Concentration of osmolyte around the backbone in a 1 M osmolyte solution plotted against measured Agtr values from Table 1 Data points corresponding to the 10 osmolytes in Fig 1 are annotated in Inset The local osmolyte concentration is given by the scaled difference between Oprefgt and Obulk described in Methods It is apparent that the backbone concentration of protecting osmolytes Agtr gt 0 is com paratively depleted osmolyte lt 10 M whereas that of denaturing os molytes Agtr lt 0 is comparatively enriched osmolyte gt 10 M 14000 wwwpnasorgcgidoi101073pnas0606236103 versely destabilizing osmolytes such as urea are preferentially accumulated near the backbone because they have a stronger propensity to interact With the backbone than water However it should be noted that the model does not take nonpolar backbone regions into account and interactions around these regions can also contribute to the actual local osmolyte concentration Discussion The model presented here establishes a connection between bulk thermodynamic quantities and the molecular interactions that give rise to these quantities In particular it was developed to explain the experimentally determined backbone transfer free energies from water to osmolyte in terms of interactions between the protein backbone and water or osmolyte molecules The model was validated by using it to predict significant experi mentally observed behavior In addition the model predicts that the free energy change for foldingunfolding Will be linearly dependent on osmolyte concentration or approximately so and for both protectants and denaturants consistent With Pace s linear extrapolation model 9 10 Our model also correctly predicts m values dAgtrdosmolyte of opposite sign and approximately equal magnitude for proteins that are either forced to fold by sarcosine or denatured by urea thereby accounting for the Wide range of effects that natural osmolytes can exert on protein stability 12 Finally Agtr values calculated by using the model correlate extremely well with experimental values R 099 illustrating that the relevant water osmolyte backbone energies are captured by the model Proteinosmolyte interactions are conspicuously weak and in such cases classical binding models are notoriously deficient 24 In particular ureabackbone interactions would have apparent binding constants slightly greater than unity Kbinding 12 3 Whereas protecting osmolytebackbone interactions would have apparent binding constants slightly less than unity Kbinding 08 In this weakbinding regime free energy effects are ostensibly additive because neither type of osmolyte occupies a significant fraction of the backbone surface so there is essentially no compe tition for backbone binding sites Such additivity is observed in experiments 25 and is consistent With the model Many previous studies have related SA calculations to thermo dynamic quantities associated With protein folding 26 32 moti vated by the early observation that the transfer of nonpolar groups from organic to aqueous solvent is accompanied by an anomalous change in heat capacity AC 33 The observed correlation between AC and nonpolar surface is often interpreted to mean Street et al that water around nonpolar surfaces differs structurally and there modynamically from water in bulk solution 34 In contrast the model proposed here focuses on solvent interactions with the protein backbone and SAs are only used here to estimate the bindingcompetent fraction of interacting molecules Several other types of solvent interactiors affecting protein stability are neglected in our model including crowding and ex cluded volume 3237 the structure ofwater in osmolyte solutiors 3amp 39 side chainsolvent interactions and binding situations in which a large osmolyte molecule can occlude more than one backbone unit In addition the model treats all nitrogens and oxygens as equally polar an obvious simplification However despite such simplicity the model captures key thermodynamic aspects of osmolyte behavior in a parameterrirsemitive fashion Therefore it seems likely that the model39s anchoring suppositiors solventprotein interactiors that depend on polarity and SA are primarily responsible for the osmolyte effect in proteins Methods Atom coordinates for TMAo betaine sucrose trehalose sarcosine sorbitol proline glycerol urea and guanidine were obtained from the HICUP database 40 Their solvent accesr sible polar and nonpolar SAs were calculated by using PyMOL 41 with a probe radius of 14 A Table 1 Guanidine differs from other osmolytes investigated here because it is intro duced into solution as a salt guanidinium hydrochloride To correct for the chloride ion associated with guanidine a small negatively charged surface of30 Azwas added to the guanidine SA although this addition does not dramatically change its calculated Ag value these values are 767 and 762 calmol with and without chloride ion addition respectively The surface of a water molecule was defined at a threshold electron demity of p 0005 giving a molecular volume of 115 A3 approximately the volume ofa 1 5A sphere The surface ofwater was decomposed into polar nonpolar and neutral regions by calculating the electrostatic potential and mappirg it onto this surface The thresholds used to delimit polar and nonpolar regions were defined by the boundary where the potential decays to 12 of its minimum and maximum values 70023 and 0037 eA respec tively The neutral region was then defined as the complement to these two regiom Both the electrostatic potential and the electron demin were calculated ab mm by using CPMD 42 The average energy of the protein backbone in various osmolyte solutions was calculated by using a statistical mes chanics model in which the backbone has three interaction sites one at the amide nitrogen and two at the carbonyl oxygen these sites are represented by the indices 1 y and k respectively At each interaction site the solvent e itherwater or osmolyte can present a positively neutral 0 or negatively charged 7 surface Accordingly the indices i y and k can take the values 0 or 7 resulting in a total of 33 27 possible microstates Interactions between the back bone and solvent are assigned energies of 71 1 and 0 kcalmol corresponding to interactions between opposite like or unr charged groups respectively The interaction energies for each site are assumed to be additive and independent These microstates and their associated energies and degeneracies are enumerated in Table 2 The degeneracy of a solvent interaction at a particular backbone interaction site reflects the number of energetically equivalent ways of making that interaction In our model the degeneracy is given by the water or osmolyte SA that can participate in the interaction Given that the three backbone interaction sites i y and k are independent the total degeneracy 1 k of a specific microst ate consisting of a 0 or r solvent interaction at sites 1 and k will be the product ofthe degeneracies as represented by their SAs at individual interaction sites Stleet etel Table 2 Solvent interactions with the protein backbone lnteractlon slte llllcrostate39 Mr Om O k E kcalrnol a ml o 0 e l o 0 o o l o e 2 r l e o 2 r e 3 o 72 o 0 ml 0 e 0 o o ml 0 o o 0 o o e l o e 0 o e o l o e e 2 e 73 o 72 7 ml 0 72 o 0 ml 0 e 0 r ml 7 o 0 The 27 rnicrostates and their associated energies and degeneracies The single arnide nitrogen and two carbonyl oxygen backbone interaction sites are indicated by N oi and 01 respectively solvent interactions With these sitesare given bytne cnarge ortneinteracting solventsurrace positive negative 7 and neutral to and l and k indices are varied over the range orvaluesror these interactions 391 is the energy or a given microstate and n is its degeneracy In SASASAk 1 These SAswill have a contribution from water SAW SAW and SAch and a contribution from osmolyte SAW SAW and SAM that depends on the osmolyte concentration At Ymolar SA 555SAW YSAW 2 SA 555SAW YSAOJ 3 SA 555SAW YSAO 4 In the model o and 7 water SAs are equal 10 A2 and the corresponding osmolyte SAs are given in Table 1 The SA calculations treat the activity of water as a constant ie that molarity ofwater in osmolyte solutions ofvarying concentration is e555 M a plausible approximation at the low cosolvent concentrations used here The probability of any given microstate is given by Meaner 5 Pwk E 2 E Milank7 l r i k where k is Boltzmann39s constant and T is 29815 K the temper ature at which Agtvalues were measured experimentally These probabilities can be used to calculate the average energy of the system PNAS l September19zoos l vol l03 l no 33 l 14ml HIOPNVSICS ltEgt E E 2 Ellen 6 i i l with 4gb values given by the difference between the average system energy at 0 and 1 M osmolyte concentrations The average occupancy of osmolytes on the backbone interaction sites can also be calculated as SAM lt0aieigt222pilltm A k In 5 SAN SAD gt 7 7 7 SAN SAW SAM SAW This value can be compared with the expected osmolyte occur pancy based solely on the bulk solution concentration ie no Wu H 1031 Chinese IPliynol V 3217344 Miisky AE Pauling L 1035 Pioc Nail Amd Sci USA 22 4307447 Schellman JA 2002 Blophy Chavrl 05 017101 Yancey PH Clark ME Hand SC Bowlus RD Somero GN 1082 Stlk tk 217 121471222 5 Record MT Jr Courtenay ES CayleyDS Guttman HJ 1008 Trends Blothzm Sci 23 1437148 6 Record MT Jr Courtenay ES Cayley S Guthnan HJ 1008 mm Blothzm Sci 23 1007104 7 Hochachka PW Somero GN 2002 Biochamcaldaaptation Oxford Univ Press Oxford 8 Tanford C 1968Avaml Wm 23 1217282 0 Greene RF Jr Pace CN 1074 IBlol Chavrl 2440 538875303 10 Santoro MM Bolen DW 1088 Biochamidiy 27 805378058 11 Auton M Bolen DW 2004 Biochamutiy 43 132071342 12 Auton M Bolen DW 2005 Pioc Natl1011 Sci USA 102 15055715058 13 Liu Y Bolen DW 1005 Biochamidiy 34 12884712801 14 Lee JC Tlmasheff SN 1081 IBlol Wm 55 710377201 15 Timasheff SN 1002 Biochamutiy 31 085770854 15 Makhatadze Gl Privalov PL 1002 IMol 101 225 4017505 17 Bolen DW Baskakov w 2001 I Mol 101 310 0557053 18 Felitsky DJ Cannon JG Capp MW HongJ Van Wynsbergie AW Anderson CF Record MT Jr 2004 Biochamidiy 43 1473214743 10 Hong J Capp MW Anderson CF Saecker RM Felitsky DJ Anderson MW Record MT Jr 2004 Biochamidiy 43 14744 714758 20 Nozaki Y Tanford C 1053 IBlol Chavrl 238 40744080 21 Roseman M Jencks WP 1074 um elm Soc 07 6317640 asme 14002 i wwwpnarorgtgidoiio1073pnar0000230103 preferential interactions with the three backbone interaction sites SA W 7 3 3 The relative difference between lt0nggt and lt0bmkgt yields a local osmolyte concentration when scaled to mo1arity All numerical calculations were performed in Python www pythonol39g We thank Buzz Baldwin and two anonymous referees for suggestions This work was supported by a Burroughs Welcome predoctoral fellowe ship to T o S National Institutes of Health Grant GM49760 to D W B and by the Mathers Foundation G D R 22 Pettersen EF GoddardTD Huang CC Couch GS Greenblatt DM Meng EC Ferrin TE 2004 I Compat Chavrl 5 150571512 23 Lin TY Tlmasheff SN 1004 Biochamidiy 33 12695712701 24 Schellman JA 1087 Biopolywm 25 5407550 5 Mello CC Darrick D 2003 PWZEWL Sci 12 152271520 25 Chothia C 1074 Name 248 3387330 27 Eisenberg D McLachlan AD 1085 Name 310 1007203 28 Spolar RS Ha JH Record MT Jr 1080 Proc Nazi1011 Sci USA 85 838278385 20 Richards FM 1077 Anna RevBlophy BIOEVLg 6 1517175 30 Lee B Richards FM 1071 IMolBlol 55 3707400 31 Hilser VJ Gomez J Freire E 1005 Fromm 25 1237133 32 Robertson AD Murphy KP 1007 elm Rev 07 15171258 33 Cohn El Edsall JT 1043 Piotaim Amlm Acids and Peptide 41 Ian and Dlpola Ion Hainer New York 34 Gallagier KR Sharp KA 2003 um Chavrl Soc 15 085370850 35 Minton AP 1008 Method Emymol 205 1277140 35 Schellman JA 2003 Bioplysr 85 1087125 37 Saunders AJ Davierearles PR Allen DL Pielak GJ Erie DA 2000 Biopolywm 53 2037307 38 Batchelor JD olteanu A Tripathy A Pielak GJ 2004 Mm Chavrl Soc 125 10581051 30 Bennion DJ Daggett V 2004 Proc Natl1011 Sci USA 101 54335438 40 Kleywegt GJ Jones TA 1998A la CvjmallogrD 54 111071131 41 DeLano WL 2002 m PYMOL Mokciaay Graphics swam DeLano Sci San Carlos CA 42 Hutter J Alayi A Deutsch T Bernasconi M Goedecker S Mark D Tucker man M Parrinello M 100772001 CPMD MaerlanckrIllsutut fur Fesckore perfoischung Stuttgart Vol 100772004 Sheet eta 395 r k a Corrections NEUROSCIENCE For the article A molecular neuroethological approach for identifying and characterizing a cascade of behav iorally regulated genes by Kazuhiro Wada Jason T Howard Patrick McConnell Osceola Whitney Thierry Lints Miriam V Rivas Haruhito Horita Michael A Patterson Stephanie A White Constance Scharff Sebastian Haesler Shengli Zhao Hironobu Sakaguchi Masatoshi Hagiwara Toshiyuki Shiraki Tomoko HirozaneKishikawa Pate Skene Yoshihide Hayash izaki Piero Carninci and Erich D Jarvis which appeared in issue 41 October 10 2006 of Proc Natl Acad Sci USA 10315212 15217 first published October 3 2006 101073 pnas0607098103 the authors note that Fig 1 appeared incor rectly due to a printer s error The corrected figure and its legend appear below T human I songbird subclusters El songpigd clusters c B so 25 d 6120 g 15 8 a 8 10 e 5 a 57 0 mRNA Variants polyA GdPOIVA Fig 1 Molecular functions and variant analysis A Distribution of putative molecular functions for 1924 clusters and 2449 subclusters of zebra finch brain cDNAs that received gene ontology annotations wwwgeneontology org compared with 27048 human genes Genes can be represented in more than one category because of multiple molecular functions and thus catego ries add up to gt100 Human values were obtained from ref 24 B mRNA variant analysis Percentage represents the proportion of a specific variant type relative tothe total number of variants from 100 randomly selected cDNA clusters containing 256 subclusters and 668 clones P lt 001 from chance distribution horizontal line t test across variant types in n 10 bins of 10 clusters each Because not all clones have full sequence coverage the abso lute distribution may change when such sequences are present Colors denote mRNA subdomains quantified alt Alternative wwwpnasorgcgidoi101073pnas0608997103 17064 17065 PNAS November72006 vol103 no45 BIOPHYSICS For the article A molecular mechanism for os molyteinduced protein stability by Timothy O Street D Wayne Bolen and George D Rose which appeared in issue 38 September 19 2006 of Proc Natl Acad Sci USA 10313997 14002 first published September 12 2006 101073pnas 0606236103 the authors note the following For Fig 2 of our article we inadvertently published a plot of the contact surface area rather than the accessible surface area as intended Also the correlation coefficient given should be 081 not 088 as in the original figure caption All other aspects of the article remain unaffected by this correction We regret the errors The cor rected figure and legend appear below 100 x I 3 g 50a U 8 a h W TMAO lt 0 Betaine 390 7 i Sucrose 7 9 0 x Trehalose a Sarcosine 5 D Sorbitol CD 4 Praline E v lecerol I Urea I 50 i Guanidine l r l l r l 0 02 04 06 08 1 osmolyte f polar surface Fig2 The polar fraction of osmolyte surface correlates with measured Agtr values Fractional polar SA fgg g 39sygfface is plotted against Agtr values from Table 1 for the 10 osmolytes in Fig 1The linear regression line solid line has a negative slope with a correlation coefficient of 081 indicating that back boneosmolyte interactions become increasingly favorable as osmolytes be come increasingly polar wwwpnasorgcgidoi101073pnas0608836103 wwwpnasorg NEUROSCIENCE For the article Neurotoxic protein expression reveals connections between the circadian clock and mating behavior iansapliiZcquot by SebastianKadener Adriana Villella Elzbieta Kula Kristyna Palm Elzbieta Pyza Juan Bot as Jeffrey c Hall and Michael Rosbash which appeared in issue 36 September 5 2006 omechtlAccd Sci USA 10313537713542 first published August 23 2006 101073pnas0605962103 the authors note that there were errors in the Acknowledgments The corrected version appears below We thank Nancy Bonini Howard Hughes Medlcal Institute University ofRennsylvania Philadelphia PA for the UASVMJDtr lines R Allada P EmeryK AbruzzlK DowerD Stoleru ands Laoadie for critical readings of the manuscript and Heather Felton for administrative asslstance SK is a recipient of a Human Frontier Sclence Program postdoctoral fellowship This work was supported in part by National Institutes ofHealth Grants NSAAzsztto M R GM66778 to I CH and M R and GM721473 and Nsssssz to I c H www pnai orgtgidoil o ionpus osoasoaloz CELL BIOLOGY For the article A biorchemormechanical model for cell contractililyquot by Vikram S Deshpande Robert M McMeeking and Anthony G Evans which appeared in issue 38 September 19 2006 of Pm Natl Amd Sci USA 103140157 14020 first published September 7 2006 101073pnas 0605837103 the autliois note that Eq 3 is incorrect The corrected equation appears below This error does not affect the conclusions of the article 0 o 1 1 3 s n 1 3gt 0 9a WWW pnai orgtgidoil o ionpus 050mm PNAS l Novembei7zoos l vol loa i no as l 17065 connEcnous
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