PROTEINS: Structure, Function, and Genetics 10171-187 (1991)
1.59 A Structure of Trypsin at 120 K: Comparison of Low Temperature and Room Temperature Structures Thomas Earnest,' Eric Fauman,' Charles S. Craik,lV2 and Robert Stroud' Departments of 'Biochemistry and Biophysics and 2Pharmuceutical Chemistry, S-964, University of California School of Medicine, San Francisco, California 94143-0448
ABSTRACT The structure of a rat trypsin mutant tS195Cl at a temperature of 120 K has been refined to a crystallographic R factor of 17.4% between 12.0 and 1.59 A and is compared with the structure of the D102N mutant at 295 K. A reduction in the unit cell dimensions in going from room temperature to low temperature is accompanied by a decrease in molecular surface area and radius of gyration. The overall structure remains similar to that at room temperature. The attainable resolution appears to be improved due to the decrease in the fall off of intensities with resolution [reduction of the temperature factor]. This decreases the uncertainty in the atomic positions and allows the localization of more protein atoms and solvent molecules in the low temperature map. The largest differences between the two models occur at residues with higher than average temperature factors. Several features can be localized in the solvent region of the 120 K map that are not seen in the 295 K map. These include severalmore water molecules as well as an interstitial sulfate ion and two interstitial benzamidine molecules. Key words: cryocrystallography, temperature factor, serine protease structure INTRODUCTION The use of low temperature methods in protein crystallography offers a number of advantages. Of primary practical importance is the decrease in Xray induced beam damage to the crystal.'P2 This is especially useful for crystal systems which require synchrotron radiation for data collection. This reduction appears to arise from three factors: (1) the decrease in the diffusion of free radicals after formation (which leads to the further disruption of covalent bonds), (2) decrease in the formation of free radicals, and (3) decrease in local heating effect^.^ Also the decrease in temperature may lead to increased stability of the lattice. A decrease in the temperature factors leads to a decrease in the fall off of intensities as a function of resolution. This effect plus the decrease in beam damage (which may allow for improved counting statistics) leads to an increase in the effective at0 1991 WILEY-LISS, INC.
tainable resolution. Since many enzyme transition states may be stablized a t low temperatures: this technique could allow for the determination of functionally important conformational changes if they can be elicited in the protein crystal. Also many important physical properties can be studied by observation of temperature induced changes in the protein structure (e.g., ref. 5). Investigation of protein structures a t low temperatures may allow for more precise studies of protein dynamics and flexibility, and structural heterogeneity in proteins and determination of whether this heterogeneity is discrete or continuous. The thermal expansion of the a-helical protein, myoglobin, was studied by Frauenfelder and coworkers5 who determined the overall thermal expansivity coefficient and found it to lie somewhere between that of water and that of hydrocarbons. As those authors point out, this is to be expected since the forces that stabilize the folded conformation of a protein are a mixture of polar, electrostatic, van der Waals, and hydrophobic interactions. The unit cell dimensions decrease by approximately 1%in going from room temperature to 80 K. They find an anisotropic thermal expansion in the protein between the 80 K and the room temperature structures with the largest changes occurring in the CD and GH corners. The structure of trypsinogen, the precursor of trypsin which is activated by the removal of the Nterminal hexapeptide, has been solved and has a substrate binding site that is more flexible than in active trypsin.6-8 Walter et al.' studied the structure of trypsinogen a t low temperature in the presense of cryosolvents in order to determine if the activation domain, which is disordered with no visible density at room temperature in their structure, becomes ordered a t low temperatures. Although the
Received June 1, 1990;revision accepted October 19,1990. Address reprint requests to Dr. Robert Stroud, Department of Biochemistry and Biophysics, University of California School of Medicine, 513 Parnassus Avenue, S-964,San Francisco, CA 94143-0448. Dr.Thomas Earnest's present address is Donner Laboratory, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720.
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average temperature factor is significantly reduced a t 173 K and 103 K compared to room temperature, no further density was observed in the activation domain when phased on a structure that lacks atoms corresponding to the activation domain. This suggests that the disorder in the structure of Walter et al.' is probably due to multiple conformations (static disorder) and not thermal in nature. Alternately, we found the activation domain in trypsinogen somewhat more flexible than in trypsin,6 with density for all but 2 amino acids is unambiguously observed and this segment clearly adopts a configuration different from that found in trypsin. We report here the structure of a mutant rat trypsin (S195C)* at 120 K and compare it to the structure of the D102N mutant of rat trypsin a t 295 K. The use of these mutant enzymes may allow for the study of enzyme-substrate complexes due to their reduced k,,Jk,. A decrease in the overall temperature factor by 66%caused by cooling from 295 K to 120 K, as calculated from Wilson plots, indicates a reduction in the fall off of intensities as a function of resolution and lower mean square displacement about the average atomic position at 120 K relative to that at 295 K. A decrease in the unit cell dimensions of approximately 1% is accompanied by a reduction in the protein surface area of 1.2% (as determined by the Connolly surface algorithm" using a 1.4 A probe sphere) and a reduction of the radius of gyration by 0.25% for all protein atoms and 0.19% for main chain atoms. The root mean square (RMS) deviation of the C, atoms is 0.178 A. Most of the larger RMS deviations occur for residues with high temperature factors. Concerted movements of secondary structural domains can also be seen when comparing the 295 K and 120 K structures. METHODS Crystals of rat trypsin** were grown by vapor difb i o n in 55% magnesium sulfate (anhydrous), 10 mM calcium chloride, 75-100 mM benzamidine, and 50 mM Tris buffer pH 8.0, a pH where the enzyme is optimally active. The protein concentration was approximately 30 mg/ml. The crystals lie in the cubic space group 123 with unit cell dimensions of 124.38 A a t 295 K and 123.12 2 .14 A at 120 K as measured on a Nicolet P2, diffractometer.
TABLE I. Statistics of Data Collection and Reduction Using the XENGEN Package13 for the S195C Mutant of Rat Trvusin at 120 K
Resolution range -2.88 2.88-2.28 2.28-1.99 1.99-1.81 1.81-1.68 1.68-1.59 -1.59
Number of independent % of reflections total R,,,t collected 7408 5.67 100 100 11.04 7198 7122 15.15 100 100 22.13 7053 100 28.14 7118 81.6 28.65 5714 96.9 10.51 41613
Average Ila(I)
82.1 34.3 19.1 10.2 6.4 4.0 27.2
N
Low Temperature D a t a Collection Freezing was performed by picking the crystal from the drop on a thin glass fiber after coating the crystal with a thin layer of Paratone-N and removal of excess solvent, then quickly plunging into liquid ethane kept near its solidification point in a dewar of liquid nitrogen. This "shock freezing" approach was originated by Parak et al." in studies of myoglobin by Mossbauer spectroscopy and was subsequently adapted for single crystal X-ray data collection.12 Recently Hope' has shown that the method is useful for a number of protein crystal systems. The crystal was rapidly transferred into a prealigned stream of cold nitrogen gas maintained at 120 K. The cold nitrogen gas was supplied from a Syntex LT-1 modified to use boil off nitrogen from the dewar and also for use on various data collection systems in our lab and at synchrotron facilities. Data was collected using CuK, radiation (A = 1.54 A) from a Rigaku rotating anode generator with graphite monochrometer and a Xentronics area detector system. The XENGEN data reduction package was of 10.51% for inused for data r e d ~ c t i 0 n . Rsymm l~ tensities down to 1.59 A was obtained from the 7fold redundant data set. Upon freezing, the unit cell length decreases by approximately 1% to 123.12 A. Area detector data statistics are shown in Table I. Refinement
*In this paper the residues are numbered continuously from 1 through 223 and the residue number in the chymotrypsin numbering system for serine proteases is placed in brackets. When referring to the mutants, the chymotrypsin number is used, e.g., S195C is used for the serine to cysteine mutation of residue 177 and D102N is the aspartate to asparagine mutation at residue 84. The numbers of the residues at the catalytic triad for the wild type trypsin are histidine 40[571, aspartate 84[1021, and serine 177[1951. **Recombinant trypsins were expressed, purified and charicterized a s described in Higaki et al.38.
The structure of rat trypsin was solved initially by molecular replacement from the model of bovine t r y p ~ i n . ' ~ The . ' ~ model for the 120 K structure was refined using a starting model of the I23 form of benzamidine-inhibited D102N rat trypsin originally solved to 2.8 A by Stroud," and subsequently refined against a 2.3 A data set to an R factor of 22.4% (J. Finer-Moore, J. Swedlow, and R. Stroud,
173
LOW TEMPERATURE TRYPSIN
TABLE 11. Summary of Refinement Statistics for 120 K and 295 K Structures* t RCW&
Resolution range Number of independent reflections
120 K 17.4 12.0-1.59 h; 37692
295 K 14.2 12.0-2.30 h; 12129
Standard deviations from ideal geometry Bond distance (h;) 1-3 distance (A) Bond angle (degrees) Restrained B factor differences Main chain bond B (A2) Main chain angle B (A2) Side chain bond B (A2) Side chain anele B (A2)
120 K
295 K
.025 .049 3.1
.020 .065 4.2
1.470
1.572 2.365 5.683 5.116
2.045 4.276 4.641
*Number of independent reflections refers to those greater than zero. Bond distances are the distances between nearest neighbor atoms. 1-3 distances are the distances between next nearest neighbor atoms. Bond angles are the angles between next nearest neighbor atoms. Main chain bond Bs are the differences in the B factors of main chain nearest neighbor atoms. Main chain angle Bs are the differences in the B factors of main chain next nearest neighbor atoms. Side chain bond Bs are the differences in the B factors of side chain nearest neighbor atoms. Side chain bond Bs are the differencesB factors of side chain next nearest neighbor atoms. The definitions of the structural parameters listed below are as in Hendrickson and Konnert"
unpublished results). The two atoms which differ between the D102N and S195C mutants were replaced using FROD0.17 Several cycles of stereochemically restrained, least-squares refinement using PROLSQ,l' of this starting model using the low temperature data, plus rebuilding using FRODO on an Evans & Sutherland PS330, led to an R factor of 17.4%using 37692 independent reflections between 12.0 and 1.59 A which are greater than zero. This model was then used as the starting model for the 2.3 A room temperature data and the R factor was reduced to 14.3%for 12129 reflections greater than zero between 12.0 and 2.3 A by PROLSQ with no rebuilding necessary except for the removal of waters which are not found in the 295 K structure. This reduction in R factor for the room temperature model most likely arises from the improved state of refinement of the new starting model. Several alternating cycles of B factor and occupancy refinement were used, similar to the method used originally for refining the 120 K model. Maps of the 120 K and 295 K structures were constructed from (2F,,-Fc)e2miae and (F,,-Fc)e2miac.A summary of the refinement statistics is given in Table 11. Residues which possess side chains that adopt two alternate positions were refined as having an occupancy of 0.5 for each conformation. The occupancies of the oxygen atoms in the water molecules were refined by several cycles of PROLSQ with alternating cycles of temperature factor and occupancy refinement.
RESULTS Increase in Resolution Wilson plots'' of the two data sets used are shown in Figure 1. Determination of the overall B factor (temperature factor) from the slopes of the best fit lines indicate that the overall B factor is significantly reduced from 26.38 hi2 a t 295 K to 9.61 A2 a t 120 K. The average B factors determined from the refined structures using the non solvent atoms are = 8.80 A2 and = 21.73 A2. As can be seen from the Wilson plots, and as a direct consequence of the lower B factor, the fall off of intensities as a function of resolution is greatly reduced for the low temperature data. This does not appear to be a general result. Crystal systems where the predominant component of the temperature factor is from static disorder (as opposed to vibrational motion) should not show a significant increase in resolution a t lower temperatures since lowering the temperature should only decrease the component of the temperature factor due to vibrational motion. Also a number of crystals show a n increase in the mosaicity upon freezing (e.g., reference 20). Accuracy of Coordinates The accuracy of the atomic positions is difficult to assess. The method of Luzzatti21 is frequently used in X-ray crystallography to estimate the error in the atomic positions by plotting the crystallographic R
174
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2
1
0
st1-2 Fig. 1. Plots of In [4>]lsum (P’2)versus sin2(0)/h2,as in Wilson,’* for the 120 K (squares) and 295 K data (triangles).Overall 6factors were determined from the line least-squares fit from 3.5 to 1.59A for the 120 K data (8=9.61A’) and 3.5 to 2.30 A for the 295 K data (6=26.38A’).
0.60
0.50
0.40
d
0.3G
0.20
0.10
-0.00 0.0
0.2
0.4
sidtheta) Fig. 2. Plots of R versus sin(0) as in Luzzatti” for the 120 K (squares) and 295 K (triangles) structures. The curves represent levels of error corresponding to, from bottom to top, 0.10, 0.15, 0.20.and 0.30A.
175
LOW TEMPERATURE TRYPSIN
30
. 8
20 A
.
A
M 0
r4
.
8 8
8
.
8
8
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10
0
10
20
30
40
1.59 A Structure of Trypsin at 120 K: Comparison of Low Temperature and Room Temperature Structures Thomas Earnest,' Eric Fauman,' Charles S. Craik,lV2 and Robert Stroud' Departments of 'Biochemistry and Biophysics and 2Pharmuceutical Chemistry, S-964, University of California School of Medicine, San Francisco, California 94143-0448
ABSTRACT The structure of a rat trypsin mutant tS195Cl at a temperature of 120 K has been refined to a crystallographic R factor of 17.4% between 12.0 and 1.59 A and is compared with the structure of the D102N mutant at 295 K. A reduction in the unit cell dimensions in going from room temperature to low temperature is accompanied by a decrease in molecular surface area and radius of gyration. The overall structure remains similar to that at room temperature. The attainable resolution appears to be improved due to the decrease in the fall off of intensities with resolution [reduction of the temperature factor]. This decreases the uncertainty in the atomic positions and allows the localization of more protein atoms and solvent molecules in the low temperature map. The largest differences between the two models occur at residues with higher than average temperature factors. Several features can be localized in the solvent region of the 120 K map that are not seen in the 295 K map. These include severalmore water molecules as well as an interstitial sulfate ion and two interstitial benzamidine molecules. Key words: cryocrystallography, temperature factor, serine protease structure INTRODUCTION The use of low temperature methods in protein crystallography offers a number of advantages. Of primary practical importance is the decrease in Xray induced beam damage to the crystal.'P2 This is especially useful for crystal systems which require synchrotron radiation for data collection. This reduction appears to arise from three factors: (1) the decrease in the diffusion of free radicals after formation (which leads to the further disruption of covalent bonds), (2) decrease in the formation of free radicals, and (3) decrease in local heating effect^.^ Also the decrease in temperature may lead to increased stability of the lattice. A decrease in the temperature factors leads to a decrease in the fall off of intensities as a function of resolution. This effect plus the decrease in beam damage (which may allow for improved counting statistics) leads to an increase in the effective at0 1991 WILEY-LISS, INC.
tainable resolution. Since many enzyme transition states may be stablized a t low temperatures: this technique could allow for the determination of functionally important conformational changes if they can be elicited in the protein crystal. Also many important physical properties can be studied by observation of temperature induced changes in the protein structure (e.g., ref. 5). Investigation of protein structures a t low temperatures may allow for more precise studies of protein dynamics and flexibility, and structural heterogeneity in proteins and determination of whether this heterogeneity is discrete or continuous. The thermal expansion of the a-helical protein, myoglobin, was studied by Frauenfelder and coworkers5 who determined the overall thermal expansivity coefficient and found it to lie somewhere between that of water and that of hydrocarbons. As those authors point out, this is to be expected since the forces that stabilize the folded conformation of a protein are a mixture of polar, electrostatic, van der Waals, and hydrophobic interactions. The unit cell dimensions decrease by approximately 1%in going from room temperature to 80 K. They find an anisotropic thermal expansion in the protein between the 80 K and the room temperature structures with the largest changes occurring in the CD and GH corners. The structure of trypsinogen, the precursor of trypsin which is activated by the removal of the Nterminal hexapeptide, has been solved and has a substrate binding site that is more flexible than in active trypsin.6-8 Walter et al.' studied the structure of trypsinogen a t low temperature in the presense of cryosolvents in order to determine if the activation domain, which is disordered with no visible density at room temperature in their structure, becomes ordered a t low temperatures. Although the
Received June 1, 1990;revision accepted October 19,1990. Address reprint requests to Dr. Robert Stroud, Department of Biochemistry and Biophysics, University of California School of Medicine, 513 Parnassus Avenue, S-964,San Francisco, CA 94143-0448. Dr.Thomas Earnest's present address is Donner Laboratory, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720.
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T. EARNEST ET AL
average temperature factor is significantly reduced a t 173 K and 103 K compared to room temperature, no further density was observed in the activation domain when phased on a structure that lacks atoms corresponding to the activation domain. This suggests that the disorder in the structure of Walter et al.' is probably due to multiple conformations (static disorder) and not thermal in nature. Alternately, we found the activation domain in trypsinogen somewhat more flexible than in trypsin,6 with density for all but 2 amino acids is unambiguously observed and this segment clearly adopts a configuration different from that found in trypsin. We report here the structure of a mutant rat trypsin (S195C)* at 120 K and compare it to the structure of the D102N mutant of rat trypsin a t 295 K. The use of these mutant enzymes may allow for the study of enzyme-substrate complexes due to their reduced k,,Jk,. A decrease in the overall temperature factor by 66%caused by cooling from 295 K to 120 K, as calculated from Wilson plots, indicates a reduction in the fall off of intensities as a function of resolution and lower mean square displacement about the average atomic position at 120 K relative to that at 295 K. A decrease in the unit cell dimensions of approximately 1% is accompanied by a reduction in the protein surface area of 1.2% (as determined by the Connolly surface algorithm" using a 1.4 A probe sphere) and a reduction of the radius of gyration by 0.25% for all protein atoms and 0.19% for main chain atoms. The root mean square (RMS) deviation of the C, atoms is 0.178 A. Most of the larger RMS deviations occur for residues with high temperature factors. Concerted movements of secondary structural domains can also be seen when comparing the 295 K and 120 K structures. METHODS Crystals of rat trypsin** were grown by vapor difb i o n in 55% magnesium sulfate (anhydrous), 10 mM calcium chloride, 75-100 mM benzamidine, and 50 mM Tris buffer pH 8.0, a pH where the enzyme is optimally active. The protein concentration was approximately 30 mg/ml. The crystals lie in the cubic space group 123 with unit cell dimensions of 124.38 A a t 295 K and 123.12 2 .14 A at 120 K as measured on a Nicolet P2, diffractometer.
TABLE I. Statistics of Data Collection and Reduction Using the XENGEN Package13 for the S195C Mutant of Rat Trvusin at 120 K
Resolution range -2.88 2.88-2.28 2.28-1.99 1.99-1.81 1.81-1.68 1.68-1.59 -1.59
Number of independent % of reflections total R,,,t collected 7408 5.67 100 100 11.04 7198 7122 15.15 100 100 22.13 7053 100 28.14 7118 81.6 28.65 5714 96.9 10.51 41613
Average Ila(I)
82.1 34.3 19.1 10.2 6.4 4.0 27.2
N
Low Temperature D a t a Collection Freezing was performed by picking the crystal from the drop on a thin glass fiber after coating the crystal with a thin layer of Paratone-N and removal of excess solvent, then quickly plunging into liquid ethane kept near its solidification point in a dewar of liquid nitrogen. This "shock freezing" approach was originated by Parak et al." in studies of myoglobin by Mossbauer spectroscopy and was subsequently adapted for single crystal X-ray data collection.12 Recently Hope' has shown that the method is useful for a number of protein crystal systems. The crystal was rapidly transferred into a prealigned stream of cold nitrogen gas maintained at 120 K. The cold nitrogen gas was supplied from a Syntex LT-1 modified to use boil off nitrogen from the dewar and also for use on various data collection systems in our lab and at synchrotron facilities. Data was collected using CuK, radiation (A = 1.54 A) from a Rigaku rotating anode generator with graphite monochrometer and a Xentronics area detector system. The XENGEN data reduction package was of 10.51% for inused for data r e d ~ c t i 0 n . Rsymm l~ tensities down to 1.59 A was obtained from the 7fold redundant data set. Upon freezing, the unit cell length decreases by approximately 1% to 123.12 A. Area detector data statistics are shown in Table I. Refinement
*In this paper the residues are numbered continuously from 1 through 223 and the residue number in the chymotrypsin numbering system for serine proteases is placed in brackets. When referring to the mutants, the chymotrypsin number is used, e.g., S195C is used for the serine to cysteine mutation of residue 177 and D102N is the aspartate to asparagine mutation at residue 84. The numbers of the residues at the catalytic triad for the wild type trypsin are histidine 40[571, aspartate 84[1021, and serine 177[1951. **Recombinant trypsins were expressed, purified and charicterized a s described in Higaki et al.38.
The structure of rat trypsin was solved initially by molecular replacement from the model of bovine t r y p ~ i n . ' ~ The . ' ~ model for the 120 K structure was refined using a starting model of the I23 form of benzamidine-inhibited D102N rat trypsin originally solved to 2.8 A by Stroud," and subsequently refined against a 2.3 A data set to an R factor of 22.4% (J. Finer-Moore, J. Swedlow, and R. Stroud,
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LOW TEMPERATURE TRYPSIN
TABLE 11. Summary of Refinement Statistics for 120 K and 295 K Structures* t RCW&
Resolution range Number of independent reflections
120 K 17.4 12.0-1.59 h; 37692
295 K 14.2 12.0-2.30 h; 12129
Standard deviations from ideal geometry Bond distance (h;) 1-3 distance (A) Bond angle (degrees) Restrained B factor differences Main chain bond B (A2) Main chain angle B (A2) Side chain bond B (A2) Side chain anele B (A2)
120 K
295 K
.025 .049 3.1
.020 .065 4.2
1.470
1.572 2.365 5.683 5.116
2.045 4.276 4.641
*Number of independent reflections refers to those greater than zero. Bond distances are the distances between nearest neighbor atoms. 1-3 distances are the distances between next nearest neighbor atoms. Bond angles are the angles between next nearest neighbor atoms. Main chain bond Bs are the differences in the B factors of main chain nearest neighbor atoms. Main chain angle Bs are the differences in the B factors of main chain next nearest neighbor atoms. Side chain bond Bs are the differences in the B factors of side chain nearest neighbor atoms. Side chain bond Bs are the differencesB factors of side chain next nearest neighbor atoms. The definitions of the structural parameters listed below are as in Hendrickson and Konnert"
unpublished results). The two atoms which differ between the D102N and S195C mutants were replaced using FROD0.17 Several cycles of stereochemically restrained, least-squares refinement using PROLSQ,l' of this starting model using the low temperature data, plus rebuilding using FRODO on an Evans & Sutherland PS330, led to an R factor of 17.4%using 37692 independent reflections between 12.0 and 1.59 A which are greater than zero. This model was then used as the starting model for the 2.3 A room temperature data and the R factor was reduced to 14.3%for 12129 reflections greater than zero between 12.0 and 2.3 A by PROLSQ with no rebuilding necessary except for the removal of waters which are not found in the 295 K structure. This reduction in R factor for the room temperature model most likely arises from the improved state of refinement of the new starting model. Several alternating cycles of B factor and occupancy refinement were used, similar to the method used originally for refining the 120 K model. Maps of the 120 K and 295 K structures were constructed from (2F,,-Fc)e2miae and (F,,-Fc)e2miac.A summary of the refinement statistics is given in Table 11. Residues which possess side chains that adopt two alternate positions were refined as having an occupancy of 0.5 for each conformation. The occupancies of the oxygen atoms in the water molecules were refined by several cycles of PROLSQ with alternating cycles of temperature factor and occupancy refinement.
RESULTS Increase in Resolution Wilson plots'' of the two data sets used are shown in Figure 1. Determination of the overall B factor (temperature factor) from the slopes of the best fit lines indicate that the overall B factor is significantly reduced from 26.38 hi2 a t 295 K to 9.61 A2 a t 120 K. The average B factors determined from the refined structures using the non solvent atoms are = 8.80 A2 and = 21.73 A2. As can be seen from the Wilson plots, and as a direct consequence of the lower B factor, the fall off of intensities as a function of resolution is greatly reduced for the low temperature data. This does not appear to be a general result. Crystal systems where the predominant component of the temperature factor is from static disorder (as opposed to vibrational motion) should not show a significant increase in resolution a t lower temperatures since lowering the temperature should only decrease the component of the temperature factor due to vibrational motion. Also a number of crystals show a n increase in the mosaicity upon freezing (e.g., reference 20). Accuracy of Coordinates The accuracy of the atomic positions is difficult to assess. The method of Luzzatti21 is frequently used in X-ray crystallography to estimate the error in the atomic positions by plotting the crystallographic R
174
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2
1
0
st1-2 Fig. 1. Plots of In [4>]lsum (P’2)versus sin2(0)/h2,as in Wilson,’* for the 120 K (squares) and 295 K data (triangles).Overall 6factors were determined from the line least-squares fit from 3.5 to 1.59A for the 120 K data (8=9.61A’) and 3.5 to 2.30 A for the 295 K data (6=26.38A’).
0.60
0.50
0.40
d
0.3G
0.20
0.10
-0.00 0.0
0.2
0.4
sidtheta) Fig. 2. Plots of R versus sin(0) as in Luzzatti” for the 120 K (squares) and 295 K (triangles) structures. The curves represent levels of error corresponding to, from bottom to top, 0.10, 0.15, 0.20.and 0.30A.
175
LOW TEMPERATURE TRYPSIN
30
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8
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