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note
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The multinomial probability for all 20 amino acids gives the probability of randomly observing a given amino acid distribution at a site but is degenerate given the redistribution of amino acids with a similar mean frequency. For example, consider a site that displays a distribution of 0.4 Ala, 0.4 Asp, and 0.2 Ile in the overall alignment and changes to 0.4 Ala, 0.2 Asp, and 0.4 Ile upon perturbation at another site. Because the mean frequency of Asp and Ile is nearly identical (Fig. 1A), the multinomial probability of these two distributions is the same, although the significant reorganization of chemical character suggests that these positions are indeed coupled. Description of the site as vectors of individual amino acid probabilities accounts for all such cases because each amino acid distribution maps to a unique vector.
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25
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0345061579
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note
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For conventional statistical mechanical systems at equilibrium, the temperature (T) of an ensemble is proportional to the mean velocity of state transitions and defines the fundamental energy unit kT, where k is Boltzmann's constant (10). Sites on a MSA can be seen as individual statistical mechanical systems that represent discrete states in an overall state space of amino acid frequencies. The "temperature" (T*) of an ensemble of such systems is again related to the mean transition rates between states, but the energy unit in such a system (kT*) is not necessarily related to that for conventional mechanical systems.
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26
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0344630994
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note
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x, we created histograms of amino acids for all 36,498 entries (as of October 1998) in the Swiss-Prot database of eukaryotic nonredundant proteins and calculated the mean values (Fig. 1A). Because all structural and functional information has been scrambled in this analysis, the frequencies of amino acids should represent that which is expected without any functional evolutionary constraint. Stirling's approximation was used for the evaluation of large factorials (> 170).
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27
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0344199283
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-
note
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For visualization and analysis, statistical energies were arbitrarily scaled by 0.01 for compatibility with GRASP and output in Microsoft Excel format or were written to a Protein Data Bank file of a representative member of the fold family. Mapping of statistical energies onto tertiary structures was done with GRASP (29). In evaluating statistical coupling, distributions at sites before and after perturbation were normalized for comparison.
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31
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0344630992
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unpublished data
-
Eukaryotic PDZ domains were collected from the nonredundant database of protein sequences with PSI-BLAST (30) (e score ≤ 0.001); four PDZ domains with known structures [(14-16); M. Socolich and R. Ranganathan, unpublished data] were used in initial searches. Alignments were created with PILEUP (Genetics Computer Group, Madison, WI), followed by structure-based manual alignment (31).
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35
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0345061576
-
-
note
-
Single-letter abbreviations for the amino acid residues are as follows: A, Ala; C, Cys; D, Asp; E, Glu; F, Phe; G, Gly; H, His; I, Ile; K, Lys; L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R, Arg; S, Ser; T, Thr; V, Val; W, Trp; X, any amino acid; and Y, Tyr.
-
-
-
-
36
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0344199277
-
-
note
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The numbering scheme for both PDZ and POZ domains used is consistent with that reported for the structures used for mapping statistical energies (14, 24).
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-
-
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37
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0344199278
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note
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2-terminal TMR adduct and were freshly diluted from a single batch of 6 μM frozen aliquots for binding measurements. For all measurements, we used the binding peptide (or mutants thereof, as indicated) co-crystallized in the original structure determination (14). Energy transfer was followed by quenching of fluorescence at 508 nm (corrected for peptide fluorescence). Transfer efficiencies measured for four or five peptide concentrations covering a 2 log-order range around the dissociation constant were used for each binding-energy calculation; each individual measurement was made three to five times. Data were fit to the Hill equation (Origin, Micro-Cat Software, Northampton, MA).
-
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-
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38
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0345061573
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note
-
Site-directed mutagenesis on the rat PSD-95 third PDZ domain (residues 294 through 402) was carried out with standard polymerase chain reaction-based techniques. Domains were expressed as COOH-terminal fusions with EGFP (32) using the pRSET-B vector (Invitrogen) in Escherichia coli [strain BL21(DE3), Stratagene]. Cultures (500 ml) in Terrific broth were grown to an optical density (600 nm) of 1.2 at 37°C, induced for 4 hours with 100 μM isopropyl-β-D-thiogalactopyranoside and harvested. Cells were lysed with B-PER (Pierce, Rockford, IL); cleared supernatants were batch-bound to a 0.5-ml bed volume of Ni-nitrilotriacetic acid agarose beads (Qiagen, Valencia, CA), prewashed in binding buffer (25 mM tris at pH 8.0, 500 mM NaCl, and 10 mM imidazole) and 0.1% Tween-20, washed with 50 column volumes of binding buffer, and eluted with elution buffer (50 mM tris at pH 8.0, 1 M NaCl, and 200 mM imidazole). The protein was dialyzed overnight into storage buffer (50 mM tris at pH 8.0, 100 mM NaCl, and 1 mM dithiothreitol) at 4°C and used immediately for binding assays or flash frozen and stored at -80°C for later use.
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Esser, L.1
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0345493081
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note
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We thank M. Wall for help with figures, N. Grishin for advice regarding manual sequence alignments, A. Pertsemlidis for help with parsing the Swiss-Prot database, and L. Aravind for communication of data before publication. We are indebted to C. F. Stevens for teaching and important discussions. R.R. is a recipient of the Burroughs-Wellcome Fund New Investigator Award in the Basic Pharmacological Sciences and is an Assistant Investigator of the Howard Hughes Medical Institute.
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