Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

Structural bases of lectin-carbohydrate affinities: comparison with protein-folding energetics.

We have made a comparative structure based analysis of the thermodynamics of lectin-carbohydrate (L-C) binding and protein folding. Examination of the total change in accessible surface area in those processes revealed a much larger decrease in free energy per unit of area buried in the case of L-C associations. According to our analysis, this larger stabilization of L-C interactions arises from a more favorable enthalpy of burying a unit of polar surface area, and from higher proportions of polar areas. Hydrogen bonds present at 14 L-C interfaces were identified, and their overall characteristics were compared to those reported before for hydrogen bonds in protein structures. Three major factors might explain why polar-polar interactions are stronger in L-C binding than in protein folding: (1) higher surface density of hydrogen bonds; (2) better hydrogen-bonding geometry; (3) larger proportion of hydrogen bonds involving charged groups. Theoretically, the binding entropy can be partitioned into three main contributions: entropy changes due to surface desolvation, entropy losses arising from freezing rotatable bonds, and entropic effects that result from restricting translation and overall rotation motions. These contributions were estimated from structural information and added up to give calculated binding entropies. Good correlation between experimental and calculated values was observed when solvation effects were treated according to a parametrization developed by other authors from protein folding studies. Finally, our structural parametrization gave calculated free energies that deviate from experimental values by 1.1 kcal/mol on the average; this amounts to an uncertainty of one order of magnitude in the binding constant.     

15N backbone dynamics of the S-peptide from ribonuclease A in its free and S-protein bound forms: toward a site-specific analysis of entropy changes upon folding.

Backbone 15N relaxation parameters (R1, R2, 1H-15N NOE) have been measured for a 22-residue recombinant variant of the S-peptide in its free and S-protein bound forms. NMR relaxation data were analyzed using the "model-free" approach (Lipari & Szabo, 1982). Order parameters obtained from "model-free" simulations were used to calculate 1H-15N bond vector entropies using a recently described method (Yang & Kay, 1996), in which the form of the probability density function for bond vector fluctuations is derived from a diffusion-in-a-cone motional model. The average change in 1H-15N bond vector entropies for residues T3-S15, which become ordered upon binding of the S-peptide to the S-protein, is -12.6+/-1.4 J/mol.residue.K. 15N relaxation data suggest a gradient of decreasing entropy values moving from the termini toward the center of the free peptide. The difference between the entropies of the terminal and central residues is about -12 J/mol residue K, a value comparable to that of the average entropy change per residue upon complex formation. Similar entropy gradients are evident in NMR relaxation studies of other denatured proteins. Taken together, these observations suggest denatured proteins may contain entropic contributions from non-local interactions. Consequently, calculations that model the entropy of a residue in a denatured protein as that of a residue in a di- or tri-peptide, might over-estimate the magnitude of entropy changes upon folding.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

Comparison of straight chain and cyclic unnatural amino acids embedded in the core of staphylococcal nuclease.

We have determined by X-ray crystallography the structures of several variants of staphylococcal nuclease with long flexible straight chain and equivalent length cyclic unnatural amino acid side chains embedded in the protein core. The terminal atoms in the straight side chains are not well defined by the observed electron density even though they remain buried within the protein interior. We have previously observed this behavior and have suggested that it may arise from the addition of side-chain vibrational and oscillational motions with each bond as a side chain grows away from the relatively rigid protein main chain and/or the population of multiple rotamers (Wynn R, Harkins P, Richards FM. Fox RO. 1996. Mobile unnatural amino acid side chains in the core of staphylococcal nuclease. Protein Sci 5:1026-1031). Reduction of the number of degrees of freedom by cyclization of a side chain would be expected to constrain these motions. These side chains are in fact well defined in the structures described here. Over-packing of the protein core results in a 1.0 A shift of helix 1 away from the site of mutation. Additionally, we have determined the structure of a side chain containing a single hydrogen to fluorine atom replacement on a methyl group. A fluorine atom is intermediate in size between methyl group and a hydrogen atom. The fluorine atom is observed in a single position indicating it does not rotate like methyl hydrogen atoms. This change also causes subtle differences in the packing interactions.     

Thermodynamics of amino acid side-chain internal rotations

The absolute Gibbs energy, enthalpy and entropy of each of the internal rotations found in protein side chains has been calculated. The calculation requires the moments of inertia of the side chains about each bond, the potential energy barrier and the symmetry number and gives the maximum possible thermodynamic consequences of restricting side chain motion when a protein folds. Hindering side chain internal rotations is unfavourable in terms of Gibbs energy and entropy; it is enthalpically favourable at 0 K. At room temperature, it is estimated that the adverse entropy of hindering buried side chain internal rotation is only 25% of the absolute entropy. The difference between absolute entropies in the folded and unfolded states gives the entropy change for folding. The estimated Gibbs energy change for restricting each residue correlates moderately well with the probability of that residue being found on the folded protein surface, rather than in the protein interior (where motion is restricted).     

Stability of yeast iso-1-ferricytochrome c as a function of pH and temperature.

Absorbance-detected thermal denaturation studies of the C102T variant of Saccharomyces cerevisiae iso-1-ferricytochrome c were performed between pH 3 and 5. Thermal denaturation in this pH range is reversible, shows no concentration dependence, and is consistent with a 2-state model. Values for free energy (delta GD), enthalpy (delta HD), and entropy (delta SD) of denaturation were determined as functions of pH and temperature. The value of delta GD at 300 K, pH 4.6, is 5.1 +/- 0.3 kcal mol-1. The change in molar heat capacity upon denaturation (delta Cp), determined by the temperature dependence of delta HD as a function of pH (1.37 +/- 0.06 kcal mol-1 K-1), agrees with the value determined by differential scanning calorimetry. pH-dependent changes in the Soret region indicate that a group or groups in the heme environment of the denatured protein, probably 1 or both heme propionates, ionize with a pK near 4. The C102T variant exhibits both enthalpy and entropy convergence with a delta HD of 1.30 kcal mol-1 residue-1 at 373.6 K and a delta SD of 4.24 cal mol-1 K-1 residue-1 at 385.2 K. These values agree with those for other single-domain, globular proteins.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Backbone Flexibility of CDR3 and Immune Recognition of Antigens

Conformational entropy is an important component of protein–protein interactions; however, there is no reliable method for computing this parameter. We have developed a statistical measure of residual backbone entropy in folded proteins by using the ?–ψ distributions of the 20 amino acids in common secondary structures. The backbone entropy patterns of amino acids within helix, sheet or coil form clusters that recapitulate the branching and hydrogen bonding properties of the side chains in the secondary structure type. The same types of residues in coil and sheet have identical backbone entropies, while helix residues have much smaller conformational entropies. We estimated the backbone entropy change for immunoglobulin complementarity-determining regions (CDRs) from the crystal structures of 34 low-affinity T-cell receptors and 40 high-affinity Fabs as a result of the formation of protein complexes. Surprisingly, we discovered that the computed backbone entropy loss of only the CDR3, but not all CDRs, correlated significantly with the kinetic and affinity constants of the 74 selected complexes. Consequently, we propose a simple algorithm to introduce proline mutations that restrict the conformational flexibility of CDRs and enhance the kinetics and affinity of immunoglobulin interactions. Combining the proline mutations with rationally designed mutants from a previous study led to 2400-fold increase in the affinity of the A6 T-cell receptor for Tax-HLAA2. However, this mutational scheme failed to induce significant binding changes in the already-high-affinity C225–Fab/huEGFR interface. Our results will serve as a roadmap to formulate more effective target functions to design immune complexes with improved biological functions.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Thermodynamic investigations of proteins. III. Thermodynamic description of lysozyme.

Standard functions of enthalpy, entropy and the Gibbs energy of native and denatured lysozyme in the range of 0-100 degrees C and pH 1.5-7.0 are represented in three-dimensional projections. The denaturational Gibbs energy change reaches 16 kcal mol-1 at conditions of maximal protein stability (0 degrees C, pH 4.5-7.0) and equals 14.5 kcal mol-1 at 25 degrees C and neutral pH. This result was found to be in agreement with the data reported from guanidine hydrochloride denaturation studies. Partial thermodynamic functions of the conformational and ionizational changes of the protein are obtained from entropy and Gibbs-energy changes in denaturation. The conformational partial entropy and Gibbs-energy change are found to be independent of pH. The pH-dependent partial ionizational entropy and Gibbs-energy changes are induced by normalization of the ionization behaviour of buried groups and cause a decrease of protein stability.     

The Shannon information entropy of protein sequences.

A comprehensive data base is analyzed to determine the Shannon information content of a protein sequence. This information entropy is estimated by three methods: a k-tuplet analysis, a generalized Zipf analysis, and a "Chou-Fasman gambler." The k-tuplet analysis is a "letter" analysis, based on conditional sequence probabilities. The generalized Zipf analysis demonstrates the statistical linguistic qualities of protein sequences and uses the "word" frequency to determine the Shannon entropy. The Zipf analysis and k-tuplet analysis give Shannon entropies of approximately 2.5 bits/amino acid. This entropy is much smaller than the value of 4.18 bits/amino acid obtained from the nonuniform composition of amino acids in proteins. The "Chou-Fasman" gambler is an algorithm based on the Chou-Fasman rules for protein structure. It uses both sequence and secondary structure information to guess at the number of possible amino acids that could appropriately substitute into a sequence. As in the case for the English language, the gambler algorithm gives significantly lower entropies than the k-tuplet analysis. Using these entropies, the number of most probable protein sequences can be calculated. The number of most probable protein sequences is much less than the number of possible sequences but is still much larger than the number of sequences thought to have existed throughout evolution. Implications of these results for mutagenesis experiments are discussed.     

Protein folding in the absence of chemical denaturants. Reversible pressure denaturation of the noncovalent complex formed by the association of two protein fragments

Small monomeric proteins are the best models for studying protein folding, but they are often too stable for denaturation using pressure as the sole perturbant. In the present work we subject [CI-2(1-40).(41-64)], a noncovalent complex formed by the association of two complementary fragments of the chymotrypsin inhibitor-2, to high pressure to investigate the folding mechanism of a model protein. Pressures up to 3.5 kilobar do not affect the intact protein, but it can be unfolded reversibly by pressure in the presence of subdenaturing concentrations of guanidine chloride, with free energy and molar volume changes of 2.5 kcal mol-1 and 42.5 ml mol-1, respectively. In contrast, the complex can be reversibly denatured by high pressure without the addition of chemical denaturants. However, the process is clearly independent of the protein concentration, indicating lack of dissociation. We determined a change in the free energy of 1.4 kcal mol-1 and a molar volume change of 35 ml mol-1 for the pressure denaturation of the complex. A persistent quenching of the tryptophan adds further evidence for the presence of residual structure in the high pressure-denatured state. This state also appears to be compact as the small volume change indicates, compared with pressure denaturation of naturally occurring dimers. Based on observations of a number of pressure-denatured states and on characteristics of large CI-2 fragments with a solvent accessible core but maintaining tertiary interactions, the structure of the pressure-denatured state of the CI-2 complex could be explained by an ordered molten globule-like conformation.     

Investigation of a side-chain-side-chain hydrogen bond by mutagenesis, thermodynamics, and NMR spectroscopy.

Anomalous NMR behavior of the hydroxyl proton resonance for Ser 31 has been reported for histidine-containing protein (HPr) from two microorganisms: Escherichia coli and Staphylococcus aureus. The unusual slow exchange and chemical shift exhibited by the resonance led to the proposal that the hydroxyl group is involved in a strong hydrogen bond. To test this hypothesis and to characterize the importance of such an interaction, a mutant in which Ser 31 is replaced by an alanine was generated in HPr from Escherichia coli. The activity, stability, and structure of the mutant HPr were assessed using a reconstituted assay system, analysis of solvent denaturation curves, and NMR, respectively. Substitution of Ser 31 yields a fully functional protein that is only slightly less stable (delta delta G(folding) = 0.46 +/- 0.15 kcal mol-1) than the wild type. The NMR results confirm the identity of the hydrogen bond acceptor as Asp 69 and reveal that it exists as the gauche- conformer in wild-type HPr in solution but exhibits conformational averaging in the mutant protein. The side chain of Asp 69 interacts with two main-chain amide proteins in addition to its interaction with the side chain of Ser 31 in the wild-type protein. These results indicate that removal of the serine has led to the loss of all three hydrogen bond interactions involving Asp 69, suggesting a cooperative network of interactions. A complete analysis of the thermodynamics was performed in which differences in side-chain hydrophobicity and conformational entropy between the two proteins are accounted for.(ABSTRACT TRUNCATED AT 250 WORDS)     

Backbone entropy of loops as a measure of their flexibility: Application to a Ras protein simulated by molecular dynamics

The flexibility of surface loops plays an important role in protein–protein and protein–peptide recognition; it is commonly studied by Molecular Dynamics or Monte Carlo simulations. We propose to measure the relative backbone flexibility of loops by the difference in their backbone conformational entropies, which are calculated here with the local states (LS) method of Meirovitch. Thus, one can compare the entropies of loops of the same protein or, under certain simulation conditions, of different proteins. These loops should be equal in size but can differ in their sequence of amino acids residues. This methodology is applied successfully to three segments of 10 residues of a Ras protein simulated by the stochastic boundary molecular dynamics procedure. For the first time estimates of backbone entropy differences are obtained, and their correlation with B factors is pointed out; for example, the segments which consist of residues 60–65 and 112–117 have average B factors of 67 and 18 Ų, respectively, and entropy difference T ΔS = 5.4 ± 0.1 kcal/mol at T = 300 K. In a large number of recent publications the entropy due to the fast motions (on the ps-ns time scale) of N–H and C–H vectors has been obtained from their order parameter, measured in nuclear magnetic resonance spin relaxation experiments. This enables one to estimate differences in the entropy of protein segments due to folding–unfolding transitions, for example. However, the vectors are assumed to be independent, and the effect of the neglected correlations is unknown; our method is expected to become an important tool for assessing this approximation. The present calculations, obtained with the LS method, suggest that the errors involved in experimental entropy differences might not be large; however, this should be verified in each case. Potential applications of entropy calculations to rational drug design are discussed. Proteins 29:127–140, 1997. © 1997 Wiley-Liss, Inc.     

Insights into the local residual entropy of proteins provided by NMR relaxation.

A simple model is used to illustrate the relationship between the dynamics measured by NMR relaxation methods and the local residual entropy of proteins. The expected local dynamic behavior of well-packed extended amino acid side chains are described by employing a one-dimensional vibrator that encapsulates both the spatial and temporal character of the motion. This model is then related to entropy and to the generalized order parameter of the popular "model-free" treatment often used in the analysis of NMR relaxation data. Simulations indicate that order parameters observed for the methyl symmetry axes in, for example, human ubiquitin correspond to significant local entropies. These observations have obvious significance for the issue of the physical basis of protein structure, dynamics, and stability.     

Binding characteristics of a major thyroid hormone metabolite, 3,3',5'-triiodo-L-thyronine, to bovine serum albumin as measured by fluorescence

The interaction between a major thyroid hormone metabolite, 3,3',5'-triiodo-L-thyronine and bovine serum albumin was investigated by fluorescence measurements. The apparent binding constants were obtained at various pHs assuming the equivalence and independence of the interaction sites on the protein from the fluorescence titration curves. The maximum binding was attained at pH 8.0, and the apparent binding constant was (5.28 +/- 0.13).10(5) M-1 with one binding site per albumin molecule. Thermodynamic parameters were also determined from the van't Hoff plot of the apparent binding constants at pH 7.5. The free energy change, enthalpy change and entropy change were -7.70 +/- 0.09 kcal.mol-1, -4.59 kcal.mol-1 and 10.2 e.u., respectively.     

Rotamer libraries and probabilities of transition between rotamers for the side chains in protein-protein binding

Conformational changes in the side chains are essential for protein-protein binding. Rotameric states and unbound- to-bound conformational changes in the surface residues were systematically studied on a representative set of protein complexes. The side-chain conformations were mapped onto dihedral angles space. The variable threshold algorithm was developed to cluster the dihedral angle distributions and to derive rotamers, defined as the most probable conformation in a cluster. Six rotamer libraries were generated: full surface, surface noninterface, and surface interface-each for bound and unbound states. The libraries were used to calculate the probabilities of the rotamer transitions upon binding. The stability of amino acids was quantified based on the transition maps. The noninterface residues' stability was higher than that of the interface. Long side chains with three or four dihedral angles were less stable than the shorter ones. The transitions between the rotamers at the interface occurred more frequently than on the noninterface surface. Most side chains changed conformation within the same rotamer or moved to an adjacent rotamer. The highest percentage of the transitions was observed primarily between the two most occupied rotamers. The probability of the transition between rotamers increased with the decrease of the rotamer stability. The analysis revealed characteristics of the surface side-chain conformational transitions that can be utilized in flexible docking protocols.     

Entropies of coding and noncoding sequences of DNA and proteins.

The entropies of protein coding genes from Escherichia coli were calculated according to Boltzmann's formula. Entropies of the coding regions were compared to the entropies of noncoding or miscoding ones. With nucleotides as code units, the entropies of the coding regions, when compared to the entropies of complete sequences (leader and coding region as well as trailer), were seen to be lower but with a marginal statistical significance. With triplets of nucleotides as code units, the entropies of correct reading frames were significantly lower than the entropies of frameshifts +1 and -1. With amino acids as code units, the results were opposite: Biologically functional proteins had significantly higher entropies than proteins translated from the frameshifted sequences. We attempt to explain this paradox with the hypothesis that the genetic code may have the ability of lowering information content (increasing entropy) of proteins while translating them from DNA. This ability might be beneficial to bacteria because it would make the functional proteins more probable (having a higher entropy) than nonfunctional proteins translated from frameshifted sequences.