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PubMed1997

A Shannon entropy analysis of immunoglobulin and T cell receptor.

In 1970, before any antigen-bound immunoglobulin structure had been solved, Elvin Kabat proposed that regions of high amino acid diversity would be the antigen binding sites of immunoglobulin (Kabat, 1970). Conversely, sites of low variability were proposed to be structural, framework regions. This variability was defined by Wu and Kabat as the number of different amino acids found at a site divided by the relative frequency of the most common amino acid at that site (Wu and Kabat, 1970). Several groups have subsequently devised improvements of Kabat-Wu variability analysis (Litwin and Jores, 1992). While these methods are somewhat better than Kabat-Wu, they still suffer from Kabat-Wu's basic limitation: they account for only the most common one or two amino acids in estimating diversity. This leads to underestimates of low diversities and exaggerations of high diversities. Shannon information analysis eliminates serious bias and is more stable than Kabat-Wu and second generation measures of diversity (Jores et al. 1990; Wu and Kabat, 1970). Statistical reliability can be measured using Shannon analysis, and Shannon measurements can be provided with error estimates. Here we use Shannon's method to analyze the amino acid diversity at each site of T cell receptor Valpha and Vbeta to identify complementarity determining regions and framework sites. Our results reveal that the T cell receptor is significantly more diverse than immunoglobulin-suggesting T cell receptor has more than the previously-discovered four complementarity determining regions. These new complementarity determining regions may represent a larger antigen combining site, additional combining sites, or an evolutionary strategy to avoid inappropriate interaction with other molecules.

Animals↗
PubMed2002

On the role of the macromolecular phase transitions in biology in response to change in solution volume or macromolecular composition: action as an entropy buffer.

We have used numerical simulation to demonstrate the potential for macromolecular precipitate solution phase transitions existing within the cell, to play a role in the minimization of changes in location or quaternary state of other macromolecular components, predicted to accompany changes in cell volume. For our modeling we have employed thermodynamic relations that take into account the large effects upon the thermodynamic activity coefficient produced by a solution environment that is highly volume occupied due to the presence of high concentrations of soluble macromolecule. The theoretical approach adopted, along with the simulated results, provide a framework for the interpretation of certain proteins' behavior (e.g. cytoskeletal elements such as tubulin and actin and possibly some prion structures) in response to cell volume change.

Buffers↗
PubMed2002

Maximum-entropy calculation of free energy distributions in tRNAs.

We have previously shown that the distribution function describing the probability that a biological macromolecule picked at random has a particular enthalpy value can be calculated from the temperature dependence of the heat capacity of the macromolecule. The free energy as a function of enthalpy (free energy distribution) can then be determined from the enthalpy probability distribution. In addition, the free energy distribution at an arbitrary temperature can be calculated from the free energy distribution at a reference temperature. Here we apply this approach to a family of similar macromolecules, namely a set of transfer RNAs, specifically tRNA(Phe), tRNA(Val), tRNA(Met), tRNA(Ser), tRNA(Asp) and tRNA(Ile). Using published heat-capacity data, we calculate the enthalpy probability distribution functions for all of these molecules at five different temperatures covering the range from 30 to 80 degrees C. We then use these distributions to give a reference free-energy distribution, from which the thermodynamics at any temperature can be calculated for each species. We compare the reference free-energy distribution for the five tRNAs and find that, while the overall form of the distributions is similar, the local behavior of the functions varies considerably between the species.

Entropy↗
PubMed2002

The proton affinity of proline analogs using the kinetic method with full entropy analysis.

The proton affinity of proline analogs, L-azetidine-2-carboxylic acid (Aze), L-proline (Pro), and L-pipecolic acid (Pip), have been measured using the Armentrout modification of the extended kinetic method in a quadrupole ion trap instrument. Experimental values of 223.0 +/- 1.5, 224.9 +/- 1.6, and 225.6 +/- 1.6 kcal/mol have been determined for the 298K proton affinities of Aze, Pro, and Pip respectively. High level theoretical calculations using both MP2 and B3LYP methods at a variety of basis sets were carried out in order to give theoretical predictions for the 298 K proton affinity and gas phase basicity of all three analogs. Recommended values for the gas phase basicity and proton affinity for proline based on our work and other recent determinations are 216 +/- 2 and 224 +/- 2 kcal/mol.

Computational Biology↗
PubMed2003

On the contribution of intramolecular H-bonding entropy to the conformational stability of alanine conformations.

The experimental and theoretical rotamerization constants for the rotameric equilibrium between the two most stable conformations of the alpha-amino acid alanine are compared. The experimental technique of matrix-isolation Fourier transform infrared spectroscopy in combination with the density functional theory (DFT) (B3LYP) and the 6-31++G** basis set is used for this study. A large disagreement between the experimental and theoretical value of the equilibrium constant is found. A relatively strong intramolecular H-bond in conformation II is at the origin of this discrepancy. From the difference between the experimental and theoretical rotamerization constant, a DeltaS degrees value of -6.6 J K(-1) mol(-1) is found for the intramolecular H-bond formation.

Alanine↗
PubMed2002

Role of entropy in protein thermostability: folding kinetics of a hyperthermophilic cold shock protein at high temperatures using 19F NMR.

We used (19)F NMR to extend the temperature range accessible to detailed kinetic and equilibrium studies of a hyperthermophilic protein. Employing an optimized incorporation strategy, the small cold shock protein from the bacterium Thermotoga maritima (TmCsp) was labeled with 5-fluorotryptophan. Although chaotropically induced unfolding transitions revealed a significant decrease in the stabilization free energy upon fluorine labeling, the protein's kinetic folding mechanism is conserved. Temperature- and guanidinium chloride-dependent equilibrium unfolding transitions monitored by (19)F NMR agree well with the results from optical spectroscopy, and provide a stringent test of the two-state folding character of TmCsp. Folding and unfolding rate constants at high temperatures were determined from the (19)F NMR spectra close to the midpoint of thermal unfolding by global line shape analysis. In combination with results from stopped-flow experiments at lower temperatures, they show that the folding rate constant of TmCsp and its temperature dependence closely resemble those of its mesophilic homologue from Bacillus subtilis, BsCspB. However, the unfolding rate constant of TmCsp is two orders of magnitude lower over the entire temperature range that was investigated. Consequently, the difference in conformational stability between the two proteins is solely due to the unfolding rate constant over a wide temperature range. A thermodynamic analysis points to an important role of entropic factors in the stabilization of TmCsp relative to its mesophilic homologues.

Bacterial Proteins↗
PubMed2004

Entropy-driven folding of an RNA helical junction: an isothermal titration calorimetric analysis of the hammerhead ribozyme.

Helical junctions are extremely common motifs in naturally occurring RNAs, but little is known about the thermodynamics that drive their folding. Studies of junction folding face several challenges: non-two-state folding behavior, superposition of secondary and tertiary structural energetics, and drastically opposing enthalpic and entropic contributions to folding. Here we describe a thermodynamic dissection of the folding of the hammerhead ribozyme, a three-way RNA helical junction, by using isothermal titration calorimetry of bimolecular RNA constructs. By using this method, we show that tertiary folding of the hammerhead core occurs with a highly unfavorable enthalpy change, and is therefore entropically driven. Furthermore, the enthalpies and heat capacities of core folding are the same whether supported by monovalent or divalent ions. These properties appear to be general to the core sequence of bimolecular hammerhead constructs. We present a model for the ion-induced folding of the hammerhead core that is similar to those advanced for the folding of much larger RNAs, involving ion-induced collapse to a structured, non-native state accompanied by rearrangement of core residues to produce the native fold. In agreement with previous enzymological and structural studies, our thermodynamic data suggest that the hammerhead structure is stabilized in vitro predominantly by diffusely bound ions. Our approach addresses several significant challenges that accompany the study of junction folding, and should prove useful in defining the thermodynamic determinants of stability in these important RNA motifs.

Animals↗
PubMed2004

Entropy effects on protein hinges: the reaction catalyzed by triosephosphate isomerase.

Many proteins utilize segmental motions to catalyze a specific reaction. The Omega loop of triosephosphate isomerase (TIM) is important for preventing the loss of the reactive enediol(ate) intermediate. The loop opens and closes even in the absence of the ligand, and the loop itself does not change conformation during movement. The conformational changes are localized to two hinges at the loop termini. Glycine is never observed in native TIM hinge sequences. In this paper, the hypothesis that limited access to conformational space is a requirement for protein hinges involved in catalysis was tested. The N-terminal hinge was mutated to P166/V167G/W168G (PGG), and the C-terminal hinge was mutated to K174G/T175G/A176G (GGG) in chicken TIM. The single-hinge mutants PGG and GGG had k(cat) values 200-fold lower than that of the wild type and K(m) values 10-fold higher. The k(cat) of double-hinge mutant P166/V167G/W168G/K174G/T175G/A176G was reduced 2500-fold; the K(m) was 10-fold higher. A combination of primary kinetic isotope effect measurements, isothermal calorimetric measurements, and (31)P NMR spectroscopic titration with the inhibitor 2-phosphoglycolate revealed that the mutants have a different ligand-binding mode than that of the wild-type enzyme. The predominant conformations of the mutants even in the presence of the inhibitor are loop-open conformations. In conclusion, mutation of the hinge residues to glycine resulted in the sampling of many more hinge conformations with the consequence that the population of the active-closed conformation is reduced. This reduced population results in a reduced catalytic activity.

Animals↗
PubMed1999

Thermodynamic and kinetic studies on carbon-cobalt bond homolysis by ribonucleoside triphosphate reductase: the importance of entropy in catalysis.

In the catalytic mechanism of nucleotide reduction, ribonucleoside triphosphate reductase (RTPR) from Lactobacillus leichmannii catalyzes the homolytic cleavage of the carbon-cobalt bond of adenosylcobalamin (AdoCbl) at a rate approximately 10(11)-fold faster than the uncatalyzed reaction. Model systems have suggested hypotheses for the thermodynamic basis of this reaction, but relevant measurements of the enzymatic reaction have been lacking. To address this question in a system for which the microscopic rate constants can be measured as a function of temperature, we examined the RTPR-catalyzed exchange reaction. RTPR, in the presence of allosteric effector dGTP and in the absence of substrate, catalyzes carbon-cobalt bond homolysis and formation of a thiyl radical from an active-site cysteine in a concerted fashion [Licht, S., Booker, S. , Stubbe, J. (1999) Biochemistry 38, 1221-1233]. Both the kinetics of cob(II)alamin formation and the amounts of cob(II)alamin formed have been studied as a function of AdoCbl concentration and temperature. Analysis of these data has allowed calculation of a DeltaH of 20 kcal/mol, a DeltaS of 70 cal mol-1 K-1, a DeltaH of 46 kcal/mol, and a DeltaS of 96 cal mol-1 K-1 for carbon-cobalt bond homolysis/thiyl radical formation. The results further show that the enzyme perturbs the equilibrium between the reactant (AdoCbl-bound) state and the product (cob(II)alamin/5'-deoxyadenosine (5'-dA)/thiyl radical state, making them approximately equal in energy. The thermodynamic perturbation, in addition to transition-state stabilization, is required for the large rate acceleration observed. Entropic, rather than enthalpic, factors make the largest contribution in both cases.

Allosteric Regulation↗
PubMed2005

Favorable entropy of aromatic clusters in thermophilic proteins.

Aromatic clusters, found with increased frequency in a set of thermophilic proteins, confer an entropic advantage over mesophilic analogues through introduction of large-amplitude oscillations; this is a source of improved free energy at high temperatures.

Amino Acid Sequence↗