Limited validity of group additivity for the folding energetics of the peptide group

The principle of group additivity is a standard feature of analyses of the energetics of protein folding, but it is known that it may not always be valid for the polar peptide group. The neighboring residue effect shows that group additivity is not strictly valid for a heteropeptide. We show here that group additivity fails seriously for peptide groups close to either peptide end, even for a homopeptide that has blocked end groups with no formal charges involved. The failure of group additivity is caused by the electrostatic character of the solvation of peptide polar groups and is illustrated with values of the electrostatic solvation free energy (ESF) calculated by DelPhi. Solvation free energies and enthalpies are known experimentally for monoamides and are often used to model the solvation of peptide groups, but ESF results show that monoamide values are very different from those of peptide groups. A main cause of the difference is that peptide solvation depends on the dipole-dipole interactions made between adjacent peptide groups, which vary with peptide conformation. Ligands that interact with the peptide backbone by an electrostatic mechanism could show a similar peptide end effect, and hydrogen exchange results from the literature confirm that exchange rates are position-dependent close to peptide ends.     

Relationship between heterozygosity and quantitative traits: intralocus interactions and multiple-locus averaging

The dependence of the expression of genotypic values (Y) on gene dosage (X) have been analyzed for four types of intralocus interactions (additivity, dominance, overdominance, and neutrality) using a linear model. Artificial numerical examples have been used to demonstrate that X and Y are positively associated with each other in the cases of additivity, dominance, and overdominance and are not associated in the case of neutrality. The averaging of single-locus genotypic values to obtain multiple-locus genotypes yields different results for different types of intralocus interactions. Genotypic values and individual heterozygosity are positively correlated with each other in the cases of dominance and overdominance and are negatively correlated in the case of additivity. In the case of neutrality, there is still no correlation after averaging. The results obtained and their interpretation suggest a new view on the experimental studies and generalizations on the relationship between heterozygosity and quantitative traits.     

Relationship between heterozygosity and quantitative traits: Intralocus interactions and multiple-locus averaging

The dependence of the expression of genotypic values (Y) on gene dosage (X) have been analyzed for four types of intralocus interactions (additivity, dominance, overdominance, and neutrality) using a linear model. Artificial numerical examples have been used to demonstrate that X and Y are positively associated with each other in the cases of additivity, dominance, and overdominance and are not associated in the case of neutrality. The averaging of single-locus genotypic values to obtain multiple-locus genotypes yields different results for different types of intralocus interactions. Genotypic values and individual heterozygosity are positively correlated with each other in the cases of dominance and overdominance and are negatively correlated in the case of additivity. In the case of neutrality, there is still no correlation after averaging. The results obtained and their interpretation suggest a new view on the experimental studies and generalizations on the relationship between heterozygosity and quantitative traits.Translated from Genetika, Vol. 41, No. 1, 2005, pp. 100–111.Original Russian Text Copyright © 2005 by Kartavtsev.     

The Concept of Additivity of Drug Combinations in the Case of Quantal Response

The concept of additivity of drug combinations is widely accepted in pharmacology and toxicology. Up to now, no general statistical methods to test that property are available. The present paper gives a mathematical formulation of additivity, a method to fit dose response surfaces under additivity assumption and a statistical test.     

Determination of in situ ruminal crude protein and starch degradation values of compound feeds from single feeds

ABSTRACT

Dairy cows are commonly fed compound feed concentrates, whose accurate formulation relies on the additivity of ruminal degradation characteristics of single feeds, and the absence of associative effects. The main aim of this study was to evaluate the additivity of single feeds in compound feeds made thereof. Twelve single feeds were used to produce eight compound feeds in mash and pelleted form. Samples of single and compound feeds were incubated in situ in three ruminally fistulated dairy cows, and effective ruminal degradation (ED) of CP and starch (ST) was computed. The ED values of examined compound feeds could be, in most cases, accurately calculated from ED values of single feeds. Observed EDCP values were significantly lower than that calculated, but differences were overall small and not exceeded 5% points. No significant differences were observed between calculated and observed EDST. The study also examined the effects of pelleting of compound feeds on in situ degradation. Pelleting significantly increased EDCP (up to 8% points), and EDST (up to 4% points) of most compound feeds. This could have been caused by the pelleting process increasing the proportion of fine feed particles with fast disappearance from the bags. It was concluded that small associative effects between the examined single feeds could be disregarded when formulating compound feeds for dairy cows, and that additivity of EDCP and EDST can be assumed in most cases.     

Exploring additivity effects of double mutations on the binding affinity of protein‐protein complexes

Additivity in binding affinity of protein‐protein complexes refers to the change in free energy of binding (ΔΔG_bind) for double (or multiple) mutations which is approximately equal to the sum of their corresponding single mutation ΔΔG_bind values. In this study, we have explored the additivity effect of double mutants, which shows a linear relationship between the binding affinity of double and sum of single mutants with a correlation of 0.90. However, the comparison of ΔΔG_bind values showed a mean absolute deviation of 0.86 kcal/mol, and 25.6% of the double mutants show a deviation of more than 1 kcal/mol, which are identified as non‐additive. The additivity effects have been analyzed based on the influence of structural features such as accessible surface area, long range order, binding propensity change, surrounding hydrophobicity, flexibility, atomic contacts between the mutations and distance between the 2 mutations. We found that non‐additive mutations tend to be closer to each other and have more contacts. We have also used machine learning methods to discriminate additive and non‐additive mutations using structure‐based features, which showed the accuracies in the range of 0.77–0.92 for protein‐protein complexes belonging to different functions. Further, we have compared the additivity effects of protein stability along with binding affinity and explored the similarities and differences between them. The results obtained in this study provide insights into the effects of various structural features on binding affinity of double mutants, and will aid the development of accurate methods to predict the binding affinity of double mutants.     

Application of the U and gamma' models in binary sweet taste mixtures

The U and Gamma' models of sensory interactions, successfully applied in olfaction for several years, are tested here using data from published studies on sweetness. The models are subsequently tested on new data obtained in studies of binary mixtures of four sodium sulfamates. The U model allows for the estimation of a global interaction, whereas the Gamma' model allows for the distinction between that which is due to an intrinsic interaction in the mixture itself and that which may be due to the power function exponents in the mixture. The models give satisfactory predictions for observed phenomena of sweet taste suppression, synergism or pure additivity. Additionally, they appear to be more suitable than other models recently applied in taste, particularly the equiratio model. Application of the models to the sulfamate mixtures, reveals additivity for sodium cyclohexylsulfamate (cyclamate)/potassium cyclohexylsulfamate and sodium cyclohexylsulfamate/sodium exo-2-norbornylsulfamate, respectively; whereas for sodium cyclohexylsulfamate/sodium 3-bromophenylsulfamate, the models revealed a slight hypo addition which is simply due to the dissimilarity values of the power function exponents of the components.     

Additivity of the proliferative effects of HGF/SF and EGF on hepatocytes

The additivity of DNA synthesis induced by hepatocyte growth factor/scatter factor (HGF/SF) and epidermal growth factor (EGF) was revealed in periportal hepatocytes (PPH), perivenous hepatocytes (PVH), and primary hepatocytes. Furthermore, additivity of the signal transduction pathway of HGF/SF and EGF was investigated (i.e., the activity of mitogen-activated protein kinase (MAPK) induced by HGF/SF and EGF), but it was not seen in PPH, PVH, or primary hepatocytes, although wortomannin, a PI 3-kinase inhibitor, abolished the additivity. The additivity of DNA synthesis induced by HGF/SF and EGF was not related to hepatocyte heterogeneity, but to a difference in the signal transduction pathway, probably another pathway that is different from the classical MAPK (MAPK/ERK1,2) path.     

Population and quantitative genetics of regulatory networks

I evolved boolean regulatory networks in a computer simulation. I varied mutation, recombination, the size of the network, and the number of connections per node. I measured the performance of networks and the heritability and epistasis of genetic effects. Networks of intermediate connectivity performed best. The distinction between metabolic and quantitative genetic additivity explained some of the variation in performance. Metabolic additivity describes the interaction between changes in a single network, whereas quantitative genetic additivity measures the consistency of phenotypic effect caused by gene substitution in randomly chosen members of the population. I analysed metabolic additivity by the distribution of epistatic effects of pairs of mutations in individual networks. I measured quantitative genetic additivity by heritability. Highly connected networks had greater metabolic additivity for perturbations to individual networks, but had lower additivity when measured by the average effect of a gene substitution (heritability). The lower heritability of highly connected nets appeared to reduce the effectiveness of recombination in searching evolutionary space.     

Analysis of a local fitness landscape with a model of the rough Mt. Fuji-type landscape: application to prolyl endopeptidase and thermolysin

A method of analysis of a local fitness landscape for a current biopolymer is presented. Based on the assumption of additivity of mutational effects in the biopolymer, we assigned a site-fitness to each residue at each site. The assigned values of site-fitnesses were obtained by the least-squares method to minimize discrepancies between experimental fitnesses and theoretical ones. As test cases, we analyzed a section of a local landscape for the thermostability of prolyl endopeptidase and that for the enzymatic activity of thermolysin. These sections were proved to be of the rough Mt. Fuji-type with straight theta values of larger than 1.0, where straight theta is defined as the ratio of the "mean slope" to the "degree of roughness" on the fitness surface. Furthermore, we theoretically explained discrepancies between the fitnesses of multiple mutants and those predicted based on strict additivity of the component mutations by using a model of the rough Mt. Fuji-type landscape. According to this model, the discrepancies depend on the local landscape property (such as the straight theta value) and the location of the wild type on the landscape and the mean change in fitness by the component mutations. Our results suggest that this model may provide a good approximation of real sections of local landscapes for current biopolymers phenomenologically.     

Functional interactions between organic calcium channel antagonists in smooth muscle

The Ca2+ channel antagonists D-600, diltiazem, and nifedipine are competitive antagonists of Ca2+ responses in K+-depolarized guinea pig taenia coli and rat mesenteric artery preparations. pA2 values for D-600, diltiazem, and nifedipine in taenia coli were 8.28, 7.44, and 9.27, respectively and in mesenteric artery, 9.6, 7.83, and 10.4, respectively. The combination of nifedipine plus diltiazem gave in both tissues antagonism greater than that calculated on the basis of additivity. This suggests, consistent with published 3H-labelled radioligand binding data, that diltiazem and nifedipine interact at distinct sites. However, the combination nifedipine plus D-600 yielded antagonism consistent with additivity of response.     

Group additivity calculations of the thermodynamic properties of unfolded proteins in aqueous solution: a critical comparison of peptide-based and HKF models

A recent paper in this journal [Amend and Helgeson, Biophys. Chem. 84 (2000) 105] presented a new group additivity model to calculate various thermodynamic properties of unfolded proteins in aqueous solution. The parameters given for the revised Helgeson-Kirkham-Flowers (HKF) equations of state for all the constituent groups of unfolded proteins can be used, in principle, to calculate the partial molar heat capacity, C(o)p.2, and volume, V2(0), at infinite dilution of any polypeptide. Calculations of the values of C(o)p.2 and V2(0) for several polypeptides have been carried out to test the predictive utility of the HKF group additivity model. The results obtained are in very poor agreement with experimental data, and also with results calculated using a peptide-based group additivity model. A critical assessment of these two additivity models is presented.     

pKa values of estrone, 17 beta-estradiol and 2-methoxyestrone

The acid ionization constants of estrone (10.77), 17 beta-estradiol (10.71) and 2-methoxyestrone (10.81) have been determined spectrophotometrically and shown to be consistent with the additivity of substituent effects of the phenol ring. Previously published values for estrone (10.914) and 17 beta-estradiol (10.078) are shown to be incorrect, at variance with the established trend for phenols, and inconcsistent with the similarity of the compounds.     

Mean activity coefficients for the simple electrolyte in aqueous mixtures of polyelectrolyte and simple electrolyte. V. common counterion mixtures of alkali-metal dextransulfates with alkali metal chlorides

Mean molal activity coefficients of simple electrolyte in aqueous solutions of Li, Na, K or Cs salts of dextransulfate (DS) with added LjCl, NaCl, KCl or CsCl are reported. The measurements were carried out by means of an electrochemical cell method using a cation exchange membrane as cation selective electrode and Ag/AgCl electrodes. For LiDS-LiCl, NaDS-NaCl and CsDS-CsCl systems the polymer concentration, m_p, was varied from 0.0088 to 0.113 m and at a given m_p the ratio X of the polymer to salt concentration was varied from 0.5 to 16. Due to the insolubility of KDS in high concentration of KCl, the measurements on KDS-KCl system were performed in the m_p range of 0.0088–0.089 m and some of the smaller X values were omitted. The activity coefficient results are compared to Manning's limiting laws, the additivity rule, and to new limiting laws. The additivity rule can give an excellent representation of the data for all m_p values when γ_p is used as an adjustable parameter.     

An enthalpic basis of additivity in biphenyl hydroxamic acid ligands for stromelysin-1

Fragment based drug discovery remains a successful tool for pharmaceutical lead discovery. Although based upon the principle of thermodynamic additivity, the underlying thermodynamic basis is poorly understood. A thermodynamic additivity analysis was performed using stromelysin-1 and a series of biphenyl hydroxamate ligands identified through fragment additivity. Our studies suggest that, in this instance, additivity arises from enthalpic effects, while interaction entropies are unfavorable; this thermodynamic behavior is masked by proton transfer. Evaluation of the changes in constant pressure heat capacities during binding suggest that solvent exclusion from the binding site does not account for the dramatic affinity enhancements observed.     

Impedance Analysis of Complex Formation Equilibria in Phosphatidylcholine Bilayers Containing Decanoic Acid or Decylamine

Bilayer lipid membranes composed of phosphatidylcholine and decanoic acid or phosphatidylcholine and decylamine were investigated using electrochemical impedance spectroscopy. Interaction between membrane components causes significant deviations from the additivity rule. Area, capacitance, and stability constant values for the complexes were calculated based on the model assuming 1:1 stoichiometry, and the model was validated by comparison of these values to experimental results. We established that phosphatidylcholine and decylamine form highly stable 1:1 complexes. In the case of decanoic acid-modified phosphatidylcholine membranes, complexes with stoichiometries other than 1:1 should be taken into consideration.     

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride have been determined. It has been observed that they increase with decreasing concentration of the polyelectrolyte. The experimental values have been compared with those calculated using Oosawa's theory of activity coefficients. The calculated values are higher than those observed, which suggests that the rodlike model on which Oosawa's theory is based is inadequate for the present case. Activity coefficients of counterions of some solutions containing NaCl and KC1, respectively, have also been determined. It has been found that the additivity rule for activity of counterions applies for these solutions.     

Directed Evolution of Canonical Loops and Their Swapping between Unrelated Serine Proteinase Inhibitors Disprove the Interscaffolding Additivity Model

Reversible serine proteinase inhibitors comprise 18 unrelated families. Each family has a distinct representative structure but contains a surface loop that adopts the same, canonical conformation in the enzyme–inhibitor complex. The Laskowski mechanism universally applies for the action of all canonical inhibitors independent of their scaffold, but it has two nontrivial extrapolations. Intrascaffolding additivity states that all enzyme-contacting loop residues act independently of each other, while interscaffolding additivity claims that these residues act independently of the scaffold. These theories have great importance for engineering proteinase inhibitors but have not been comprehensively challenged. Therefore, we tested the interscaffolding additivity theory by hard-randomizing all enzyme-contacting canonical loop positions of a Kazal- and a Pacifastin-scaffold inhibitor, displaying the variants on M13 phage, and selecting the libraries on trypsin and chymotrypsin. Directed evolution delivered different patterns on both scaffolds against both enzymes, which contradicts interscaffolding additivity. To quantitatively assess the extent of non-additivity, we measured the affinities of the optimal binding loop variants and their binding loop-swapped versions. While optimal variants have picomolar affinities, swapping the evolved loops results in up to 200,000-fold affinity loss. To decipher the underlying causes, we characterized the stability, overall structure and dynamics of the inhibitors with differential scanning calorimetry, circular dichroism and NMR spectroscopy and molecular dynamic simulations. These studies revealed that the foreign loop destabilizes the lower-stability Pacifastin scaffold, while the higher-stability Kazal scaffold distorts the foreign loop. Our findings disprove interscaffolding additivity and show that loop and scaffold form one integrated unit that needs to be coevolved to provide high-affinity inhibition.     

Spectral analysis of chromatin and its components in the vacuum ultraviolet region of the spectrum

Electronic absorption spectra of thin films of chromatin and chromatin components in ultraviolet (140-280 nm) were investigated. The absorption coefficients mu (lambda) of chromatin, nucleosomes with and without histone H1, total histones (TH), DNA were compared. The spectra of nucleosomes and chromatin differ from summary spectra of DNA + TH. The lack of additivity of absorption coefficients at different wavelengths may be explained by different conformational changes of free DNA, TH and DNA, TH in nucleosomes and chromatin during the process of drying aqueous solutions for the preparations of thin films. The obtained mu (lambda) values are necessary for the estimation of the DNA and TH parts of absorption in chromatin and nucleosomes in the investigations of UV and VUV irradiation damages.     

Kinetic study of the mechanisms of eliminating substrate inhibition of lactate dehydrogenase by anions and pH

The dependence of lactate dehydrogenase inhibition at high pyruvate concentrations on pH and neutral salt anions was studied. It was shown that Cl- anions compete with the substrate within the ternary inhibitory complex, ENADpyr in equilibrium ENADCl-, as a result of which the pyruvate-induced inhibition is eliminated. The KD values for Cl- (50 mM) and I- (27 mM) were calculated from the substrate velocity curves at high concentrations of pyruvate. It was supposed that pyruvate inhibition elimination by OH- proceeds via the same kinetic mechanism. The pK value (7.1 +/- 0.1) calculated from this model corresponds to pKn of essential His-195. The additivity of OH- and Cl- function was demonstrated.