Conformational study of galphimines A and B.

A conformational study has been performed for galphimines A and B, which differ from each other only in an acetate moiety on ring B of galphimine A. Mechanical molecular calculations showed that the predominant conformers in a Boltzman distribution are those which establish an intramolecular hydrogen bond between the hydroxyls on rings A and B, keeping a similar conformation on the rest of the molecule. The existence of these conformers was confirmed by NMR spectroscopy in (D6) DMSO solution. Furthermore, an unbound hydrogen conformation was found. These types of conformations very probably coexist in solution, for both types of galphimines A and B. Additional experiments suggest that the acetate group on galphimine A does not distort rings B and A, neither does it disturb the intramolecular hydrogen bond formation that also shows galphimine B. Finally, it does not present a steric effect on ring A to avoid any type of interaction of the functional groups on this ring with the biological receptor. The acetate group, which is responsible for the lost of activity of galphimine A very probably prevent that the hydroxyls OH4 and OH7 from interacting, either in a hydrogen bounded or free form, with the receptor, indicating the importance that these hydroxyls play in the biological activity of the molecule.

(Tetrakis(2-pyridylmethyl)ethylenediamine)iron(II) perchlorate. Study of density functional methods.

On the basis of the data obtained by X-ray diffraction, the properties of two independent crystallographic subsystems in the [Fe(tpen)](ClO4)2.2/3H2O complex are studied in detail with the density functional method B3LYP. The energies of singlet, triplet, and quintet states at different temperatures are obtained, the influences of geometry on energy changes are analyzed, the regularity of the spin-state interconversions is investigated, and the effect of the triplet and action of the anion on spin crossover are discussed. This investigation demonstrates that (1) the energy difference between the high-spin state and singlet state decreases as the Fe-N distance and geometric distortion increase, (2) the spin-equilibrium system is predominantly in low-spin form below room temperature and the proportion of high-spin state rapidly increases above room temperature, (3) one of the two cation sites has a greater presence of the high-spin content, (4) the triplet state may be responsible for the fast rate of spin-state interconversions, and (5) the B3LYP method proves to be very adequate to study the spin-state transition of this complex.

Evolution of the structural repertoire of the human V(H) and Vkappa germline genes.

Variable genes of human Ig are classified in families and clans which reflect the early events of gene duplication in the evolution of the locus. This organization in multiple copies of variable genes plus the somatic processes of recombination and hypermutation allows the immune system to generate an antibody repertoire of great diversity. At present the role that somatic processes play in the generation of that diversity is understood with some detail. It is a matter of hard controversy, however, which selective pressures have shaped the evolution of the germline genes of Ig and, consequently, what the role of this germline component in the generation of the antibody diversity actually is. Previous studies of our group have showed that the structural repertoire of Ig-determined by the canonical structures-is an important factor to determine the recognition properties of the antibodies. Complete knowledge of the sequences of the human V(H) and Vkappa loci is available to analyze the evolution of the structural repertoire of these loci. Two phylogenetic gene trees were built from the functional germline genes and the evolution of the structural repertoire was studied. We report that for both loci the canonical structures are not randomly distributed within the tree. Conversely, it is shown that the evolution of the structural repertoire follows a gradual process of diversification. This indicates a correlation between the evolution of genes and the structural repertoire, although important differences are found in the patterns of evolution of the structural repertoire between V(H) and Vkappa. Based on those results we propose a primordial structural repertoire for V(H) and Vkappa. The general properties and an outline of the three-dimensional structure of this primordial repertoire are given.

Antibody-antigen recognition: a canonical structure paradigm.

The antibodies of known three-dimensional structure exhibit a definite number of conformations (canonical structures) for five of six hypervariable loops. In the present study it was found that approximately 85% of the immunoglobulin sequences analyzed fall into a small number of canonical structure combinations, representing only 3% of the total possible. These structures were classified into six distinct groups, depending on the type of antigen with which they interact. Within each loop, the positions responsible for maintaining these canonical structures show a use frequency of amino acids that fits an inverse power law, whereas the use frequency of the amino acids responsible for the detailed antigenic specificity follows an exponential distribution. We propose an evolutionary interpretation that connects these data, using the fact that the inverse power law is generated by statistical processes of the type that yield a wealth curve and the fact that exponential distribution is generated by processes that are not biased by past history.

Frequency analysis of amino acids in the recognition regions of T-cell receptors.

In immunoglobulins (Igs), key amino acids in the Complementarity Determining Regions (CDR) are responsible for maintaining specific conformations called canonical structures. In T-cell receptors (TCRs), protein members of the Ig superfamily, the corresponding residues for maintaining these canonical structures have not been found. In previous studies we have found in Igs that the frequency of use of amino acids in some positions of the CDRs follows an inverse power law distribution, while the frequency of amino acids in the rest of the positions of the CDRs follows an exponential law distribution. The positions that follow the inverse power law distribution are precisely those involved in maintaining the canonical structures, while those positions for which the distribution fits the exponential distribution are those that should be properly involved in the recognition mechanism. In this paper, when the same analysis is applied to the use frequency of amino acids on the CDRs of TCRs, it is found that some positions that have been previously identified as having a structural role are those fitting the inverse power law. That finding combined with the cooperative or long-range interaction properties of systems that follow the inverse power law leads us to propose that the lack of determined key residues in certain positions is compensated by "equivalent' residues in other positions within the CDRs in order to maintain the canonical structures. Other positions that follow the exponential distribution are those which can be involved in the recognition process. These results coincide with a computer-generated model of TCR/peptide/MHC interaction previously published by the authors.

Canonical structure repertoire of the antigen-binding site of immunoglobulins suggests strong geometrical restrictions associated to the mechanism of immune recognition.

Is the structural repertoire of immunoglobulins free to adopt an almost infinite number of conformations to build the diversity of the immune response or does it take advantage of only a few conformations? In this paper we study this question by applying the canonical structure model to characterize the structural repertoire of immunoglobulins. The results found, indicate that only ten combinations out of the 300 possible different canonical structure classes (combinations of canonical structures), make up 87% of 381 sequences analyzed. This suggests that the structural repertoire of immunoglobulins is restricted to the preferential use of a small number of canonical structure classes. The possible functional significance of these results was studied by analyzing the correspondence between the observed canonical structural repertoire implicit in Ig sequences and the types of antigens recognized. Two different sets of canonical structure classes were distinguished: one with preference for some specific types of antigens like proteins, polysaccharides or haptens, and the other with multi-specific binding capabilities. Analysis of antibodies of known three-dimensional structure shows that for two specific classes, the canonical conformations of H2 and L1 determine the geometrical characteristics of the antigen-binding site, while at least in one multi-specific class, the changes in the general geometry of the antigen-binding site are produced by different conformations of H3. Implications of these results for the molecular recognition process mediated by immunoglobulins are discussed.

Molecular modeling of a T-cell receptor bound to a major histocompatibility complex molecule: implications for T-cell recognition.

The main functions of the T-cell receptor (TCR) involve its specific interaction with short and linear antigenic peptides bound to the major histocompatibility complex (MHC) molecules. In the absence of a 3D structure for TCR and for the TCR/peptide/MHC complex, several attempts to characterize the structural components of the TCR/peptide/MHC interaction have been made. However, this subject is still troublesome. In this paper a computer-based 3D model for a TCR/peptide/MHC complex (5C.C7/moth cytochrome c [MCC] peptide 93-103/I-Ek) was obtained. The complex surface shows a high complementarity between the 5C.C7 structure and the peptide/I-Ek molecule. The mapping of residues involved in the TCR/peptide/MHC interaction shows close agreement with mutational experiments (Jorgensen JL, Reay PA, Ehrich EW, Davis MM, 1992b, Annu Rev Immunol 10:835-873). Moreover, the results are consistent with a recent variability analysis of TCR sequences using three variability indexes (Almagro JC, Zenteno-Cuevas R, Vargas-Madrazo E, Lara-Ochoa F, 1995b, Int J Pept Protein Res 45:180-186). Accordingly, the 3D model of the 5C.C7/MCC peptide 93-103/I-Ek complex provides a framework to generate testable hypotheses about TCR recognition. Thus, starting from this model, the role played by each loop that forms the peptide/MHC binding site of the TCR is discussed.

Distributions of the use frequencies of amino acids in the hypervariable regions of immunoglobulins.

Two types of distributions for the frequencies of occurrence of amino acids in each position of hypervariable regions CDR-1 and CDR-2 were obtained for 2,000 immunoglobulins. The results show that some positions fit an inverse power-law distribution, while others fit an exponential-type distribution. As a result of comparison with structural data in the literature it is proposed that sites in which the frequency distribution fits the inverse power law are critical to maintaining canonical shapes of the recognition regions or are involved in modulating these canonical conformations, while those sites where the distribution fits the exponential law are those which should be exclusively involved in the recognition mechanism.

Structural repertoire in VH pseudogenes of immunoglobulins: comparison with human germline genes and human amino acid sequences.

In the pool of human immunoglobulin VH gene segments, pseudogenes amount to roughly 30% of the total number of genes. Some of them are highly conserved among unrelated individuals. These facts suggest a possible functional role for pseudogenes in the human immune response diversity. This paper intends to provide additional information about the structure of VH pseudogene sequences to evaluate the possible role of pseudogenes in the immune response. Mutations capable of altering framework stability in human VH pseudogenes were analyzed. Results indicate that VH pseudogenes are about 14 times as divergent as human VH functional germline genes on the one hand, and four times as divergent in the case of human VH amino acid sequences on the other. The high number of disruptive mutations in pseudogenes is an expected result because of the lack of functionality of these genes. In the second part of the work we analyze whether or not the same takes place in the positions that determine the existence of canonical structures in the hypervariable loops in VH pseudogenes. An extension of such analysis is applied to all species with reported VH pseudogenes. In contrast with results concerning framework positions, 69% of known human VH pseudogenes have canonical structures in the first hypervariable loop, while 48% do so in the second one. Comparison of these results with those found in human VH functional germline genes and human VH amino acid sequences shows that in the former as many as 100% and in the latter 96% have canonical structures. In VH amino acid sequences the result is similar to pseudogenes for H1. For H2, such value lies between the percentage of germline genes (96%) and the percentage of pseudogenes (48%). The possible significance of the existence of canonical structures in the hypervariable loops of VH pseudogenes is discussed.

Variability analysis of the T-cell receptors using three variability indexes.

In the absence of a three-dimensional structure for TCR molecules, several attempts to identify their hypervariable regions by variability methods have been made; this subjects is still troublesome. In this paper three different variability indexes were used: (i) the Kabat index, which is the classical measure of sequence variability, (ii) the modified Kabat index, successfully used in the beta-chain of T-cell receptors and (iii) an information-theoretical entropy concept, recently proposed as an improved measure of the variability. In order to identify the hypervariable regions in the TCR sequences, a Fourier filtering was applied on each variability profile. Results show that the three variability indexes have distinct resolutions for different levels of variability. Thus, the simultaneous use of these indexes compensates for the deficiency of any one of them in estimating variability. Applying the Fourier filtering, it is found that the hypervariable regions here identified, roughly coincide with the defined CDR-2 and CDR-3 in TCR by analogy with Ig. However, no hypervariable in the CDR-1 of alpha- and beta-chains was found. The study on the influence of sample size in variability analysis, indicates that results are independent of the sample size. Considering current structural models of TCR-peptide-MHC interaction, one can suggest that the low-variability characteristics of these regions is inherently related to the interaction with relatively conserved region on the alpha-helices of MHC.

VIR: a computational tool for analysis of immunoglobulin sequences.

In this paper a microcomputer software named VIR (Variable domains of the Immune Receptors) is reported. This package can be used in sequence studies of immunoglobulin variable domains. The main features of the VIR software in the sequences management are: (1) ease of information recovery/extraction from amino acid sequences; and (2) its capability to obtain multiple sequence alignments with predefined characteristics (i.e. specie and/or specificity). As an analytical tool, the VIR package employs such multiple sequence alignments to compute: (1) tables showing amino acid frequencies; (2) three variability indexes; (3) identity matrices; (4) random samples; and (5) sequences with possible canonical structures. Thus the software reported here is proposed as a useful tool to carry out detailed studies of immunoglobulin variable domains.

Patterns in the complementary determining regions of immunoglobulins (CDRs).

An analysis of the frequency of use of amino acids on the CDR-1 and CDR-2 of 1500 immunoglobulins showed that the frequencies of amino acids in different positions could be fitted by two types of distribution. For some positions the frequencies were fitted by an inverse power law and for other positions by an exponential distribution. In order to see whether the more frequently used amino acids for specific positions had physicochemical properties or attributes in common, they were clustered using an algorithm normally applied to artificial intelligence problems. It was found that the amino acids in those positions fitted by the inverse power law have similar hydrophobicity and volume, which are commonly attributes of amino acids in structural positions. Thus, if these positions are critical to maintaining the structural features of the CDR domains, the rest of the positions should be either properly involved in the recognition process or irrelevant. The frequencies of amino acids in these recognition positions were fitted by the exponential law, and it was found by the clustering analysis that these amino acids share properties of a more general type, such as capability of forming hydrogen bonds, polarity, etc. This suggests that at least part of the recognition mechanism requires general properties rather than specific amino acids. Amino acids sharing the required attributes for each one of these positions are then used with random frequency.

A skewed distribution of amino acids at recognition sites of the hypervariable region of immunoglobulins.

Antibody binding site are formed by six hypervariable regions or complementarity determining regions (CDRs). The CDRs, three from the heavy chain and three from the light chain, are known as hypervariable segments and provide a surface complementary to that of the epitope. In recent work it was found that the amino acids in these positions fulfill different functions: Some play a structural role and others are involved in the specificity-determining function. It is reported here that the frequency of amino acids at hypervariable sites is skewed. By means of an informational algorithm, key physicochemical attributes of the dominant residues were identified for some of those sites. The results for about 1,500 antibodies suggest that approximately 35% of sites involved in the recognition process require only general properties such as composition, volume, and bulk or hydrogen bonding which are satisfied by a small set of amino acids instead of any one particular complementary amino acid.

A dynamical model for a co-operative enzyme.

Proteins partially immersed in the hydrophobic portion of a lipid bilayer interact by means of London-van der Waals non-bonding dispersion forces. Moreover, in certain organelles, enzymes are structured in a lattice or ordered matrix. These conditions may facilitate the establishment of long-range correlations between proteins. We studied the dynamical properties of a model for an enzyme endowed with a highly co-operative conformational transition between two reactive states. Two cases were considered, a closed system and an open system. In the closed system for different degrees of interaction among the proteins, it was found that for a substrate concentration greater than a certain threshold an abrupt change of enzymatic activity occurs. This biphasic behavior has been observed in the enzymatic activity of crystalline mitochondrial aspartate aminotransferase and for some other crystalline enzymes. In the analysis of the open system, for a specific input rate of the substrate, two different dynamics were found depending on the selected degree of interaction. For a certain value of a parameter phi, representing the degree of interaction among the reacting units, three steady states co-exist. This multiplicity confers excitable properties to the model. For larger values of phi, limit cycle type solutions were obtained. Thus, a sustained oscillatory product formation of the enzymatic reaction is observed. These results are compared with experimental observations of enzyme extracts detected by NMR.

A dynamical model for phospholipid-calcium binding.

A model for an isothermal gel-liquid crystalline transition induced by ionic binding is proposed. A Ginsburg-Landau functional was used to describe the long-range order that spontaneously arises during the transition. By calculation of the corresponding chemical potential we obtain the mass current of phospholipids in gel-phase described by an order parameter. In the conservation of mass equation the kinetics of the phospholipids-calcium interaction is introduced, together with the flux divergency. A circular membrane is considered for the analysis, so that the model can be studied in polar coordinates. A solution approximated to first order shows an heterogeneous distribution of domains of phospholipids in gel and liquid crystalline phases. These spatial domains have been detected experimentally by diverse methods in vesicles and cellular membranes. Spatial heterogeneities may cause destabilization of the membrane in the boundaries between domains. This may explain the enhanced vesicle fusion observed in the presence of Ca2+.

A dynamical model for phase transitions of lipids induced by calcium ions.

Lipid membranes exist essentially in two different phases. A phase transition can be triggered off either by changing the temperature or, isothermally, by varying an external factor such as ionic concentration, pH, organic solvents, etc. Since the isothermal transition may be induced at physiological temperature, it may play an important regulatory role in diverse cellular functions. Based on the Landau-Ginsburg theory, the thermotropic transitions of lipids has been described by a number of models. In the present work a dynamical model for an isothermal phase transition of phospholipids induced by ionic binding is proposed. The properties of the model show that by ionic binding, phospholipids may form spatial heterogeneous distributions of lipids in fluid and crystalline phases. This heterogeneity possibly being the cause of membrane instabilities, which favour enhanced vesicle fusions observed in the presence of Ca2+.

On the skew distribution of immunoglobulins and the inverted protein-folding problem.

The question of antibody specificity is discussed in the framework of the inverted protein-folding problem (i.e. the characterization of protein sequences with a common fold). A stochastic model of the immune response, patterned after a model for the distribution of words in natural languages is proposed. It is shown that the steady-state probability distribution of immunoglobulin variable-region frequencies is the Yule distribution.

Density dependent diffusional model of an infective population.

In this work, we present a density-dependent diffusional model which, coupled to three different types of growth, permitted us to study the infective potential of a bacteria species. The results show that those species with strong internal competency have the higher colonizing capacity in terms of invasion speed. Here, we also advanced a model for the static spatial inhomogeneous distribution that some species establish after migration. It is proposed that the origin of these patterns is the result of a balance between the dispersal tendency and the attractive behavior. The results obtained were compared with the observed behavior of Rhizobium spp. during infection of leguminous roots. A possible explanation of the observed morphologies of nodule development in different legumes is suggested.

A model for aggregation-dispersion dynamics of a population.

An important feature that distinguishes the movement of living systems from the random motion of inorganic material is a delicate balance between spreading and concentrating. This movement is based on the kind of interactions which a bacterial colony may establish during migration. Namely, the antagonistic effects of dispersal which take place preferentially down the population gradient and the tendency in grouping together. In this work a model is proposed which considers these effects. The phase plane analysis and the numerical calculations reveal the existence of stable sharp wave front solutions. The speed of the wave front is modulated by the compromise between the tendencies of spreading and aggregating. The results obtained were compared with experimental observations in cultures of Escherichia coli and Streptococcus faecalis. The agreement between both types of results supports the hypothesis on which the model was based.