A protein self-assembly model guided by electrostatic and hydrophobic dipole moments

The influence of the Debye-Hückel factor in estimating the distance between interacting monomers in self-assembling proteins

In the study of protein self-assembly, knowledge of the extent of electrical and hydrophobic interactions is important. In previous work our group deduced an expression for the hydrophobic energy between the monomers of an assembly. This energy decays exponentially with a characteristic distance rH. The object of this work is to obtain a more precise physical interpretation of rH. In very simple systems, according to our model, rH turns out to be the distance between the hydrophobic dipole moment vectors H. As systems become more complex and the action of the electrostatic dipole moment vectors D appear, discrepancies begin to be seen between the values obtained for rH and the distances between vectors. It is observed that the simple application of Coulomb's law is not sufficient to explain these discrepancies. We introduce the (D-H) factor into the electrostatic interaction, since proteins interact within an ionic medium. This formulation implies the appearance of an exponential decay factor rD, which is the thickness of the ionic atmosphere surrounding protein molecules. The distance adopted by two interacting monomers in a protein assembly is affected by both types of interaction and therefore is a function of both rH and rD. In a number of cases, the electrostatic interaction between D vectors is repulsive, generating a potential barrier that monomers are able to cross thanks to an overwhelmingly attractive hydrophobic potential well. In other cases both interactions are attractive and the distance between monomers appears as a compromise of both rH and rD.

How hydrophobicity shapes the architecture of protein assemblies

The interactions that give rise to protein self-assembly are basically electrical and hydrophobic in origin. The electrical interactions are approached in this study as the interaction between electrostatic dipoles originated by the asymmetric distribution of their charged amino acids. However, hydrophobicity is not easily derivable from basic physicochemical principles. Its treatment is carried out here considering a hydrophobic force field originated by "hydrophobic charges". These charges are indices obtained experimentally from the free energies of transferring amino acids from polar to hydrophobic media. Hydrophobic dipole moments are used here in a manner analogous to electric dipole moments, and an empirical expression of interaction energy between hydrophobic dipoles is derived. This methodology is used with two examples of self-assembly systems of different complexity. It was found that the hydrophobic dipole moments of proteins tend to interact in such a way that they align parallel to each other in a completely analogous way to how phospholipids are oriented in biological membranes to form the well-known double layer. In this biological membrane model (BM model), proteins tend to interact in a similar way, although in this case this alignment is modulated by the tendency of the corresponding electrostatic dipoles to counter-align. Helical conformation of influenza virus PDBid: 6Z5L. Two monomers are shown in cyan and green. The corresponding dipole moment vectors are shown in red (electric dipoles) and blue (hydrophobic dipoles). From the inset figure, it can be seen that the growth of the helix is due to electrical attraction of the monomers, overcoming a hydrophobic repulsion (see text).

The use of vector formalism in the analysis of hydrophobic and electric driving forces in biological assemblies

Hydrophobic forces are known to have a crucial part not only in the conformation of the three-dimensional structure of proteins, but also in the build-up of DNA–protein complexes. Electric forces also play an important role both in the tertiary as well in the quaternary structure of macromolecular associations. Sometimes both hydrophobic and electric interactions add up their strengths to accomplish these structures but in most cases they act in opposite directions. This fact, together with being overall interactions with different ranges, provides a nuanced equilibrium also modulated by the need to comply with steric hindrances and geometric frustration effects. This review focuses on the utility of using the hydrophobic and electrical dipole moment vectors to describe the interactions that give rise to the structures of biological macromolecules. Although different definitions of both electric dipole and hydrophobic moments have been described in the literature, results obtained in biological assemblies demonstrate the principle of the biological membrane model. According to this model, postulated by our group, biological macromolecules tend to associate by aligning their hydrophobic moments in a similar manner to phospholipids in a membrane. Examples of both closed and open structures are used to assess the predictability of our model. We seek agreement between our results with those described in the current literature. The review ends with possible future projections using this formalism.

The importance of hydrophobic interactions in the structure of transcription systems

Hydrophobic forces play a crucial role in both the stability of B DNA and its interactions with proteins. In the present study, we postulate that the hydrophobic effect is an essential component in establishing specificity in the interaction transcription factor proteins with their consensus DNA sequence partners. The PDB coordinates of more than 50 transcription systems have been used to analyze the hydrophobic attraction of proteins towards their DNA consensus. This analysis includes computing the hydrophobic energy of the interacting molecules by means of their hydrophobic moments. Hydrophobic moments have successfully been used in previous studies involving self-assembly protein systems. In the present case, in spite of some variability, we found specificity in transcription factors when interacting with their respective consensus DNA sequences. By applying our model of biological membrane pattern for hydrophobic interactions, we postulate that hydrophobic forces constitute the necessary intermediate interaction between the unspecific electrostatic attraction for DNA phosphate groups and the very short-range interaction promoting hydrogen bonds. We conclude that hydrophobic interactions serve as the intermediate force guiding transcriptions factors towards the proper hydrogen bonds to their DNAs.