Aeolotopic interactions of globular proteins

Abstract

Protein crystallization, aggregation, liquidliquid phase separation, and self-assembly are important in protein structure determination in the industrial processing of proteins and in the inhibition of protein condensation diseases. To fully describe such phase transformations in globular protein solutions, it is necessary to account for the strong spatial variation of the interactions on the protein surface. One difficulty is that each globular protein has its own unique surface, which is crucial for its biological function. However, the similarities amongst the macroscopic properties of different protein solutions suggest that there may exist a generic model that is capable of describing the nonuniform interactions between globular proteins. In this paper we present such a model, which includes the short-range interactions that vary from place to place on the surface of the protein. We show that this aeolotopic model [from the Greek aiolos (''variable'') and topos (''place'')] describes the phase diagram of globular proteins and provides insight into protein aggregation and crystallization.Simple isotropic models that treat the protein molecules as spherical particles with short-range attractive interactions explain certain features of the protein phase diagram (1-5). In particular, liquid-liquid coexistence turns out to be metastable with respect to solidification when the range of interaction is less than one quarter of the particle diameter (6-10). This metastability has been observed for a variety of protein solutions (11-15) and in colloidal solutions (16-18), but not in simple fluids where the range of interaction is long (19). The isotropic model, however, fails to describe the phase diagram of protein solutions quantitatively and cannot address phenomena such as protein aggregation and self-assembly.We use a simple model in which the energy of each particle depends only on its position relative to other particles and on its own orientation but is independent of the orientation of other particles. In this model, the pair potential of particles i and j has the form w(Here, r ij is the vector distance between particles i and j while ⍀ represents the three Euler angles that define the orientation of the particle. For such an additive model, it is possible to define the orientation-averaged free energy, f i ({r ij }), of an individual particle asAs usual, N is the number of particles, and ␤ ϭ 1͞k B T, where k B is Boltzmann's constant and T is the absolute temperature. The free energy f i ({r ij }) of a particle depends on the positions of all of the particles with which it interacts. . To study the conditions under which the aeolotopic potential u(⍀ i , r ij ) is ''averageable,'' i.e., accurately approximated by the effective potential U(r ij ), we use the following modified squarewell model. A protein molecule is represented by a spherical particle with a ''map'' of attractive regions covering a fractional area a of the surface. In this work, maps consisted of s non-overlapping spots of equal area...

Altered phase diagram due to a single point mutation in human γD-crystallin

“…Indeed, in such a model a change in the attractive energy as a result of the mutation must have a proportional effect on both the coexistence curve and the solubility line. In reality, however, as we have emphasized previously (37), the interprotein interactions are highly anisotropic and localized. The analysis of our data indicates that a mutation at site 23 dramatically affects the temperature dependence of the interprotein interaction.…”

“…This observation finds its natural explanation in the framework of the aeolotopic model (37). In this model, we have shown that the thermodynamic properties of the liquid phase can be described by a spatial thermodynamic average of the highly anisotropic actual potential.…”

“…Using the expression for the effective attractive energy given in ref. 37, suitably generalized for attractive spots with different energies and areas, it is possible to show that for a protein with Ͼ30 attractive spots, the aforementioned change of Ϸ2.4 kT 0 in the energy of one spot will translate into a Ͻ0.3% change in the thermodynamically averaged effective energy in the solution phase. This corresponds to Ϸ1°C shift in the coexistence curve, which is within the level of uncertainty in the measurements of LLPS.…”

Phase diagram of a tetrahedral patchy particle model for different interaction ranges

“…In a rough approximation, proteins can be regarded as patchy particles since their interactions are short-ranged and highly directional. [6][7][8] The study of patchy interactions can therefore be helpful in understanding the mechanisms of protein crystallization.…”

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

“…For example, theoretical calculations based on anisotropic attractive interactions successfully describe both the width of the binodal and the gap between the binodal, and the fluid-solid transition for aqueous protein solutions without additives. 60,79,80 Anisotropic attractive interactions are indeed induced by hydrophobic patches on the lysozyme surface, and have been taken into account in a patchy sphere model by Curtis et al 81 Anisotropic attractions as well as repulsions, e.g., as due to an anisotropic charge distribution or van der Waals interaction, are not taken into account in our DLVO model. Our model furthermore neglects nonelectrostatic contributions to the lysozyme pair potential that originate from dispersion forces between the micro-ions and proteins.…”