It is shown from molecular statistical considerations that a demixing instability exists in the moment space of a microbial protein expression profile. Although avoidance of demixing is generally requisite for biological function, a comparison with proteomic and genomic data suggests that many microbes lie close to the onset of this instability. Over evolutionary time scales, straying too close or into the immiscible domain may be associated with intracellular compartmentalization. DOI: 10.1103/PhysRevLett.94.178105 PACS numbers: 87.16.-b Molecular statistical approaches to demixing thermodynamics have long focused on industrially important contexts such as polymer blends, colloids and crude oil [1]. Similar avenues might also present useful insights into the intracellular thermodynamics of microbial organisms. Odijk [2] for example, proposes an equilibrium thermodynamic view of the bacterial nucleoid according to which, under conditions of excess salt, DNA tends to reversibly collapse and demix from the cytosol proteome.The proteome itself features only as a secondary focus in Odijk's particular analysis, but it is also of interest to examine how from a statistical mechanical perspective microbes apparently manage to avoid a similar intraproteomic demixing effect [3]. Expressed proteins of course do not disperse in perfectly miscible souplike fashion, but we can reasonably suppose that they must remain essentially miscible in respect of their macroscopic phase behavior. It is known for molecular mixtures in general that miscibility is sensitive to low moments of the size distribution [4], so we might anticipate that microbial intracellular stability depends analogously on moments of the proteomic expression level profile with respect to sequence length. Our principal objective here is to demonstrate this more explicitly within a model framework.Consider a crude molecular statistical formulation of the Helmholtz free energy F U ÿ TS describing the expressed protein ensemble, where U and S denote, respectively, internal energy and entropy at temperature T. We assume a continuous distribution l over length l in amino acid residues. With the total protein number density, l dl is the concentration in the cytosol having length between l and l dl. Assuming proteins with the same l can be considered indistinguishable with respect to their mutual interactions, we can then write for the entropy density over volume V of the cytosolwhere k B is Boltzmann's constant.Next we assume that the dominant contribution to the internal energy U comes from nonspecific adhesive interaction between proteins. For a system of monodisperse adhesive well particles U=V ' ÿ 2 2 ad 2 , where d is the particle diameter, a is the well width, and is its depth. In this spirit, we writewhere h. . .i denotes the distribution-averaged moment.Here we have identified a with the amino acid length scale, and set d al 1=3 to represent a compact protein comprising l residues. To look for a miscibility gap in the parameter space of this description, we...

The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In the presence of polymer the particles behave as if they attracted each other. It is shown how the polymer's correlation length may be determined from a scattering experiment performed on the spheres

We study the electrical double layer at the interface between a protein crystal and a salt solution or a dilute solution of protein, and estimate the double layer's contribution to the interfacial tension of this interface. This contribution is negative and decreases in magnitude with increasing salt concentration. We also consider briefly the interaction between a pair of protein surfaces

Homogeneous nucleation of the new phase of one transition near a second phase transition is considered. The system has two phase transitions, we study the nucleation of the new phase of one of these transitions under conditions such that we are near or at the second phase transition. The second transition is an Ising-like transition and lies within the coexistence region of the first transition. It effects the formation of the new phase in two ways. The first is by reducing the nucleation barrier to direct nucleation. The second is by the system undergoing the second transition and transforming to a state in which the barrier to nucleation is greatly reduced. The second way occurs when the barrier to undergoing the second phase transition is less than that of the first phase transition, and is in accordance with Ostwald's rule.

The deposition of protective coatings from thermosetting polymer powders is an ecological, economic and energy-efficient technology. A frequent problem encountered with powder coatings is a rough surface (with undulations on a length scale much greater than the powder particle size) that detracts from the visual appearance. The levelling (i.e. flattening) of the surface of a polymer melt is driven by the minimization of the surface energy but opposed by the (possibly time-dependent) viscosity of the melt. We address the problem by developing a model of surface levelling to consider flow in two directions, building upon a one-dimensional model already in the literature. We have performed simulations to predict the final coating profiles starting with a Gaussian profile and using experimentally determined values of polymer viscosity. To compare to the simulations, we have measured experimentally the dimensions of surface undulations on coatings formed from thermosetting acrylic powder layers having purposely created features of known dimensions. There is good agreement between simulation and experiment. Both find that the levelling proceeds to a greater extent with increasing coating thickness and with decreasing lateral dimension of the surface undulation. Our results open up the possibility of predicting final surface topography given the rheological properties of a polymer.