A protein model exhibiting three folding transitions

We explain the physical basis of a model for small globular proteins with water interactions. The water is supposed to access the protein interior in an "all-or-none" manner during the unfolding of the protein chain. As a consequence of this mechanism (somewhat speculative), the model exhibits fundamental aspects of protein thermodynamics, as cold, and warm unfolding of the polypeptide chain, and hence decreasing the temperature below the cold unfolding the protein folds again, accordingly the heat capacity has three characteristic peaks. The cold and warm unfolding has a sharpness close to a two-state system, while the cold folding is a transition where the intermediate states in the folding is energetical close to the folded/unfolded states, yielding a less sharp transition. The entropy of the protein chain causes both the cold folding and the warm unfolding.Comment: 13 pages LaTeX, 4 Postscript figure

Heat Capacity of Protein Folding

We construct a Hamiltonian for a single domain protein where the contact enthalpy and the chain entropy decrease linearly with the number of native contacts. The hydration effect upon protein unfolding is included by modeling water as ideal dipoles that are ordered around the unfolded surfaces, where the influence of these surfaces, covered with an ``ice-like'' shell of water, is represented by an effective field that directs the water dipoles. An intermolecular pair interaction between water molecules is also introduced. The heat capacity of the model exhibits the common feature of small globular proteins, two peaks corresponding to cold and warm unfolding, respectively. By introducing vibrational modes, we obtain quantitatively good accordance with experiments.Comment: 14 pages, LaTex, 4 figure

Pathways in Two-State Protein Folding

The thermodynamics of proteins indicate that folding/unfolding takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of the two-state process indicate that folding is guided. We reconcile these two seemingly contradictory observations quantitatively in a schematic model of protein folding. We propose a new dynamical transition temperature which is lower than the thermodynamic one, in qualitative agreement with in vivo measurement of protein stability using E.coli. Finally we demonstrate that our framework is easily generalized to encompass cold unfolding, and make predictions that relate the sharpness of the cold and hot unfolding transitions.Comment: 4 pages RevTeX, 5 Postscript figur

A Model for the Thermodynamics of Globular Proteins

Comments: 6 pages RevTeX, 6 Postscript figures. We review a statistical mechanics treatment of the stability of globular proteins based on a simple model Hamiltonian taking into account protein self interactions and protein-water interactions. The model contains both hot and cold folding transitions. In addition it predicts a critical point at a given temperature and chemical potential of the surrounding water. The universality class of this critical point is new

The Anomalous Issue Class

The modern class action is a litigation superstar. The device’s potential for opening the courthouse doors to “small people,” holding big business accountable, and enacting sweeping reform is second to none. In recent years, however, the star has waned. Judicial hostility has made it harder for plaintiffs to certify a class while making it easier for defendants to avoid class actionsentirely. Certifying a mass tort class has become nearly impossible. Plaintiff lawyers’ creative attempts to work around these roadblocks have been shut down one after another by the Supreme Court. It is in this scorched mass litigation landscape that commentators and lower courts alike are increasingly turning to a once controversial tool—Rule 23(c)(4) of the Federal Rules of Civil Procedure (“Rule 23(c)(4)” or “(c)(4)”). The proponents of an expansive reading of this subsection argue that it empowers courts to certify “issue classes” with the aim to adjudicate only those issues that are common to the class, before leaving the plaintiffs to litigate their individual issues separately in other forums. Notably, the proponents of this reading maintain that a (c)(4) issue class may be certified even when the claim, viewed as a whole, would fail the predominance requirement of Rule 23(b)(3). This has been referred to as the issue class “end-run.” For reasons discussed in Part III, this Comment refers to issue classes enabled by the predominance end-run as “anomalous issue classes.” This Comment seeks to contribute to the current discourse regarding the proper interpretation of Rule 23(c)(4) and the propriety of the issue class end- run. While the expansive reading of (c)(4) is currently dominant, the Fifth Circuit and some commentators have rejected it in favor of a “limited” reading that views the subsection as a “housekeeping tool” designed to make already certifiable classes more manageable, rather than an independent ground for class certification

Four-states phase diagram of proteins

A four states phase diagram for protein folding as a function of temperature and solvent quality is derived from an improved 2-d lattice model taking into account the temperature dependence of the hydrophobic effect. The phase diagram exhibits native, globule and two coil-type regions. In agreement with experiment, the model reproduces the phase transitions indicative of both warm and cold denaturations. Finally, it predicts transitions between the two coil states and a critical point.Comment: 7 pages, 5 figures. Accepted for publication in Europhysics Letter

Use of actuator disc model for modelling axial compressor dynamics

In the work described herein, simplified ways of modelling the flow in axial compressors were investigated. In general full mathematical simulations of multi-stage axial compressors are not efficient in terms of calculation time and resources needed. Therefore to deal with such problems simplified models are used to represent compressor dynamics. The actuator disc model (ADM) is one of these. It gives the possibility to calculate the pressure rise between the areas upstream and downstream of the blading in the compressor as a function of the axial velocity.The first question addressed in the research was whether the accuracy of the classical ADM can be increased by adding so called internal degrees of freedom to it. The number of internal degrees of freedom needed for a significant increase of accuracy was estimated by comparing the response of a blade row to time-periodic excitations represented by an actuator disk with internal degrees of freedom and by the linearized Navier-Stokes equations. It was found that in the case of subsonic flow one internal degree of freedom can be considered as the most important, both for the design and off-design regimes. In the case of transonic flow in the off-design regime two internal degrees of freedom are more important than the rest. However, for the transonic design regime no internal degrees of freedom could be distinguished as being especially significant.In the second part of the research a modified classical ADM was used for numerical simulation of rotating stall onset in a low-speed axial compressor. The model was modified by adding one degree of freedom describing a hysteresis loop in the compressor characteristic. Laboratory experiments show that there are two different stall inception patterns in low-speed axial compressors: one modal and one spike-lik

Origin of entropy convergence in hydrophobic hydration and protein folding

An information theory model is used to construct a molecular explanation why hydrophobic solvation entropies measured in calorimetry of protein unfolding converge at a common temperature. The entropy convergence follows from the weak temperature dependence of occupancy fluctuations for molecular-scale volumes in water. The macroscopic expression of the contrasting entropic behavior between water and common organic solvents is the relative temperature insensitivity of the water isothermal compressibility. The information theory model provides a quantitative description of small molecule hydration and predicts a negative entropy at convergence. Interpretations of entropic contributions to protein folding should account for this result.Comment: Phys. Rev. Letts. (in press 1996), 3 pages, 3 figure

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte

Soluble oligomerization provides a beneficial fitness effect on destabilizing mutations

Mutations create the genetic diversity on which selective pressures can act, yet also create structural instability in proteins. How, then, is it possible for organisms to ameliorate mutation-induced perturbations of protein stability while maintaining biological fitness and gaining a selective advantage? Here we used a new technique of site-specific chromosomal mutagenesis to introduce a selected set of mostly destabilizing mutations into folA - an essential chromosomal gene of E. coli encoding dihydrofolate reductase (DHFR) - to determine how changes in protein stability, activity and abundance affect fitness. In total, 27 E.coli strains carrying mutant DHFR were created. We found no significant correlation between protein stability and its catalytic activity nor between catalytic activity and fitness in a limited range of variation of catalytic activity observed in mutants. The stability of these mutants is strongly correlated with their intracellular abundance; suggesting that protein homeostatic machinery plays an active role in maintaining intracellular concentrations of proteins. Fitness also shows a significant correlation with intracellular abundance of soluble DHFR in cells growing at 30oC. At 42oC, on the other hand, the picture was mixed, yet remarkable: a few strains carrying mutant DHFR proteins aggregated rendering them nonviable, but, intriguingly, the majority exhibited fitness higher than wild type. We found that mutational destabilization of DHFR proteins in E. coli is counterbalanced at 42oC by their soluble oligomerization, thereby restoring structural stability and protecting against aggregation