Design of Toy Proteins Capable to Rearrange Conformations in a Mechanical Fashion

We design toy protein mimicking a machine-like function of an enzyme. Using an insight gained by the study of conformation space of compact lattice polymers, we demonstrate the possibility of a large scale conformational rearrangement which occurs (i) without opening a compact state, and (ii) along a linear (one-dimensional) path. We also demonstrate the possibility to extend sequence design method such that it yields a "collective funnel" landscape in which the toy protein (computationally) folds into the valley with rearrangement path at its bottom. Energies of the states along the path can be designed to be about equal, allowing for diffusion along the path. They can also be designed to provide for a significant bias in one certain direction. Together with a toy ligand molecule, our "enzimatic" machine can perform the entire cycle, including conformational relaxation in one direction upon ligand binding and conformational relaxation in the opposite direction upon ligand release. This model, however schematic, should be useful as a test ground for phenomenological theories of machine-like properties of enzymes.Comment: 13 pages, 12 figure

Solvation vs. freezing in a heteropolymer globule

We address the response of a random heteropolymer to preferential solvation of certain monomer types at the globule-solvent interface. For each set of monomers that can comprise the molecule's surface, we represent the ensemble of allowed configurations by a Gaussian distribution of energy levels, whose mean and variance depend on the set's composition. Within such a random energy model, mean surface composition is proportional to solvation strength under most conditions. The breadth of this linear response regime arises from approximate statistical independence of surface and volume energies. For a diverse set of monomer types, the excess of solvophilic monomers at the surface is large only for very strong solvent preference, even in the ground state.Comment: 10 pages, 1 figur

How Accurate Must Potentials Be for Successful Modeling of Protein Folding?

Protein sequences are believed to have been selected to provide the stability of, and reliable renaturation to, an encoded unique spatial fold. In recently proposed theoretical schemes, this selection is modeled as ``minimal frustration,'' or ``optimal energy'' of the desirable target conformation over all possible sequences, such that the ``design'' of the sequence is governed by the interactions between monomers. With replica mean field theory, we examine the possibility to reconstruct the renaturation, or freezing transition, of the ``designed'' heteropolymer given the inevitable errors in the determination of interaction energies, that is, the difference between sets (matrices) of interactions governing chain design and conformations, respectively. We find that the possibility of folding to the designed conformation is controlled by the correlations of the elements of the design and renaturation interaction matrices; unlike random heteropolymers, the ground state of designed heteropolymers is sufficiently stable, such that even a substantial error in the interaction energy should still yield correct renaturation.Comment: 28 pages, 3 postscript figures; tared, compressed, uuencode

Equilibrium swelling properties of polyampholytic hydrogels

The role of counter ions and ion dissociation in establishing the equilibrium swelling of balanced and unbalanced polyampholytic hydrogels has been investigated experimentally and theoretically. The swelling dependence on both the net charge offset and the external bath salt concentration has been examined using an acrylamide based polyampholytic hydrogels. By careful consideration of the swelling kinetics, we illustrate the effects of ion dissociation equilibria and counter ion shielding in polyampholytic hydrogels near their balance point where both polyelectrolyte and polyampholyte effects are present. The theory considers a Flory type swelling model where the Coulombic interactions between fixed ions in the hydrogel resemble those of an ionic solid with a Debye screening factor. Theoretical predictions from this model are in qualitative agreement with our experimental [email protected] ; [email protected]

Primary Sequences of Protein-Like Copolymers: Levy Flight Type Long Range Correlations

We consider the statistical properties of primary sequences of two-letter HP copolymers (H for hydrophobic and P for polar) designed to have water soluble globular conformations with H monomers shielded from water inside the shell of P monomers. We show, both by computer simulations and by exact analytical calculation, that for large globules and flexible polymers such sequences exhibit long-range correlations which can be described by Levy-flight statistics.Comment: 4 pages, including 2 figures; several references added, some formulations improve

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure

Is Heteropolymer Freezing Well Described by the Random Energy Model?

It is widely held that the Random Energy Model (REM) describes the freezing transition of a variety of types of heteropolymers. We demonstrate that the hallmark property of REM, statistical independence of the energies of states over disorder, is violated in different ways for models commonly employed in heteropolymer freezing studies. The implications for proteins are also discussed.Comment: 4 pages, 3 eps figures To appear in Physical Review Letters, May 199

Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur