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

Shape Imprinting Due to Variable Disulfide Bonds in Polyacrylamide Gels

Through the use of variable disulfide crosslinkers, we have created polyacrylamide gels whose shape can be altered after polymerization. N,N\u27-bisacryloylcystamine is incorporated as a crosslinker, along with a smaller amount of a permanent crosslinker. After polymerization, the disulfide bonds are cleaved into thiols through reduction. By reoxidizing the thiols with the gel held in a new macroscopic shape, a new set of disulfide bonds is formed, and the gel is forced to adopt the new shape. Retension of the new shape improves with greater distortion from the original shape, as well as with increased concentration of variable disulfide bonds. A simple theoretical model has been developed to explain these data, although the enigmatic kinetics of relaxation remain unexplained

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]

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

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

Random walks in the space of conformations of toy proteins

Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as a random walk in an abstract (discrete) space of conformations. To test the geometry of this space, we examine the return probability $P(T)$, which is the probability to find the polymer in the native state after $T$ Monte Carlo steps, provided that it starts from the native state at the initial moment. Comparing computational data with the theoretical expressions for $P(T)$ for random walks in a variety of different spaces, we show that conformational spaces of polymer loops may have non-trivial dimensions and exhibit negative curvature characteristic of Lobachevskii (hyperbolic) geometry.Comment: 4 pages, 3 figure

Shrinking-induced instability in gels

Polymer gels can undergo a volume phase transition (either continuous or discontinuous) when an external condition such as temperature or solvent composition is altered. This phase transition is either a shrinking or a swelling. We investigate the instability of a tubular fluid gel after shrinking. When gels are immersed in a solvent, the polymer network undergoes a diffusion inducing an osmosis pressure through the gel. A bubble and a bamboo pattern were observed under such conditions (E. Sato-Matsuo and T. Tanaka, Nature, 358, 482 (1992)). In this paper we investigate these pattern formations as a mechanical instability.published or submitted for publicationis peer reviewe

Gels for molecular recognition, accumulation and release. Final report, grant from DOE

The proposal was to establish a general principle with which polymer gels can specifically recognize a target molecule and reversibly change their affinity to the target by orders of magnitude. The polymer consists of two species of monomers, each having a different role. The majority monomer species control network density and make the gel to swell and shrink reversibly in response to an environmental change such as temperature. The minority monomers come into sufficient proximity to each other when the supporting gel shrinks and then they become able to function as multi-group absorption centers for the target molecules. This absorption can be switched on and off by the reversible gel phase transition. The multiple point absorption is the key, not only for reversibility, but also an essential ingredient for possible specificity of target recognition by polymers. Multivalent metal ions and multicharged pyranine are used as target molecules to demonstrate the principles, although the method will be applicable to a wide range of target molecules. The project established and demonstrated the guiding principles for design and synthesis of molecular recognition gels. Such gels should find use in a wide variety of applications including cleaning and recovery of chemicals from toxic waste, recovery and concentration of precious molecules from ocean and biological products and catalysis of chemical reactions

Experimental Methods In Polymer Science

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