Measurements of lysozyme diffusion within the “depletion zone” of the (110) face of lysozyme crystals are reported. The measurements were performed using the technique of microscope light scattering , capable of measuring small sampling areas (∼2μm2). Measurements within such small areas allowed for the determination of intensity correlation functions at precise locations (at ∼10μm intervals) adjacent to the (110) crystal face. From the intensity correlation functions, diffusion coefficients of lysozyme molecules adjacent to the (110) crystal face and in solution were determined. The diffusion coefficients were observed to decrease as the surface of the crystal was approached.

The effect of salt concentration on the affinity of a thermosensitive heteropolymer gel for various multiple-point adsorbing target molecules was examined. The gel has positively charged adsorber monomers which can interact electrostatically with negatively charged groups on the target molecules. Adsorption of the targets was found to depend strongly on the salt concentration. The adsorption affinity decreased by several orders of magnitude with a slight increase of the salt concentration, showing that, quite unlike the trivial Donnan potential effect, the negative ions of the salt compete with target molecules for the adsorption sites. We have found the power law relationship between the affinity for the target and the concentration of the coexistent salt for gels in the collapsed state.

With the aim of developing polymeric gels sensitive to external stimuli and able to reversibly adsorb and release divalent ions, copolymer gels of N-isopropylacrylamide (NIPA) and methacrylic (MAA) monomers were prepared. We chose calcium as a target divalent ion. Two MAAs form a complex with a calcium ion, and the NIPA component allows the polymers to swell and shrink reversibly in response to temperature. The adsorbing site develops an affinity to target ions when the adsorbing molecules come into proximity, but when they are separated, the affinity diminishes. To enhance the affinity to calcium, an imprinting technique was applied using Ca2+ and Pb2+ ions as templates in methylsulfoxide and dioxane media, respectively. The adsorption capacity of the imprinted gels was compared with that of the nonimprinted gels, and the effects of the templates, the solvents, and the amount of methacrylic monomers used in the synthesis and the medium temperature over the Ca2+ adsorption capacity of the gels from aqueous solutions were evaluated. The analysis of the adsorption revealed that (a) the adsorption can be described by the Langmuir isotherms; (b) there is an approximately linear relationship between saturation and methacrylic monomer concentration; (c) the affinity depends on the degree of gel swelling or shrinkage that can be switched on and off by temperature; (d) in the shrunken state, the affinity depends approximately linearly on the MAA concentration in the imprinted gels, whereas in the nonimprinted gels it is proportional to the square of MAA concentration; (e) the imprinted gels adsorb more than the nonimprinted gels when MAA concentration is less than that of permanent cross linkers. The success of imprinting of CaMAA2 and PbMAA2 complex is evidence for memory of such complex onto the weakly cross-linked gel.

We report the data on-concurrent multiple point adsorption of two oppositely charged species of "target molecules" (aluminum ions and 1,3,6,8-pyrenetetrasulfonic sodium salt' (Py-4)) by a polyampholyte gel of N-isopropylacrylamide (NIPA, 6 M) with methacrylic acid (MAA, 80 mM) and methacrylamidopropyl trimethylammonium chloride(MAPTAC, 80 mM). The goal of this study is to test the mutual frustrations created by adsorption of one species on the adsorption of the other. Understanding these frustrations is an important step toward elucidating the memory of conformations in heteropolymer systems. We found that in the absence of aluminum, the adsorption of Py-4 was suppressed by gel collapse, presumably because of an increase in MAA/MAPTAC ionic pairs that prevents the formation of potential adsorbing centers. Adding a moderate amount of aluminum significantly enhances adsorption of Py-4 by the collapsed gel, indicating that aluminum ions compete for bonds with MAA and help release vacant MAPTAC centers. Finally, with further increase of aluminum, the Py-4 multiple point adsorption is again suppressed; pointing out the frustrations created by aluminum-mediated effective cross-links. We analyze also the cooperativity of the adsorption process.

Imprinted gels incorporating two different breakable cross linkers, a PbMAA(2) complex and a disulfide (S-S) bond, were prepared by radical polymerization. After the lead ions were removed by washing, these gels showed a high affinity for calcium ions. Breakage and subsequent reconnection of the S-S bonds in the absence of Ca2+ decreases the Ca2+ binding affinity of the gel. This indicates that random reconnection of the S-S bonds produces a frustration in the adsorption of Ca2+ by the carboxyl groups. However, if the S-S bonds were reconnected in the presence of Ca2+ and the Ca2+ was subsequently removed (the post-imprinting technique), the resulting gels showed a higher binding affinity for Ca2+. This indicates that the post-imprinting technique creates a more favorable conformation for Ca2+ binding in the polymer network. We interpret our data to mean that "memory" of target binding sites was encoded effectively into the polymer network by the initial imprinting technique and then enhanced by the post-imprinting technique.

The work is motivated by the experimental observation of B. Chu et al. [Macromolecules 28, 180 (1995)] which suggests that, while polymer globules in dilute solution in poor solvent are supposed to be very sticky, in actuality they collide many hundreds of times before merging and before aggregation starts. We argue that this slow-down is caused by an “entanglement force” which is operational on the prereptational time scale. This force arises from the fact that two touching globules cannot enjoy the mixing entropy gain expected in equilibrium until after they explore all conformations, including entangled ones. We report a molecular dynamics simulation in which we were able to measure the entanglement force as a function of distance. The important conclusion we can formulate so far is qualitative; the entanglement force exists and is sufficient to explain the observed slow-down of aggregation.

Polymer gels can undergo a volume phase transition (either continuous or discontinuous) when an external condition such as temperature or solvent composition is altered [1, 2]. This phase transition is either a shrinking or a swelling. We investigate the instability of a tubular uid gel after shrinking. When gels are immersed in a solvent, the polymer network undergoes a di usion 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 this pattern formations as a mechanical instability.

Protein folding has become one of the most actively studied problems in modem molecular biophysics. Approaches to the problem combine ideas from the physics of disordered systems, polymer physics, and molecular biology. Much can be learned from the statistical properties of model heteropolymers, the chain molecules having different monomers in irregular sequences. Even in highly evolved proteins, there is a strong random element in the sequences, which gives rise td a statistical ensemble of sequences for a given folded shape. Simple analytic models give rise to phase transitions between random, glassy, and folded states, depending on the temperature T and the design temperature T-des of the ensemble of sequences. Besides considering the analytic results obtainable in a random-energy model and in the Flory mean-field model of polymers, the article reports on confirming numerical simulations.

Weakly cross-linked heteropolymer gels that memorize molecular pairs have been designed and synthesized. The polymer consists of a main monomer component responsible for volume phase transition, methacrylic acid that adsorbs one divalent ion as a pair, and cross-links; The memory of pairing of methacrylic acids within the gels was encoded in the primary sequence of main monomers, methacrylic acids and cross-links within the gels, which was achieved by "imprinting", namely, by synthesizing gels while methacrylic monomers were paired prior to polymerization. The control gels, where methacrylic monomers were randomly distributed, showed frustration in forming pairs, whereas such frustration was completely diminished in the imprinted gels allowing the memory of pair formation.

We report the first accurate measurements of the partial heat capacity of poly(N-isopropylacrylamide) hydrogels with varying cross-link density. When the cross-link density is increased, the transition broadens and the transition temperature decreases, while the enthalpy, entropy, and heat capacity increment of the transition do not practically change. The transition heat capacity increment is negative, Delta C-t(p) = -0.63 +/- 0.04 J/g/K. This indicates the formation of a hydrophobic core of the gel upon the transition. The partial heat capacity of polymer network in the gel approaches the partial heat capacity of the unfolded linear poly(N-isopropylacrylamide) at low temperatures, indicating a complete disordering of the gel under these conditions. On the basis of the calorimetric data, thermodynamic functions of the transition were calculated from 0 to 150 degreesC. They allow one to compare enthalpic and entropic contributions to the stabilization of the collapsed gel. This state is found to be most stable at about 100 degreesC, and a reswelling transition could be expected only above 150 degreesC. Contributions of the dehydration of apolar and polar groups as well as residual factors to the transition enthalpy, entropy, and free energy were calculated. The role of apolar dehydration, i.e., of the hydrophobic effect, was not found to be predominant. Apparently, interactions of residues (van der Waals interactions and/or hydrogen bonding) contribute mainly to the stabilization of the collapsed state.

We report development of a polymer gel with a catalytic activity that can be switched on and off when the solvent composition is changed. The gel consists of two species of monomers. The major component, N-isopropylacrylamide, makes the gel swell and shrink in response to a change in composition of ethanol/water mixtures. The minor component, vinylimidazole, which is capable of catalysis, is copolymerized into the gel network. The reaction rate for catalytic hydrolysis of p-nitrophenyl caprylate was small when the gel was swollen. In contrast, when the gel was shrunken, the reaction rate increased 5 times. The activity changes discontinuously as a function of solvent composition, thus the catalysis can be switched on and off by an infinitesimal change in solvent composition. The kinetics of catalysis by the gel in the shrunken state is well described by the Michaelis-Menten formula, indicating that the absorption of the substrate by the hydrophobic environment created by the N-isopropylacrylamide polymer in the shrunken gel is responsible for enhancement of catalytic activity, In the swollen state, the rate vs. active site concentration is linear, indicating that the substrate absorption is not a primary factor determining the kinetics, Catalytic activity of the gel is studied for substrates with various alkyl chain lengths; of those studied the switching effect is most pronounced for p-nitrophenyl caprylate.

The behavior of randomly charged polyampholytes against a wide range of the Coulomb coupling parameter Gamma (the ratio of the Coulomb energy to thermal energy) is studied with the use of molecular dynamics simulations. Neutral polyampholyte collapses for Gamma>1, where large volume changes are due to multichain effects. Charged chains reptate significantly in a globule. Polyampholyte with widely extensible bonds condenses to a cubic crystal for Gamma>>1, while that with finitely extensible bonds remains in an imperfectly ordered glass structure. Non-neutral polyampholyte whose charge offset exceeds 1 / 2N(1/2) behaves as polyelectrolyte: it consists of nonoverlapped chains for Gamma>1, and shrinks to the noncharged polymer regime for Gamma<1 (N is the number of charged monomers). Condensed counterions on polyampholyte screen the electric field, making non-neutral polyampholyte close to the neutral one. Added salt of comparable charge density as that of the polyampholyte further compactifies it. However, the addition of more salt results in the weakening of the polyampholyte nature and reentrant swelling of non-neutral polyampholyte.

A poly(4-acrylamidosalicylic acid) gel exhibits multiple phases as characterized by distinct degrees of swelling; the gel can take one of four different swelling values, but none of the intermediate values. The multiple phase behavior appears as a result of the combination of hydrogen bonding and hydrophobic interaction between polymer segments. The gel has remarkable memory: The phase behavior of the gel depends on whether the gel has experienced the most swollen phase or the most collapsed phase in the immediate past. The information is stored and reversibly erased in the form of a macroscopic phase transition behavior. These phenomena are explained by a mean field theory where the number of hydrogen bonds is added to the equation of the state of a gel.

Due to its biological signiicance and physical complexity, understanding protein folding has become one of the greatest problems in modern molecular biophysics, bridging ideas from the physics of disordered systems, polymer physics, and molecular biology. We review the statistical mechanics of heteropolymers (chain molecules with quenched disordered sequence of links) as well as the resulting insights into the physics of proteins. Although we emphasize analytic treatments, we complement the theory with computer simulations, as well as discuss comparisons to available protein experiments. This physical approach explains how general heteropolymeric properties related to their phase behavior account for the biologically important aspects of proteins, including how to design sequences to fold to a particular, preselected conformation; the stability of protein ground states to perturbations, such as mutations and other errors in folding; and how proteins may have evolved. CONTENTS I. Introduction: Protein folding as a physical problem 2 A. Historical background and an overview of the eld 2 1. Molecular biology perspective 2 2. Polymer physics perspective 3 3. Disordered systems and spin glasses 4 B. What is protein folding, and why is it a problem? 4 1. Basic terminology 4 2. Levinthal paradox 4 3. Evolution \paradox" 5 4. Folding and structure prediction 5 C. Freezing and design 5 1. Freezing transition 5 2. Sequence design 6 3. Applications of design concepts to proteins 6 a. Experiments on protein-like peptide chains 6 b. Correlations in protein sequences 7 II. Building models 7 A. Microscopic model: compact globular heteropolymer 7 1. Energy 7 2. Conformations 8 a. Nature of conformation space 8 b. Contacts of monomers and overlap of conformations 9 c. Contact maps 9 3. Interactions 9 4. Sequences: microcanonical and canonical design 10 B. Phenomenological models 11 1. Go model 11 2. Random Energy Model (REM) 11 3. Modiications of REM 12 a. DREM 12