Kinetics of the Collapse Transition

For proteins, the problem is seen as follows When an egg is boiled, the proteins it contains unfold. Can this procedure be reversed in theory Or, in other words, can the encrypted code of protein folding be deciphered from the sequence [112,113]. 

The fastest proteins fold amazingly quickly some as fast as a millionth of a second. While this time is very fast on a person s timescale, it is remarkably long for computers to simulate. In fact, there is about a 1000-fold gap between the simulation timescales and the times at which the fastest proteins fold. This is why the simulation of collapse kinetics is extremely computationally demanding. Thus, the current challenge lies in understanding how particular chemical sequences in coarse-grained copolymer models lead to particular collapse features. This is a fundamental issue in the problem. 

The formation of a compact globule in copolymers requires them to have specific conformations, which are reached through local conformational fluctuations. A characteristic collapse time may be defined as for instance the time for which the gyration radius reaches its equilibrium value. This time measures the approach to equilibrium for the system and is related to the mean first passage time. 

Let us compare the kinetics of the selective-solvent-induced collapse of protein-like copolymers with the collapse of random and random-block copolymers [18]. Several kinetic criteria were examined using Langevin molecular dynamics simulations. There are some general results, which seem to be independent of the nature of interactions or the kinetic criteria monitored during the collapse. Here, we restrict our analysis to the evolution of the characteristic ratio f = (Rgp/Rg ) that combines the partial mean-square radii of gyration calculated separately for hydrophobic and hydrophilic beads, k2n and Rg . This ratio takes into account both the properties of compactness and solubility for a heteropolymer globule [70] (compactness is directly related to the mean size of the hydrophobic core, whereas solubility should be dependent on the size of the hydrophilic shell). 

Using the f value, let us define the time-dependent quality 2 [f (f)/f (0) - 1] and three intermediate folding times fi/4, t]/2, and 3/4, describing its evolution, as well as the corresponding sequence-averaged probability distribution functions Wi/4, Wi/2, and W3/4. The distribution of folding times averaged over 1000 different sequences of 128-unit HP copolymers with random, random-block, and protein-like statistics are shown in Fig. 26. 

Let us compare the kinetics of the selective-solvent-induced collapse of protein-like copolymers with the collapse of random and random-block copolymers [18]. Several kinetic criteria were examined using Langevin molecular dynamics simulations. There are some general results, which seem to be independent of the nature of interactions or the kinetic criteria monitored during the collapse. Here, we restrict our analysis to the evolution of the char- 

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An electron transfer alone to the nitro compound is not sufficient to promote oxygen transfer, since the nitroarene radical anion, independently generated by electrochemical techniques in the presence of phosphine, did not afford any phosphine oxide. An ion pair is a reasonable representation of the rate-limiting transition state and neither the N-0 bond breaking nor the P-0 bond making are determining factors in the kinetics of the oxygen-transfer process. The actual transfer must be facile and the collapse of the ion pair via a cyclic intermediate like ... 

The respective kinetics correlates with and can be predicted from the glass transition temperature of the carrier materials. Plasticization by water absorption under conditions of high humidity may cause reduction of the glass transition temperature below room temperature. Then, the structural change in the wall material leads to collapse of the food powder, resulting in flavor release from the rubber state of the carrier matrices (Ubbink and Schoonman, 2003). 

For NIPAAm free polymers in NIPAAm gel, the polymer chains also contract in response to the increased temperature, but they do so more quickly because they are not constrained by the gel network. The slow kinetics of the NIPAAm volume phase transition has been e q)lained in terms of a non-uniform collapse of the gel network (6). The gel near the sur ce collapses first, forming a dense layer of hydrophobic gel, and it is the diffusion of water through this layer that is responsible for the slow kinetics. The NIPAAm free polymer can produce... 

The transition from the expanded state to the collapsed one and vice versa is controlled by diffusion of the solvent in the gel [56, 57], It was found [56] that the kinetics of swelling and deswelling of the gel is determined by local motions controlled by the diffusion equation in which the diffusion coefficient is given by the ratio of the bulk modulus to the frictional factor (between network and liquid). Whereas in our samples with a volume 1 cm3, the transition from one to another equilibrium state takes several days, for submicron spheres this time... 

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