Monte Carlo Calculations on the Dynamics of Polymers in Dilute Solution

Verdier, Peter H.; Stockmayer, W. H.

doi:10.1063/1.1732301

Cited by 539 publications

(208 citation statements)

References 15 publications

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“…The shapes of these two curves are consistent with the general trend of the effect of excluded volume on the shape of the distribution function , as pointed out by VenEer and Stockmayer [9]. Compared to the Gaussian distribution, the distribution function is deficient at low valu es of 1'.…”

Section: For a Gaussian Chain (T = 2) And For A Nonse1£ Intersecting supporting

confidence: 88%

“…However, the behavior of the distribution function as r-70 is hard to ascertain owing to the lattice effects. The indications on the basis of previous Monte Carlo calculations [8][9][10] are that l> 2 represents a better description near the origin, than the case with l = 2.…”

Section: For a Gaussian Chain (T = 2) And For A Nonse1£ Intersecting mentioning

confidence: 96%

“…W all, Windwer, and Gans [8]; Verdier a nd Stockmayer [9], an d Schatzki [10] have demonstrated, on t he basis of Monte Carlo computations, that the distribution of end-to-end distances in a polymer chain is non-Gaussian. Similarly, Fisher and Hiley [11] have demonstra ted t he same thin g USUlg theu' chaincounting method.…”

Section: On the Incompatibility Of Excluded Volume Effects With Gaussmentioning

confidence: 99%

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Distribution function of the end-to-end distances of linear polymers with excluded volume effects

Mazur¹

1965

J. RES. NATL. BUR. STAN. SECT. A.

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The distribution function of t he absolute values of chain lengths of a polymer molec ule which displays t he excluded volume effect cannot assume a Ga ussia n form . This fact follows directly from t heoretical considerations based on the application of t he Central Limit Theorem t o the theory of Markov chains . In order t o determine the exact s hape of the polymer cha in-end distribution function we calculated its vario us momel:ts taken a bou t t he ori"in a nd t heir dependence on the number of polymer segmen ts, USll1g a Mo nte Carlo tech nique for gener ating poly m er chains on a lattice. The res ults obta ined from t he extrapolation of various combinations of t hese mome nts of the general form arc used to determine t he s hap e of t he poly mer distribu t ion fun ction. It is found that t he cha in-end distribution function can be approximated by t he following form :wit h t= 3.2 and a being a parameter, determina ble from the average m ean square cha in-end dis tances.

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Section: For a Gaussian Chain (T = 2) And For A Nonse1£ Intersecting supporting

confidence: 88%

Section: For a Gaussian Chain (T = 2) And For A Nonse1£ Intersecting mentioning

confidence: 96%

Section: On the Incompatibility Of Excluded Volume Effects With Gaussmentioning

confidence: 99%

See 1 more Smart Citation

Distribution function of the end-to-end distances of linear polymers with excluded volume effects

Mazur¹

1965

J. RES. NATL. BUR. STAN. SECT. A.

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“…The kinetics of the model have been calculated using MC simulations: single-site Verdier's lattice dynamics (Verdier & Stockmeyer, 1967), which satisfy: ( I ) the connectivity constraints; (2) self-avoidance, which prevents two beads from occupying the same lattice site; and (3) Metropolis algorithm (Metropolis et al, 1953). The breakage of a disulfide bond is energetically unfavorable.…”

Section: Minimal Lattice Models and Computational Detailsmentioning

confidence: 99%

Denaturants can accelerate folding rates in a class of globular proteins

Camacho

Thirumalai

1996

Protein Science

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We present a lattice Monte Carlo study to examine the effect of denaturants on the folding rates of simplified models of proteins. The two-dimensional model is made from a three-letter code mimicking the presence of hydrophobic, hydrophilic, and cysteine residues. We show that the rate of folding is maximum when the effective hydrophobic interaction eH is approximately equal to the free energy gain es upon forming disulfide bonds. In the range 1 5 t H / e S 5 3, multiple paths that connect several intermediates to the native state lead to fast folding. It is shown that at a fixed temperature and eS the folding rate increases as eH decreases. An approximate model is used to show that eH should decrease as a function of the concentration of denaturants such as urea or guanidine hydrochloride. Our simulation results, in conjunction with this model, are used to show that increasing the concentration of denaturants can lead to an increase in folding rates. This occurs because denaturants can destabilize the intermediates without significantly altering the energy of the native conformation. Our findings are compared with experiments on the effects of denaturants on the refolding of bovine pancreatic trypsin inhibitor and ribonuclease TI. We also argue that the phenomenon of denaturant-enhanced folding of proteins should be general.Keywords: denaturants; energy landscape; folding rates; lattice model It is believed that, in most instances, denaturants such as urea or guanidine hydrochloride (Gdn-Hcl) strongly decrease the rate of folding as their concentration is increased. However, there are examples in which the rate of folding is increased as the concentration of denaturants increases. One of the earliest experiments that demonstrated this effect was in the refolding of carbonic anhydrase (McCoy et al., 1980). Two more recent examples in which this has been illustrated nicely is the refolding of ribonuclease TI (Kiefhaber et al., 1992) and the rearrangement of a kinetically trapped native-like intermediate in bovine pancreatic trypsin inhibitor (BPTI) (Weissman & Kim, 1991). We now discuss the features of these experiments as they pertain to this article.It has been suggested that the folding kinetics of RNase T1 (Kiethaber et al., 1992) is complex, involving parallel pathways. In the predominant pathway, the rapidly formed partially ordered structure reaches the native conformation through a series of two slow kinetic steps. Kiefhaber et al. have argued that the slowest step in this pathway, with time constant of 7,000 s at pH 5 at 10 "C, involves proline isomerization. The very small rate constant for this first-order kinetics is apparently unusually slow compared with other proteins whose rate-determining step also involves pro- line isomerization. These experiments seem to indicate that the incorrect isomer (the C conformation in RNase TI) is trapped in a stable native-like conformation. Consequently, the addition of urea or Gdn-Hcl in concentrations that does not denature the protein could destabilize t...

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“…The statistical method we have used is due to Metropolis et al [S] . It was applied for the first time to the conformational analysis of polymers by Verdier and Stockmayer [6]. Following this method, the set of accepted conformations is assimilated to the space of the states of a Markovian chain.…”

Section: Introductionmentioning

confidence: 99%