Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I: Dependence on native structures and amino acid sequences

Haruo Abe, Hiroshi Wako

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a 1, a 2, b 1, and b 2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a 1 and a 2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b 1 and b 2, but their native conformation is different from that of proteins a 1 and a 2. However, the chevron plots of proteins a 1 and a 2 are very similar to each other, and those of proteins b 1 and b 2 differ considerably. Since the contact orders of proteins b 1 and b 2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.

Original languageEnglish
Pages (from-to)3442-3454
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Volume388
Issue number17
DOIs
Publication statusPublished - 2009 Sep 1

Fingerprint

Protein Folding
Unfolding
Amino Acid Sequence
Folding
folding
amino acids
Kinetics
proteins
Protein
acids
kinetics
Free Energy
Conformation
plots
free energy
Model
Amino Acids
Long-range Interactions
Relaxation Time
profiles

Keywords

  • Chevron plot
  • Chevron rollover
  • Contact order
  • Folding/unfolding kinetics
  • Long-range interaction
  • Protein folding

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistics and Probability

Cite this

@article{3933903a9d5b49b299be894d945db1c6,
title = "Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I: Dependence on native structures and amino acid sequences",
abstract = "The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a 1, a 2, b 1, and b 2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a 1 and a 2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b 1 and b 2, but their native conformation is different from that of proteins a 1 and a 2. However, the chevron plots of proteins a 1 and a 2 are very similar to each other, and those of proteins b 1 and b 2 differ considerably. Since the contact orders of proteins b 1 and b 2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.",
keywords = "Chevron plot, Chevron rollover, Contact order, Folding/unfolding kinetics, Long-range interaction, Protein folding",
author = "Haruo Abe and Hiroshi Wako",
year = "2009",
month = "9",
day = "1",
doi = "10.1016/j.physa.2009.05.020",
language = "English",
volume = "388",
pages = "3442--3454",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "17",

}

TY - JOUR

T1 - Folding/unfolding kinetics of lattice proteins studied using a simple statistical mechanical model for protein folding, I

T2 - Dependence on native structures and amino acid sequences

AU - Abe, Haruo

AU - Wako, Hiroshi

PY - 2009/9/1

Y1 - 2009/9/1

N2 - The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a 1, a 2, b 1, and b 2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a 1 and a 2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b 1 and b 2, but their native conformation is different from that of proteins a 1 and a 2. However, the chevron plots of proteins a 1 and a 2 are very similar to each other, and those of proteins b 1 and b 2 differ considerably. Since the contact orders of proteins b 1 and b 2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.

AB - The folding/unfolding kinetics of a three-dimensional lattice protein was studied using a simple statistical mechanical model for protein folding that we developed earlier. We calculated a characteristic relaxation rate for the free energy profile starting from a completely unfolded structure (or native structure) that is assumed to be associated with a folding rate (or an unfolding rate). The chevron plot of these rates as a function of the inverse temperature was obtained for four lattice proteins, namely, proteins a 1, a 2, b 1, and b 2, in order to investigate the dependency of the folding and unfolding rates on their native structures and amino acid sequences. Proteins a 1 and a 2 fold to the same native conformation, but their amino acid sequences differ. The same is the case for proteins b 1 and b 2, but their native conformation is different from that of proteins a 1 and a 2. However, the chevron plots of proteins a 1 and a 2 are very similar to each other, and those of proteins b 1 and b 2 differ considerably. Since the contact orders of proteins b 1 and b 2 are identical, the differences in their kinetics should be attributed to the amino acid sequences and consequently to the interactions between the amino acid residues. A detailed analysis revealed that long-range interactions play an important role in causing the difference in the folding rates. The chevron plots for the four proteins exhibit a chevron rollover under both strongly folding and strongly unfolding conditions. The slower relaxation time on the broad and flat free energy surfaces of the unfolding conformations is considered to be the main origin of the chevron rollover, although the free energy surfaces have features that are rather complicated to be described in detail here. Finally, in order to concretely examine the relationship between changes in the free energy profiles and the chevron plots, we illustrate some examples of single amino acid substitutions that increase the folding rate.

KW - Chevron plot

KW - Chevron rollover

KW - Contact order

KW - Folding/unfolding kinetics

KW - Long-range interaction

KW - Protein folding

UR - http://www.scopus.com/inward/record.url?scp=67349136316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349136316&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2009.05.020

DO - 10.1016/j.physa.2009.05.020

M3 - Article

AN - SCOPUS:67349136316

VL - 388

SP - 3442

EP - 3454

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 17

ER -