arXiv subjects

D. Thirumalai

Publications and source records attributed to D. Thirumalai.

175 records · Page 10Linked to original sources

arXiv1998

Linking Rates of Folding in Lattice Models of Proteins with Underlying Thermodynamic Characteristics

We investigate the sequence-dependent properties of proteins that determine the dual requirements of stability of the native state and its kinetic accessibility using simple cubic lattice models. Three interaction schemes are used to describe the potentials between residues. We show that, under the simulation conditions when the native basin of attraction (NBA) is stable, there is an excellent correlation between folding times (τ_{F}) and the dimensionless parameter (σ_{T} = (T_θ - T_{F})/T_θ), where (T_θ) is the collapse temperature and (T_{F}) is the folding transition temperature. There is also a significant correlation between (τ_{F}) and Z-score (Z=(E_{N}-E_{ms})/δ), where (E_{N}) is the energy of the native state, (E_{ms}) is the average energy of the ensemble of misfolded structures, and (δ) is the dispersion in contact energies. An approximate relationship between (σ_{T}) and the Z-score is derived, which explains the superior correlation seen between (τ_{F}) and (σ_{T}). For two state folders (τ_{F}) is linked to the free energy difference between the unfolded states and the NBA.

cond-mat.soft↗

arXiv1998

Cooperativity in Protein Folding: From Lattice Models with Side Chains to Real Proteins

We consider equilibrium folding transitions in lattice protein models with and without side chains. A dimensionless measure, $Omega_{c}$, is introduced to quantitatively assess the degree of cooperativity in lattice models and in real proteins. We show that larger values of $Ω_{c}$ resembling those seen in proteins are obtained in lattice models with side chains (LMSC). The enhanced cooperativity in LMSC is due to the possibility of denser packing of side chains in the interior of the model protein. We also establish that $Ω_{c}$ correlates extremely well with (σ= (T_θ -T_{f} )/T_θ), where (T_θ) and (T_{f}) are collapse and folding transition temperatures, respectively. These theoretical ideas are used to analyze folding transitions in various real proteins. The values of $Ω_{c}$ extracted from experiments show a correlation with $σ$. We conclude that the degree of cooperativity can be expressed in terms of the single parameter $σ$, which can be estimated from experimental data.

cond-mat.soft↗

arXiv1997

Distribution Function of the End-to-End Distance of Semiflexible Polymers

The distribution function of the end-to-end distance of a semiflexible polymer, G(R;L) (where R denotes the end-to-end distance and L the contour length), is calculated using a meanfield-like approach. The theory yields an extremely simple expression for G(R;L) which is in excellent agreement with Monte Carlo simulations. The second and fourth moments of G(R;L) agree with exact results for a semiflexible polymer in both the random coil and the rod limit.

cond-mat.stat-mech↗

arXiv1997

Thermodynamic stability of folded proteins against mutations

By balancing the average energy gap with its typical change due to mutations for protein-like heteropolymers with M residues, we show that native states are unstable to mutations on a scale M* ~ (lambda/sigma_mu)^(1/zeta_s), where lambda is the dispersion in the interaction free energies and sigma_mu their typical change. Theoretical bounds and numerical estimates (based on complete enumeration on four lattices) of the instability exponent zeta_s are given. Our analysis suggests that a limiting size of single-domain proteins should exist, and leads to the prediction that small proteins are insensitive to random mutations.

cond-mat.soft↗

arXiv1997

Kinetic Partitioning Mechanism as a Unifying Theme in the Folding of Biomolecules

We present a unified framework for folding kinetics of proteins and RNA. The basis for this framework relies on the notion of topological frustration, which gives rise to several competing basins of attraction (CBA) in addition to the native basin of attraction (NBA) on the free energy surface. A rough free energy surface results in direct and indirect pathways to the NBA, i.e., a kinetic partitioning mechanism (KPM). The unified framework for folding kinetics allows us to propose a foldability principle, according to which fast folding sequences are characterized by the folding transition temperature $T_{F}$ being close to the collapse transition temperature $T_{θ}$. Biomolecules, for which foldability principle is satisfied, such as small proteins and tRNAs, are expected to fold rapidly with two-state kinetics. Estimates for the multiple time scales in KPM are also given.

cond-mat.soft↗

arXiv1997

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities η, decrease as 1/ηat large ηand have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn α-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.

cond-mat.soft↗

arXiv1997

Statistical Mechanics of Semiflexible Chains: A Meanfield Variational Approach

We describe a simple meanfield variational approach to study a number of properties of intrinsically stiff chains which are appropriate models for a large class of biopolymers. We present the calculation of the distribution of end-to-end distance and the elastic response of stiff chains under tension using this approach. In the former example we find that the simple expression almost quantitatively fits the results of computer simulation. For the case of the stiff chain under tension we recover analytically all the known limits. We obtain quantitative agreement with recent experiments on the stretching of DNA. The limitations of our approach are also discussed.

cond-mat.soft↗

arXiv1996

Protein Folding Kinetics: Time Scales, Pathways, and Energy Landscapes in Terms of Sequence Dependent Properties

The folding kinetics of a number of sequences for off-lattice continuum model of proteins is studied using Langevin simulations at two values of the friction coefficient. We show that there is a remarkable correlation between folding times, $τ_{F}$, and $σ= (T_{θ} - T_{F})/T_{θ} $, where $T_{θ}$ and $T_{F}$ are the equilibrium collapse and folding transition temperatures, respectively. The microscopic dynamics reveals several scenarios for the refolding kinetics depending on the values of $σ$. Proteins with small $σ$ reach the native conformation via a nucleation collapse mechanism and their energy landscape is characterized by single dominant native basin of attraction. Proteins with large $σ$ get trapped in competing basins of attraction, in which they adopt misfolded structures. In this case only a small fraction of molecules $Φ$ access the native state rapidly, the majority of them approach the native state by a three stage multipathway mechanism. The partition factor $Φ$ is determined by $σ$: smaller the value of $σ$ larger is $Φ$. The qualitative aspects of our results are found to be independent of the friction coefficient. Estimates for time scales for folding of small proteins via a nucleation collapse mechanism are presented.

cond-mat.stat-mech↗

arXiv1996

Reply to Comment on "Criterion that Determines the Foldability of Proteins"

We point out that the correlation between folding times and $σ= (T_{θ} - T_{f})/T_{θ}$ in protein-like heteropolymer models where $T_{θ}$ and $T_{f}$ are the collapse and folding transition temperatures was already established in 1993 before the other presumed equivalent criterion (folding times correlating with $T_{f}$ alone) was suggested. We argue that the folding times for these models show no useful correlation with the energy gap even if restricted to the ensemble of compact structures as suggested by Karplus and Shakhnovich (cond-mat/9606037).

cond-mat↗

arXiv1996

Factors Governing the Foldability of Proteins

We use a three dimensional cubic lattice model of proteins to study their properties that determine folding to the native state. The protein chain is modeled as a sequence of $N$ beads. The interactions between beads are taken from a Gaussian distribution of energies. We studied 56 sequences with unique ground states for $N = 15$ and $27$. Thermodynamic and kinetic properties were determined using Monte Carlo simulations and exhaustive enumeration. For all sequences we find collapse temperature, $T_θ$, at which the protein collapses into compact structure, and folding temperature, $T_{f}$, at which the protein acquires the native state. We show that parameter $σ= (T_θ - T_{f})/T_θ$ correlates extremely well with folding times. Fast folders reach the native state via a nucleation collapse mechanism without forming any intermediates, whereas for moderate and slow folders only a fraction of molecules $Φ$ reaches the native state by this process. The remaining fraction folds via three stage multipathway process. The simultaneous requirement of native state stability and kinetic accessibility can be achieved for the sequences with small values of $σ$.

cond-mat↗

arXiv1996

Semiflexible Chains under Tension

A functional integral formalism is used to derive the extension of a stiff chain subject to an external force. The force versus extension curves are calculated using a meanfield approach in which the hard constraint $u^2(s)=1$ is replaced by a global constraint $ < u^2(s) > = 1$ where $ u(s)$ is the tangent vector describing the chain and $s$ is the arc length. The theory ``quantitatively'' reproduces the experimental results for DNA that is subject to a constant force. We also treat the problems of a semiflexible chain in a nematic field. In the limit of weak nematic field strength our treatment reproduces the exact results for chain expansion parallel to the director. When the strength of nematic field is large, a situation in which there are two equivalent minima in the free energy, the intrinsically meanfield approach yields incorrect results for the dependence of the persistence length on the nematic field.

cond-mat↗

arXiv1996

A Criterion That Determines Fast Folding of Proteins: A Model Study

We consider the statistical mechanics of a full set of two-dimensional protein-like heteropolymers, whose thermodynamics is characterized by the coil-to-globular ($T_θ$) and the folding ($T_f$) transition temperatures. For our model, the typical time scale for reaching the unique native conformation is shown to scale as $τ_f\sim F(M)\exp(σ/σ_0)$, where $σ=1-T_f/T_θ$, $M$ is the number of residues, and $F(M)$ scales algebraically with $M$. We argue that $T_f$ scales linearly with the inverse of entropy of low energy non-native states, whereas $T_θ$ is almost independent of it. As $σ\rightarrow 0$, non-productive intermediates decrease, and the initial rapid collapse of the protein leads to structures resembling the native state. Based solely on {\it accessible} information, $σ$ can be used to predict sequences that fold rapidly.

chem-ph↗

arXiv1996

Localization of a Polymer with Internal Constraints

We argue that Kantor and Kardar's assertion that their simulation results contradict our criterion for the localization of a softly constrainted ideal polymer is incorrect. Our criterion is inapplicable to the model used in these simulations. We argue that our criterion for localization of as polymer with internal constraints strongly suggests that the models with soft and hard constraints belong to different universality classes. The size measure used by Kantor and Kardar is also not adequate for studying polymer localization. We also show that, in spite of these contrasts, combining the simulation results with our criterion for ideal chains seems to uncover some intriguing physics.

cond-mat↗