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Julian Lee

Publications and source records attributed to Julian Lee.

At least 37 records · Page 2Linked to original sources
arXiv2012

Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model

An analytic formula for the density of states of Wako-Saito-Munoz-Eaton model, for a simple class of beta-hairpins, is obtained. Under certain simplifying assumptions on the structure of the native contacts and the values of local entropy, the partition function zeros are also obtained in analytic forms. The zeros are uniformly distributed on a circle, exhibiting a first-order-like nature of the folding transition. After introducing hydrophobic core at the central region of the hairpin, the zeros are shown to distribute uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformations. The dependence of the distribution of the zeros on the position of the hydrophobic core, is shown to have a clear physical interpretation. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are also numerically computed, and their loci are also shown to be closely approximated by concentric circles.

cond-mat.stat-mech↗
arXiv2012

Microcanonical Origin of the Maximum Entropy Principle for Open Systems

The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To make the connection between these two apparently distinct methods for deriving the Boltzmann distribution, it is first shown that the uniform distribution for a microcanonical distribution is obtained from the Maximum Entropy Principle applied to a closed system. Then I show that the target function in the Maximum Entropy Principle for the open system, is obtained by partial maximization of Gibbs-Shannon entropy of the closed universe over the microstate probability distributions of the heat bath. Thus, microcanonical origin of the Entropy Maximization procedure for an open system, is established in a rigorous manner, showing the equivalence between apparently two distinct approaches for deriving the Boltzmann distribution. By extending the mathematical formalism to dynamical paths, the result may also provide an alternative justification for the principle of path entropy maximization as well.

cond-mat.stat-mech↗
arXiv2012

A derivation of the master equation from path entropy maximization

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order Markov processes and the master equation as unique solutions to an inverse problem. In particular, we find that when the constraints are not enough to uniquely determine the stochastic model, the n-th order Markov process emerges as the unique maximum entropy solution to this otherwise under-determined problem. This gives a rigorous alternative for justifying such models while providing a systematic recipe for generalizing widely accepted stochastic models usually assumed to follow from first principles.

cond-mat.stat-mech↗
arXiv2012

Collapse transition of a square-lattice polymer with next nearest-neighbor interaction

We study the collapse transition of a polymer on a square lattice with both nearest-neighbor and next nearest-neighbor interactions, by calculating the exact partition function zeros up to chain length 36. The transition behavior is much more pronounced than that of the model with nearest-neighbor interactions only. The crossover exponent and the transition temperature are estimated from the scaling behavior of the first zeros with increasing chain length. The results suggest that the model is of the same universality class as the usual theta point described by the model with only nearest-neighbor interaction.

cond-mat.stat-mech↗
arXiv2012

Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudo-transition.

cond-mat.stat-mech↗
arXiv2011

Parallel Algorithm for Calculation of the Exact Partition Function of a Lattice Polymer

We develop a parallel algorithm that calculates the exact partition function of a lattice polymer, by enumerating the number of conformations for each energy level. An efficient parallelization of the calculation is achieved by classifying the conformations according to the shape of the box spanned by a conformation, and enumerating only those in a given box at a time. The calculation time for each box is reduced by preventing the conformations related by symmetries from being generated more than once. The algorithm is applied to study the collapse transition of a lattice homopolymer on a square lattice, by calculating the specific heat for chain lengths up to 36.

cond-mat.stat-mech↗
arXiv2011

Exact partition function zeros and the collapse transition of a two-dimensional lattice polymer

We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy value, and the exact distributions of the partition function zeros are found in the complex temperature plane by solving a polynomial equation. We observe that the locus of zeros closes in on the positive real axis as the chain length increases, providing the evidence for the onset of the collapse transition. By analyzing the scaling behavior of the first zero with the polymer length, we estimate the transition temperature and the crossover exponent.

cond-mat.stat-mech↗
arXiv2003

Design of a Protein Potential Energy Landscape by Parameter Optimization

We propose an automated protocol for designing the energy landscape of a protein energy function by optimizing its parameters. The parameters are optimized so that not only the global minimum energy conformation becomes native-like, but also the conformations distinct from the native structure have higher energies than those close to the native one. We successfully apply our protocol to the parameter optimization of the UNRES potential energy, using the training set of betanova, 1fsd, the 36-residue subdomain of chicken villin headpiece (PDB ID 1vii), and the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd). The new protocol of the parameter optimization shows better performance than earlier methods where only the difference between the lowest energies of native-like and non-native conformations was adjusted without considering various degrees of native-likeness of the conformations. We also perform jackknife tests on other proteins not included in the training set and obtain promising results. The results suggest that the parameters we obtained using the training set of the four proteins are transferable to other proteins to some extent.

cond-mat.soft↗
arXiv2003

Full Optimization of Linear Parameters of a United Residue Protein Potential

We apply the general protocol of parameter optimization (Lee, J. et al. Phys. Chem. B 2001, 105, 7291) to the UNRES potential. In contrast to the earlier works where only the relative weights of various interaction terms were optimized, we optimize all linear parameters of the potential. The method exploits the high efficiency of the conformal space annealing method in finding distinct low energy conformations. For a given training set of proteins, the parameters are modified to make the native-like conformations energetically more favorable than the non-native ones. Linear approximation is used to estimate the energy change due to the parameter modification. The parameter change is followed by local energy reminimization and new conformational searches to find the energies of native-like and non-native local minima of the energy function with new parameters. These steps are repeated until the potential predicts a native-like conformation as one of the low energy conformations for each protein in the training set. We consider a training set of crambin (PDB ID 1ejg), 1fsd, and the 10-55 residue fragment of staphylococcal protein A (PDB ID 1bdd). As the first check for the feasibility of our protocol, we optimize the parameters separately for these proteins and find an optimal set of parameters for each of them. Next we apply the method simultaneously to these three proteins. By refining all linear parameters, we obtain an optimal set of parameters from which the native-like conformations of the all three proteins are retrieved as the global minima, without introducing additional multi-body energy terms.

cond-mat.soft↗
arXiv2003

Unbiased Global Optimization of Lennard-Jones Clusters for N <= 201 by Conformational Space Annealing Method

We apply the conformational space annealing (CSA) method to the Lennard-Jones clusters and find all known lowest energy configurations up to 201 atoms, without using extra information of the problem such as the structures of the known global energy minima. In addition, the robustness of the algorithm with respect to the randomness of initial conditions of the problem is demonstrated by ten successful independent runs up to 183 atoms. Our results indicate that the CSA method is a general and yet efficient global optimization algorithm applicable to many systems.

cond-mat.stat-mech↗
arXiv2003

Folding Mechanism of Small Proteins

Extensive Monte Carlo folding simulations for four proteins of various structural classes are carried out, using a single atomistic potential. In all cases, collapse occurs at a very early stage, and proteins fold into their native-like conformations at appropriate temperatures. The results demonstrate that the folding mechanism is controlled not only by thermodynamic factors but also by kinetic factors: The way a protein folds into its native structure, is also determined by the convergence point of early folding trajectories, which cannot be obtained by the free energy surface.

cond-mat.stat-mech↗
arXiv2001

Tunneling between the giant gravitons in AdS5 x S5

I consider the giant gravitons in AdS5 x S5. By numerical simulation, I show a strong indication that there is no instanton solution describing the direct tunneling between the giant graviton in the S5 and its dual counterpart in the AdS5. I argue that it supports the supersymmetry breaking scenario suggested in hep-th/0008015

hep-th↗
arXiv2000

Exact Zeros of the Partition Function for a Continuum System with Double Gaussian Peaks

We calculate the exact zeros of the partition function for a continuum system where the probability distribution for the order parameter is given by two asymmetric Gaussian peaks. When the positions of the two peaks coincide, the two separate loci of zeros which used to give first-order transition touch each other, with density of zeros vanishing at the contact point on the positive real axis. Instead of the second-order transition of Ehrenfast classification as one might naively expect, one finds a critical behavior in this limit.

cond-mat.stat-mech↗
arXiv1999

Mass Spectrum of D=11 Supergravity on AdS2 x S2 x T7

We compute the Kaluza-Klein mass spectrum of the D=11 supergravity compactified on AdS2 x S2 x T7 and arrange it into representations of the SU(1,1|2) superconformal algebra. This geometry arises in M theory as the near horizon limit of a D=4 extremal black-hole constructed by wrapping four groups of M-branes along the T7. Via AdS/CFT correspondence, our result gives a prediction for the spectrum of the chiral primary operators in the dual conformal quantum mechanics yet to be formulated.

hep-th↗
arXiv1999

Duality in SU(N) x SU(N') Product Group from M theory

We generalize the M-theoretic duality of Schmaltz and Sundrum to the product group SU(N) x SU(N') case. We show that the type IIA brane configurations for dual gauge theories are in fact two special limits of the same M-theory 5-brane, just as in the case of the simple SU(N) group.

hep-th↗
arXiv1999

Statistical Entropy and AdS/CFT Correspondence in BTZ Black Holes

We study AdS/CFT correspondence in the case of AdS3. We obtain the statistical entropy of the BTZ black hole in terms of the correct central charge and the conformal dimensions for the states corresponding to the BTZ black hole. We point out the difference between our method and the old fashioned approaches based on SL(2,R) Wess-Zumino-Witten model or Liouville theory.

hep-th↗
arXiv1998

Hamiltonian formulation of the D-brane action and the light-cone Hamiltonian

We present the Hamiltonian formulation of the bosonic Dirichlet p-brane action. We rewrite the recently proposed quadratic D-brane action in terms of generalized shift vector and lapse function. The first class and the second class constraints are explicitly separated for the bosonic case. We then impose the gauge conditions in such a way that only time-independent gauge transformations are left. In this gauge we obtain the light-cone Hamiltonian which is quadratic in the field momenta of scalar and vector fields. The constraints are explicitly solved to eliminate part of the canonical variables. The Dirac brackets between the remaining variables are computed and shown to be equal to simple Poisson brackets.

hep-th↗