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Eok Kyun Lee

Publications and source records attributed to Eok Kyun Lee.

18 recordsLinked to original sources
arXiv2026

Smooth $\%$MinMax: A Differentiable Relaxation for Codon Harmonization

Codon harmonization aims to adapt the coding sequences for heterologous expression while preserving the native-like patterns of frequent and rare codons that may influence local translation dynamics and co-translational protein folding. However, widely used harmonization metrics, such as $\%$MinMax, are defined on discrete codon sequences and are, therefore, not readily compatible with gradient-based neural codon design. Here, we introduce Smooth $\%$MinMax, denoted as $\%{\rm MinMax}_{(s)}$, a differentiable relaxation of the conventional hard $\%$MinMax metric, denoted as $\%{\rm MinMax}_{(h)}$. $\%{\rm MinMax}_{(s)}$ replaces the discrete codon-usage values with probability-weighted synonymous-codon usage values and replaces the hard $\%$Max/$\%$Min branch with a sigmoid-gated interpolation. This formulation preserves the signed interpretation of $\%{\rm MinMax}_{(h)}$, while enabling optimization with respect to the synonymous-codon probabilities and learnable parameters. In human-to-Escherichia coli codon harmonization experiments, $\%{\rm MinMax}_{(s)}$ closely approximates $\%{\rm MinMax}_{(h)}$ and supports gradient-based profile matching in synonymous-codon probability space. These results suggest $\%{\rm MinMax}_{(s)}$ as a practical bridge between profile-based codon harmonization and neural synonymous-sequence design.

q-bio.QM↗
arXiv2026

MOSAIC: Codon Harmonization of Monte Carlo-Based Simulated Annealing for Linked Codons in Heterologous Protein Expression

Codon usage bias has a crucial impact on the translation efficiency and co-translational folding of proteins, necessitating the algorithmic development of codon optimization/harmonization methods, particularly for heterologous recombinant protein expression. Codon harmonization is especially valuable for proteins sensitive to translation rates, because it can potentially replicate native translation speeds, preserving proper folding and maintaining protein activity. This work proposes a Monte Carlo-based codon harmonization algorithm, MOSAIC (Monte Carlo-based Simulated Annealing for Linked Codons), for the harmonization of a set of linked codons, which differs from conventional codon harmonization, by focusing on the codon sets rather than individual ones. Our MOSAIC demonstrates robust computational performance on ribosomal proteins (S18, S15, S10, and L11) as model systems. Among them, the harmonized gene of RP S18 was expressed and compared with the expression of the wild-type gene. The harmonized gene clearly yielded a larger quantity of the protein, from which the amount of the soluble protein was also significant. These results underscored the potential of the linked codon harmonization approach to enhance the expression and functionality of sensitive proteins, setting the stage for more efficient production of recombinant proteins in various biotechnological and pharmaceutical applications.

q-bio.QM↗
arXiv2023

Understanding Dynamics in Coarse-Grained Models: III. Roles of Rotational Motion and Translation-Rotation Coupling in Coarse-Grained Dynamics

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

physics.chem-ph↗
arXiv2022

MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties

The graph neural network (GNN) has been a powerful deep-learning tool in chemistry domain, due to its close connection with molecular graphs. Most GNN models collect and update atom and molecule features from the fed atom (and, in some cases, bond) features, which are basically based on the two-dimensional (2D) graph representation of 3D molecules. Correspondingly, the adjacency matrix, containing the information on covalent bonds, or equivalent data structures (e.g., lists) have been the main core in the feature-updating processes, such as graph convolution. However, the 2D-based models do not faithfully represent 3D molecules and their physicochemical properties, exemplified by the overlooked field effect that is a "through-space" effect, not a "through-bond" effect. The GNN model proposed herein, denoted as MolNet, is chemically intuitive, accommodating the 3D non-bond information in a molecule, with a noncovalent adjacency matrix $\bf{\bar A}$, and also bond-strength information from a weighted bond matrix $\bf{B}$. The noncovalent atoms, not directly bonded to a given atom in a molecule, are identified within 5 $\unicode{x212B}$ of cut-off range for the construction of $\bf{\bar A}$, and $\bf{B}$ has edge weights of 1, 1.5, 2, and 3 for single, aromatic, double, and triple bonds, respectively. Comparative studies show that MolNet outperforms various baseline GNN models and gives a state-of-the-art performance in the classification task of BACE dataset and regression task of ESOL dataset. This work suggests a future direction of deep-learning chemistry in the construction of deep-learning models that are chemically intuitive and comparable with the existing chemistry concepts and tools.

physics.chem-ph↗
arXiv2020

InteractionNet: Modeling and Explaining of Noncovalent Protein-Ligand Interactions with Noncovalent Graph Neural Network and Layer-Wise Relevance Propagation

Expanding the scope of graph-based, deep-learning models to noncovalent protein-ligand interactions has earned increasing attention in structure-based drug design. Modeling the protein-ligand interactions with graph neural networks (GNNs) has experienced difficulties in the conversion of protein-ligand complex structures into the graph representation and left questions regarding whether the trained models properly learn the appropriate noncovalent interactions. Here, we proposed a GNN architecture, denoted as InteractionNet, which learns two separated molecular graphs, being covalent and noncovalent, through distinct convolution layers. We also analyzed the InteractionNet model with an explainability technique, i.e., layer-wise relevance propagation, for examination of the chemical relevance of the model's predictions. Separation of the covalent and noncovalent convolutional steps made it possible to evaluate the contribution of each step independently and analyze the graph-building strategy for noncovalent interactions. We applied InteractionNet to the prediction of protein-ligand binding affinity and showed that our model successfully predicted the noncovalent interactions in both performance and relevance in chemical interpretation.

q-bio.BM↗
arXiv2019

Density-Dependent Finite System-Size Effects in Equilibrium Molecular Dynamics Estimation of Shear Viscosity: Hydrodynamic and Configurational Study

We study the intrinsic nature of the finite system-size effect in estimating shear viscosity of dilute and dense fluids within the framework of the Green-Kubo approach. From extensive molecular dynamics simulations, we observe that the size effect on shear viscosity is characterized by an oscillatory behavior with respect to system size $L$ at high density and by a scaling behavior with an $L^{-1}$ correction term at low density. Analysis of the potential contribution in the shear-stress autocorrelation function reveals that the former is configurational and is attributed to the inaccurate description of the long-range spatial correlations in finite systems. Observation of the long-time inverse-power decay in the kinetic contribution confirms its hydrodynamic nature. The $L^{-1}$ correction term of shear viscosity is explained by the sensitive change in the long-time tail obtained from a finite system.

physics.chem-ph↗
arXiv2018

Nature of Intrinsic Uncertainties in Equilibrium Molecular Dynamics Estimation of Shear Viscosity for Simple and Complex Fluids

We study two types of intrinsic uncertainties, statistical errors and system size effects, in estimating shear viscosity via equilibrium molecular dynamics simulations and compare them with the corresponding uncertainties in evaluating the self-diffusion coefficient. Uncertainty quantification formulas for the statistical errors in the shear-stress autocorrelation function and shear viscosity are obtained under the assumption that shear stress follows a Gaussian process. Analyses of simulation results for simple and complex fluids reveal that the Gaussianity is more pronounced in the shear-stress process (related to shear viscosity estimation) compared with the velocity process of an individual molecule (related to self-diffusion coefficient). At relatively high densities corresponding to a liquid state, we observe that the shear viscosity exhibits complex size-dependent behavior unless the system is larger than a certain length scale, beyond which reliable shear viscosity values are obtained without any noticeable scaling behavior with respect to the system size. We verify that this size-dependent behavior is configurational and relate the characteristic length scale to the shear-stress correlation length.

physics.chem-ph↗
arXiv2018

Molecular Hydrodynamics: Vortex Formation and Sound Wave Propagation

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.

physics.flu-dyn↗
arXiv2017

Nature of self-diffusion in two-dimensional fluids

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the velocity autocorrelation function. An asymptotic decay law of the velocity autocorrelation function resembles the previously known self-consistent form, $1/(t\sqrt{\ln t})$, however with a rescaled time.

cond-mat.soft↗
arXiv2014

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.

cond-mat.soft↗
arXiv2010

Brownian motion from molecular dynamics

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.

physics.chem-ph↗
arXiv2009

Rate description of Fokker-Planck processes with time-periodic parameters

The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equations of motion are formulated for these three sets of functions and strategies are discussed how to solve them. These methods are illustrated and their usefulness is demonstrated by means of the example of a bistable Brownian oscillator within a large range of driving frequencies from the slow semiadiabatic to the fast driving regime.

cond-mat.stat-mech↗
arXiv2005

Quantum key distribution using superposition of the vacuum and single photon states

B92-type and BB84-type quantum cryptography schemes using superposed states of the vacuum and single particle states which are robust against PNS attacks are studied. The number of securely transferred classical bits per particle (not per qubit) sent in these schemes is calculated and found to have upper bounds. Possible experimental realizations using the cavity QED or linear optics are suggested.

quant-ph↗
arXiv2003

Quantum Cryptography Using Single Particle Entanglement

A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.

quant-ph↗
arXiv2002

Stochastic Processes and the Dirac Equation with External Fields

The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and the backward moving particles in time are discussed.

hep-th↗
arXiv2002

Qubit geometry and conformal mapping

Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and Möbius transformations on the extended complex plane.

quant-ph↗
arXiv2001

Quantum Shift Register

We consider a quantum circuit in which shift and rotation operations on qubits are performed by swap gates and controlled swap gates. These operations can be useful for quantum computers performing elementary arithmetic operations such as multiplication and a bit-wise comparison of qubits.

quant-ph↗