arXiv subjects

Xiangting Li

Publications and source records attributed to Xiangting Li.

15 recordsLinked to original sources

arXiv2026

A generalized work theorem for stopped stochastic chemical reaction networks

We establish a generalized work theorem for stochastic chemical reaction networks (CRNs). By using a compensated Poisson jump process, we identify a martingale structure in a generalized entropy defined relative to an auxiliary backward process and extend nonequilibrium work relations to processes stopped at bounded arbitrary times. Our results apply to discrete, mesoscopic chemical reaction networks and remain valid for singular initial conditions and state-dependent termination events. We show how martingale properties emerge directly from the structure of reaction propensities without assuming detailed balance. Stochastic simulations of a simple chemical kinetic proofreading network are used to explore the dependence of the exponentiated entropy production on initial conditions and model parameters, validating our new work theorem relationships. Our results provide new quantitative tools for analyzing biological circuits ranging from metabolic to gene regulation pathways.

cond-mat.stat-mech↗

arXiv2025

Martingale properties of entropy production and a generalized work theorem with decoupled forward and backward processes

By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work theorems that uses tools from stochastic calculus instead of path-integration. We further strengthen the equality in work theorems by evaluating expectations conditioned on an arbitrary initial state value. These generalizations extend the applicability of work theorems and offer new interpretations of entropy production in stochastic systems. Lastly, we discuss the violation of work theorems in far-from-equilibrium systems.

cond-mat.stat-mech↗

arXiv2025

Reconstructing Noisy Gene Regulation Dynamics Using Extrinsic-Noise-Driven Neural Stochastic Differential Equations

Proper regulation of cell signaling and gene expression is crucial for maintaining cellular function, development, and adaptation to environmental changes. Reaction dynamics in cell populations is often noisy because of (i) inherent stochasticity of intracellular biochemical reactions (``intrinsic noise'') and (ii) heterogeneity of cellular states across different cells that are influenced by external factors (``extrinsic noise''). In this work, we introduce an extrinsic-noise-driven neural stochastic differential equation (END-nSDE) framework that utilizes the Wasserstein distance to accurately reconstruct SDEs from trajectory data from a heterogeneous population of cells (extrinsic noise). We demonstrate the effectiveness of our approach using both simulated and experimental data from three different systems in cell biology: (i) circadian rhythms, (ii) RPA-DNA binding dynamics, and (iii) NF$\kappa$B signaling process. Our END-nSDE reconstruction method can model how cellular heterogeneity (extrinsic noise) modulates reaction dynamics in the presence of intrinsic noise. It also outperforms existing time-series analysis methods such as recurrent neural networks (RNNs) and long short-term memory networks (LSTMs). By inferring cellular heterogeneities from data, our END-nSDE reconstruction method can reproduce noisy dynamics observed in experiments. In summary, the reconstruction method we propose offers a useful surrogate modeling approach for complex biophysical processes, where high-fidelity mechanistic models may be impractical.

q-bio.QM↗

arXiv2024

An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks

We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides both upper and lower bounds associated with the discrepancies in the drift, diffusion, and jump amplitude functions between the two jump-diffusion processes. Then, we propose a temporally decoupled squared $W_2$-distance method for efficiently reconstructing unknown jump-diffusion processes from data using parameterized neural networks. We further show its performance can be enhanced by utilizing prior information on the drift function of the jump-diffusion process. The effectiveness of our proposed reconstruction method is demonstrated across several examples and applications.

stat.ML↗

arXiv2024

Perturbative adaptive importance sampling for Bayesian LOO cross-validation

Importance sampling (IS) is an efficient stand-in for model refitting in performing (LOO) cross-validation (CV) on a Bayesian model. IS inverts the Bayesian update for a single observation by reweighting posterior samples. The so-called importance weights have high variance -- we resolve this issue through adaptation by transformation. We observe that removing a single observation perturbs the posterior by $\mathcal{O}(1/n)$, motivating bijective transformations of the form $T(\theta)=\theta + h Q(\theta)$ for $0<h\ll 1.$ We introduce several such transformations: partial moment matching, which generalizes prior work on affine moment-matching with a tunable step size; log-likelihood descent, which partially invert the Bayesian update for an observation; and gradient flow steps that minimize the KL divergence or IS variance. The gradient flow and likelihood descent transformations require Jacobian determinants, which are available via auto-differentiation; we additionally derive closed-form expressions for logistic regression and shallow ReLU networks. We tested the methodology on classification ($n\ll p$), count regression (Poisson and zero-inflated negative binomial), and survival analysis problems, finding that no single transformation dominates but their combination nearly eliminates the need to refit.

stat.ME↗

arXiv2024

Reliable ligand discrimination in stochastic multistep kinetic proofreading: First passage time vs. product counting strategies

Cellular signaling, crucial for biological processes like immune response and homeostasis, relies on specificity and fidelity in signal transduction to accurately respond to stimuli amidst biological noise. Kinetic proofreading (KPR) is a key mechanism enhancing signaling specificity through time-delayed steps, although its effectiveness is debated due to intrinsic noise potentially reducing signal fidelity. In this study, we reformulate the theory of kinetic proofreading (KPR) by convolving multiple intermediate states into a single state and then define an overall "processing" time required to traverse these states. This simplification allows us to succinctly describe kinetic proofreading in terms of a single waiting time parameter, facilitating a more direct evaluation and comparison of KPR performance across different biological contexts such as DNA replication and T cell receptor (TCR) signaling. We find that loss of fidelity for longer proofreading steps relies on the specific strategy of information extraction and show that in the first-passage time (FPT) discrimination strategy, longer proofreading steps can exponentially improve the accuracy of KPR at the cost of speed. Thus, KPR can still be an effective discrimination mechanism in the high noise regime. However, in a product concentration-based discrimination strategy, longer proofreading steps do not necessarily lead to an increase in performance. However, by introducing activation thresholds on product concentrations, can we decompose the product-based strategy into a series of FPT based strategies to better resolve the subtleties of KPR-mediated product discrimination. Our findings underscore the importance of understanding KPR in the context of how information is extracted and processed in the cell.

q-bio.MN↗

arXiv2024

Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations

We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on this analysis, we propose the use of a squared $W_2$ distance-based loss functions in the \textit{reconstruction} of SDEs from noisy data. To demonstrate the practicality of our Wasserstein distance-based loss functions, we performed numerical experiments that demonstrate the efficiency of our method in reconstructing SDEs that arise across a number of applications.

math.PR↗

arXiv2023

A Spectral Approach for Learning Spatiotemporal Neural Differential Equations

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms. In this paper, we propose a novel neural-ODE based method that uses spectral expansions in space to learn spatiotemporal DEs. The major advantage of our spectral neural DE learning approach is that it does not rely on spatial discretization, thus allowing the target spatiotemporal equations to contain long range, nonlocal spatial interactions that act on unbounded spatial domains. Our spectral approach is shown to be as accurate as some of the latest machine learning approaches for learning PDEs operating on bounded domains. By developing a spectral framework for learning both PDEs and integro-differential equations, we extend machine learning methods to apply to unbounded DEs and a larger class of problems.

cs.LG↗

arXiv2023

Stochastic nucleosome disassembly mediated by remodelers and histone fragmentation

We construct and analyze monomeric and multimeric models of the stochastic disassembly of a single nucleosome. Our monomeric model predicts the time needed for a number of histone-DNA contacts to spontaneously break, leading to dissociation of a non-fragmented histone from DNA. The dissociation process can be facilitated by DNA binding proteins or processing molecular motors that compete with histones for histone-DNA contact sites. Eigenvalue analysis of the corresponding master equation allows us to evaluate histone detachment times under both spontaneous detachment and protein-facilitated processes. We find that competitive DNA binding of remodeling proteins can significantly reduce the typical detachment time but only if these remodelers have DNA-binding affinities comparable to those of histone-DNA contact sites. In the presence of processive motors, the histone detachment rate is shown to be proportional to the product of the histone single-bond dissociation constant and the speed of motor protein procession. Our simple intact-histone model is then extended to allow for multimeric nucleosome kinetics that reveal additional pathways of disassembly. In addition to a dependence of complete disassembly times on subunit-DNA contact energies, we show how histone subunit concentrations in bulk solution can mediate the disassembly process by rescuing partially disassembled nucleosomes. Moreover, our kinetic model predicts that remodeler binding can also bias certain pathways of nucleosome disassembly, with higher remodeler binding rates favoring intact-histone detachment.

q-bio.BM↗

arXiv2023

The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus

Recent studies show that newly sampled monkeypox virus (MPXV) genomes exhibit mutations consistent with Apolipoprotein B mRNA Editing Catalytic Polypeptide-like3 (APOBEC3)-mediated editing, compared to MPXV genomes collected earlier. It is unclear whether these single nucleotide polymorphisms (SNPs) result from APOBEC3-induced editing or are a consequence of genetic drift within one or more MPXV animal reservoirs. We develop a simple method based on a generalization of the General-Time-Reversible (GTR) model to show that the observed SNPs are likely the result of APOBEC3-induced editing. The statistical features allow us to extract lineage information and estimate evolutionary events.

q-bio.PE↗

arXiv2023

Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions

There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in predation or harvesting. Here, we apply a recently formulated kinetic population theory to formally construct an age-structured single-species population model that includes a cannibalistic interaction in which older individuals prey on younger ones. Depending on the age-dependent structure of this interaction, our model can exhibit transient or steady-state overcompensation of an increased death rate as well as oscillations of the total population, both phenomena that have been observed in ecological systems. Analytic and numerical analysis of our model reveals sufficient conditions for overcompensation and oscillations. We also show how our structured population partial integrodifferential equation (PIDE) model can be reduced to coupled ODE models representing piecewise constant parameter domains, providing additional mathematical insight into the emergence of overcompensation.

q-bio.PE↗

arXiv2022

Stochastic dynamics and ribosome-RNAP interactions in Transcription-Translation Coupling

Under certain cellular conditions, transcription and mRNA translation in prokaryotes appear to be "coupled," in which the formation of mRNA transcript and production of its associated protein are temporally correlated. Such transcription-translation coupling (TTC) has been evoked as a mechanism that speeds up the overall process, provides protection during the transcription, and/or regulates the timing of transcript and protein formation. What molecular mechanisms underlie ribosome-RNAP coupling and how they can perform these functions have not been explicitly modeled. We develop and analyze a continuous-time stochastic model that incorporates ribosome and RNAP elongation rates, initiation and termination rates, RNAP pausing, and direct ribosome and RNAP interactions (exclusion and binding). Our model predicts how distributions of delay times depend on these molecular features of transcription and translation. We also propose additional measures for TTC: a direct ribosome-RNAP binding probability and the fraction of time the translation-transcription process is "protected" from attack by transcription-terminating proteins. These metrics quantify different aspects of TTC and differentially depend on parameters of known molecular processes. We use our metrics to reveal how and when our model can exhibit either acceleration or deceleration of transcription, as well as protection from termination. Our detailed mechanistic model provides a basis for designing new experimental assays that can better elucidate the mechanisms of TTC.

q-bio.SC↗

arXiv2014

Dynamic synchrotron X-ray imaging study of effective temperature in a vibrated granular medium

We present a dynamic synchrotron X-ray imaging study of the effective temperature $T_{eff}$ in a vibrated granular medium. By tracking the directed motion and the fluctuation dynamics of the tracers inside, we obtained $T_{eff}$ of the system using Einstein relation. We found that as the system unjams with increasing vibration intensities $Γ$, the structural relaxation time $τ$ increases substantially which can be fitted by an Arrhenius law using $T_{eff}$. And the characteristic energy scale of structural relaxation yielded by the Arrhenius fitting is $E = 0.21 \pm 0.02$ $pd^3$, where $p$ is the pressure and $d$ is the background particle diameter, which is consistent with those from hard sphere simulations in which the structural relaxation happens via the opening up of free volume against pressure.

cond-mat.soft↗

arXiv2007

Time-Reversal Coherent Control in Nanoplasmonics

We introduce an approach to determining the required waveforms to coherently control the optical energy localization in plasmonic nanosystems. This approach is based on the impulsive localized excitation of the nanosystem and time reversal of the generated far-zone field at a single point with one polarization. Despite strong interaction and significant dephasing and dissipation in metal plasmonic systems, and incompleteness of this time reversal, the proposed approach proves to be very efficient in controlling the nanoscale optical fields. Possible applications include nanoscale spectroscopy and photomodification, ultradense memory, and information processing on the nanoscale.

cond-mat.dis-nn↗

arXiv2005

New Method to Calculate Electrical Forces Acting on a Sphere in an Electrorheological Fluid

We describe a method to calculate the electrical force acting on a sphere in a suspension of dielectric spheres in a host with a different dielectric constant, under the assumption that a spatially uniform electric field is applied. The method uses a spectral representation for the total electrostatic energy of the composite. The force is expressed as a certain gradient of this energy, which can be expressed in a closed analytic form rather than evaluated as a numerical derivative. The method is applicable even when both the spheres and the host have frequency-dependent dielectric functions and nonzero conductivities, provided the system is in the quasistatic regime. In principle, it includes all multipolar contributions to the force, and it can be used to calculate multi-body as well as pairwise forces. We also present several numerical examples, including host fluids with finite conductivities. The force between spheres approaches the dipole-dipole limit, as expected, at large separations, but departs drastically from that limit when the spheres are nearly in contact. The force may also change sign as a function of frequency when the host is a slightly conducting fluid.

cond-mat.mtrl-sci↗