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Noise plays a crucial role in the regulation of cellular and organismal function and behavior. Exploring noise's impact is key to understanding fundamental biological processes, such as gene expression, signal transduction, and the mechanisms of development and evolution. Currently, a comprehensive method to quantify dynamical behavior of cellular noise within these biochemical systems is lacking. In this study, we introduce an optically-controlled perturbation system utilizing the light-sensitive Phytochrome B (PhyB) from \textit{Arabidopsis thaliana}, which enables precise noise modulation with high spatial-temporal resolution. Our system exhibits exceptional sensitivity to light, reacting consistently to pulsed light signals, distinguishing it from other photoreceptor-based promoter systems that respond to a single light wavelength. To characterize our system, we developed a stochastic model for phytochromes that accounts for photoactivation/deactivation, thermal reversion, and the dynamics of the light-activated gene promoter system. To precisely control our system, we determined the rate constants for this model using an omniscient deep neural network that can directly map rate constant combinations to time-dependent state joint distributions. By adjusting the activation rates through light intensity and degradation rates via N-terminal mutagenesis, we illustrate that out optical-controlled perturbation can effectively modulate molecular expression level as well as noise. Our results highlight the potential of employing an optically-controlled gene perturbation system as a noise-controlled stimulus source. This approach, when combined with the analytical capabilities of a sophisticated deep neural network, enables the accurate estimation of rate constants from observational data in a broad range of biochemical reaction networks., Comment: 33 pages, 4 figures

In this paper, we propose a novel quantum classifier utilizing dissipative engineering. Unlike standard quantum circuit models, the classifier consists of a central spin-qubit model. By subjecting the auxiliary qubits to carefully tailored strong dissipations, we establish a one-to-one mapping between classical data and dissipative modes. This mapping enables the encoding of classical data within a decoherence-free subspace, where the central qubit undergoes evolution. The dynamics of the central qubit are governed by an effective Lindblad master equation, resulting in relaxation towards a steady state. We first demonstrate the capability of our model to prepare arbitrary single-qubit states by training the inter-coupling of the system and the external dissipations. By elucidating the underlying classification rule, we subsequently derive a quantum classifier. Leveraging a training set with labeled data, we train the dissipative central spin-qubit system to perform specific classification tasks akin to classical neural networks. Our study illuminates the untapped potential of the dissipative system for efficient and effective classification tasks in the realm of quantum machine learning.

Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of the state space. In this study, we propose repurposing language models as a machine learning approach to solve master equations. We design a prompt-based neural network to map rate parameters, initial conditions, and time values directly to the state joint probability distribution that exactly matches the input contexts. In this way, we approximate the solution of the master equation in its most general form. We train the network using the policy gradient algorithm within the reinforcement learning framework, with feedback rewards provided by a set of variational autoregressive models. By applying this approach to representative examples, we observe high accuracy for both multi-module and high-dimensional systems. The trained network also exhibits extrapolating ability, extending its predictability to unseen data. Our findings establish the connection between language models and master equations, highlighting the possibility of using a single pretrained large model to solve any master equation., Comment: To be published in Proceedings of the National Academy of Sciences

In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we reviewed the random time simulation algorithm and gave the implementations for the parallel version of next reaction random time algorithm. The discussion of computational complexity suggested a factor of $M$ (which is the connection number of the network) folds time consuming reduction for random time simulation algorithm as compared to other exact stochastic simulation algorithms, such as the Gillespie algorithm. For large-scale system, such like the protein-protein interaction network, $M$ is on order of $10^8$. We further demonstrate the power of random time simulation with a GPGPU parallel implementation which achieved roughly 100 folds acceleration as compared with CPU implementations. Therefore the stochastic simulation method we developed here can be of great application value for simulating time evolution process of large-scale network.

Real-time PCR, or Real-time Quantitative PCR (qPCR) is an effective approach to quantify nucleic acid samples. Given the complicated reaction system along with thermal cycles, there has been long-term confusion on accurately calculating the initial nucleic acid amounts from the fluorescence signals. Although many improved algorithms had been proposed, the classical threshold method is still the primary choice in the routine application. In this study, we will first illustrate the origin of the linear relationship between the threshold value and logarithm of the initial nucleic acid amount by reconstructing the PCR reaction process with stochastic simulations. We then develop a new method for the absolute quantification of nucleic acid samples with qPCR. By monitoring the fluorescence signal changes in every stage of the thermal cycle, we are able to calculate a representation of the step-wise efficiency change. This is the first work calculated PCR efficiency change directly from the fluorescence signal, without fitting or sophisticated analysis. Our results revealed that the efficiency change during the PCR process is complicated and can not be modeled simply by monotone function model. Based on the calculated efficiency, we illustrate a new absolute qPCR analysis method for accurately determining nucleic acid amount. The efficiency problem is completely avoided in this new method.