The Negative Binomial (NB) distribution is widely used to approximate transcript count distributions in single-cell RNA sequencing (scRNA-seq) data, yet the reason for its ubiquity is not fully understood. Here, we employ a computationally efficient model selection technique to map the relationship between the best-fit models - Beta-Poisson (Telegraph), NB, and Poisson - and the kinetic parameters that govern gene expression stochasticity. Our findings reveal that the NB distribution closely approximates simulated data (incorporating both biological and technical noise) within an intermediate range of the sum of the gene activation and inactivation rates normalized by the mRNA degradation rate. This range expands with decreasing mean expression, increasing technical noise, and larger sample sizes. The results imply that: (i) good NB fits occur in diverse parameter regimes without exclusively indicating transcriptional bursting; (ii) for small sample sizes, biological noise predominantly shapes the NB profile even when technical noise is present; (iii) under steady-state conditions, gene-specific parameters (burst size and frequency) estimated in regions where the NB model fits well, typically show large relative errors, even after corrections for technical noise, and (iv) gene ranking by burst frequency remains reliably accurate, suggesting that burst parameters are most informative in a relative sense. Finally, applying technical-noise-corrected model fitting to scRNA-seq data confirms that a substantial fraction of mammalian genes fall within these NB-fitting regimes, despite lacking transcriptional bursting.

SUMMARY: DelaySSAToolkit.jl is a Julia package for modelling reaction systems with non-Markovian dynamics, specifically those with time delays. These delays implicitly capture multiple intermediate reaction steps and hence serve as an effective model reduction technique for complex systems in biology, chemistry, ecology and genetics. The package implements a variety of exact formulations of the delay stochastic simulation algorithm. AVAILABILITY AND IMPLEMENTATION: The source code and documentation of DelaySSAToolkit.jl are available at https://github.com/palmtree2013/DelaySSAToolkit.jl.

Optimal iterative learning control (OILC) has been recognized as an excellent model-based means for regulating batch process with abundant successful applications reported in the past decades but also received considerable criticisms for its poor robustness against model mismatch that is common for many industrial situations. Despite numerous attempts to address the issue, many of them are still not able to yield satisfactory control performance particularly in the presence of a possible combination of time-varying uncertainties and conservatively designed controllers, which may compromise the learning mechanism, hence rendering the robustness issue of OILC far from well explored. This article intends to investigate the aforementioned issue by proposing a new OILC method resting upon the minimization of a dynamic upper bound on tracking error which is distilled from better exploitation of the time variation of uncertainties. We also show that the problem can be formulated in the framework of convex–concave game that can be efficiently solved by a subgradient method with an excellent balance of optimality and computation time. Such a formulation enables us to gain: 1) guaranteed monotonic convergence on tracking error; 2) remarkably reduced conservatism on controller synthesis; and 3) controllable computation complexity. It is further shown that the proposed method is capable of handling nonlinearity, for example Volterra system, a classic representation of nonlinear process. The efficacy of the method is verified by numerical experiments on a continuous stirred tank reactor model.

In this study, a predictive-p control system is developed for the level process in an industrial coke fractionation tower. Such processes typically have integrating and nonlinear dynamics causing the performance of conventional control designs and tuning to be poor or to require significant effort in practice. The process model is derived using data of step-response test and control implementation is designed through a new state-space structure. The closed-loop control system contains both the improved predictive control and P control. The performance of the proposed control for regulatory/servo, disturbance rejection, and measurement noise problems are studied and the obtained results show that the control system is of simple implementation with more robustness and provides better responses than conventional predictive control.