Branching processes with resetting as a model for cell division

We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to an identical copy of itself, and resetting, by which some properties of the daughter cells (such as their size or age) are reset to new values following division. We derive the first and second laws of Stochastic Thermodynamics for this process, and identify separate contributions due to branching and resetting. We apply our framework to well-known models of cell size control, such as the sizer, the timer, and the adder. We show that the entropy production of resetting is negative and that of branching is positive for these models in the regime of exponential growth of the colony. This property suggests an analogy between our model for cell growth and division and heat engines, and the introduction of a thermodynamic efficiency, which quantifies the conversion of one form of entropy production to another.

Branching Process Modelling of COVID-19 Pandemic Including Immunity and Vaccination

We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected individuals. The development of the epidemic process depends on the reproduction rate as well as on additional facets as immigration, adaptive immunity, and vaccination. Usually, in the existing deterministic and stochastic models, the officially reported and publicly available data are not sufficient for estimating model parameters. An important advantage of the proposed model, in addition to its simplicity, is the possibility of direct computation of its parameters estimates from the daily available data. We illustrate the proposed model and the corresponding data analysis with data from Bulgaria, however they are not limited to Bulgaria and can be applied to other countries subject to data availability.

Homogeneous Branching Processes with Non-Homogeneous Immigration

The stationary immigration has a limited effect over the asymptotic behavior of the underlying branching process. It affects mostly the limiting distribution and the life-period of the process. In contrast, if the immigration rate changes over time, then the asymptotic behavior of the process is significantly different and a variety of new phenomena are observed. In this review we discuss branching processes with time non-homogeneous immigration. Our goal is to help researchers interested in the topic to familiarize themselves with the current state of research.

Asymptotic behavior of projections of supercritical multi-type continuous-state and continuous-time branching processes with immigration

Under a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.

A novel adenylate isopentenyltransferase 5 regulates shoot branching via the ATTTA motif in Camellia sinensis

Background Shoot branching is one of the important agronomic traits affecting yields and quality of tea plant (Camellia sinensis). Cytokinins (CTKs) play critical roles in regulating shoot branching. However, whether and how differently alternative splicing (AS) variant of CTKs-related genes can influence shoot branching of tea plant is still not fully elucidated. Results In this study, five AS variants of CTK biosynthetic gene adenylate isopentenyltransferase (CsA-IPT5) with different 3′ untranslated region (3ˊ UTR) and 5ˊ UTR from tea plant were cloned and investigated for their regulatory effects. Transient expression assays showed that there were significant negative correlations between CsA-IPT5 protein expression, mRNA expression of CsA-IPT5 AS variants and the number of ATTTA motifs, respectively. Shoot branching processes induced by exogenous 6-BA or pruning were studied, where CsA-IPT5 was demonstrated to regulate protein synthesis of CsA-IPT5, as well as the biosynthesis of trans-zeatin (tZ)- and isopentenyladenine (iP)-CTKs, through transcriptionally changing ratios of its five AS variants in these processes. Furthermore, the 3′ UTR AS variant 2 (3AS2) might act as the predominant AS transcript. Conclusions Together, our results indicate that 3AS2 of the CsA-IPT5 gene is potential in regulating shoot branching of tea plant and provides a gene resource for improving the plant-type of woody plants.

Mathematical Modeling of Locoregional Recurrence Caused by Premalignant Lesions Formed Before Initial Treatment

Locoregional recurrence after surgery is a major unresolved issue in cancer treatment. Premalignant lesions are considered a cause of cancer recurrence. A study showed that premalignant lesions surrounding the primary tumor drove a high local cancer recurrence rate after surgery in head and neck cancer. Based on the multistage theory of carcinogenesis, cells harboring an intermediate number of mutations are not cancer cells yet but have a higher risk of becoming cancer than normal cells. This study constructed a mathematical model for cancer initiation and recurrence by combining the Moran and branching processes in which cells require two specific mutations to become malignant. There are three populations in this model: (i) normal cells with no mutation, (ii) premalignant cells with one mutation, and (iii) cancer cells with two mutations. The total number of healthy tissue is kept constant to represent homeostasis, and there is a rare chance of mutation every time a cell divides. If a cancer cell with two mutations arises, the cancer population proliferates, violating the homeostatic balance of the tissue. Once the number of cancer cells reaches a certain size, we conduct computational resection and remove the cancer cell population, keeping the ratio of normal and premalignant cells in the tissue unchanged. After surgery, we considered tissue dynamics and eventually observed the second appearance of cancer cells as recurrence. Consequently, we computationally revealed the conditions where the time to recurrence became short by parameter sensitivity analysis. Particularly, when the premalignant cells’ fitness is higher than normal cells, the proportion of premalignant cells becomes large after the surgical resection. Moreover, the mathematical model was fitted to clinical data on disease-free survival of 1,087 patients in 23 cancer types from the TCGA database. Finally, parameter values of tissue dynamics are estimated for each cancer type, where the likelihood of recurrence can be elucidated. Thus, our approach provides insights into the concept to identify the patients likely to experience recurrence as early as possible.