The mathematical modeling of tumor growth has a long history, and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using mathematical tools from statistical physics. To this extent, we introduce a novel kinetic model of growth which highlights the role of microscopic transitions in determining a variety of equilibrium distributions. At variance with other approaches, the mesoscopic description in terms of elementary interactions allows to design precise microscopic feedback control therapies, able to influence the natural tumor growth and to mitigate the risk factors involved in big sized tumors. We further show that under a suitable scaling both the free and controlled growth models correspond to Fokker-Planck type equations for the growth distribution with variable coefficients of diffusion and drift, whose steady solutions in the free case are given by a class of generalized Gamma densities which can be characterized by fat tails. In this scaling the feedback control produces an explicit modification of the drift operator, which is shown to strongly modify the emerging distribution for the tumor size. In particular, the size distributions in presence of therapies manifest slim tails in all growth models, which corresponds to a marked mitigation of the risk factors. Numerical results confirming the theoretical analysis are also presented.

The aim of this work is to provide a mathematical model to describe the early stages of the embryonic development of zebrafish posterior lateral line (PLL). In particular, we focus on evolution of PLL proto-organ (said primordium), from its formation to the beginning of the cyclical behavior that amounts in the assembly of immature proto-neuromasts towards its caudal edge accompanied by the deposition of mature proto-neuromasts at its rostral region. Our approach has an hybrid integro-differential nature, since it integrates a microscopic/discrete particle-based description for cell dynamics and a continuous description for the evolution of the spatial distribution of chemical substances (i.e., the stromal-derived factor SDF1a and the fibroblast growth factor FGF10). Boolean variables instead implement the expression of molecular receptors (i.e., Cxcr4/Cxcr7 and fgfr1). Cell phenotypic transitions and proliferation are included as well. The resulting numerical simulations show that the model is able to qualitatively and quantitatively capture the evolution of the wild-type (i.e., normal) embryos as well as the effect of known experimental manipulations. In particular, it is shown that cell proliferation, intercellular adhesion, FGF10-driven dynamics, and a polarized expression of SDF1a receptors are all fundamental for the correct development of the zebrafish posterior lateral line.

Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the tissue. This dynamic homeostasis is maintaned by numerous governing mechanisms which are finely tuned in such a way that the tissue remains in a homeostatic state, even across large timescales. Some of these governing mechanisms include cell motion, and cell fate selection through inter cellular signalling. However, it is not yet clear how to link these two processes, or how they may affect one another across the tissue. In this paper, we present a multicellular, multiscale model, which brings together the two phenomena of cell motility, and inter cellular signalling, to describe cell fate selection on a dynamic tissue. We find that the affinity for cellular signalling to occur greatly influences a cells ability to differentiate. We also find that our results support claims that cell differentiation is a finely tuned process within dynamic tissues at homeostasis, with excessive cell turnover rates leading to unhealthy (undifferentiated and unpatterned) tissues.

Prostate cancer is one of the most prevalent cancers in men, with increasing incidence worldwide. This public health concern has inspired considerable effort to study various aspects of prostate cancer treatment using dynamical models, especially in clinical settings. The standard of care for metastatic prostate cancer is hormonal therapy, which reduces the production of androgen that fuels the growth of prostate tumor cells prior to treatment resistance. Existing population models often use patients' prostate-specific antigen levels as a biomarker for model validation and for finding optimal treatment schedules; however, the synergistic effects of drugs used in hormonal therapy have not been well-examined. This paper describes the first mathematical model that explicitly incorporates the synergistic effects of two drugs used to inhibit androgen production in hormonal therapy. The drugs are cyproterone acetate, representing the drug family of anti-androgens that affect luteinizing hormones, and leuprolide acetate, representing the drug family of gonadotropin-releasing hormone analogs. By fitting the model to clinical data, we show that the proposed model can capture the dynamics of serum androgen levels during intermittent hormonal therapy better than previously published models. Our results highlight the importance of considering the synergistic effects of drugs in cancer treatment, thus suggesting that the dynamics of the drugs should be taken into account in optimal treatment studies, particularly for adaptive therapy. Otherwise, an unrealistic treatment schedule may be prescribed and render the treatment less effective. Furthermore, the drug dynamics allow our model to explain the delay in the relapse of androgen the moment a patient is taken off treatment, which supports that this delay is due to the residual effects of the drugs.

Evolution of metabolism is a longstanding yet unresolved question, and several hypotheses were proposed to address this complex process from a Darwinian point of view. Modern statistical bioinformatic approaches targeted to the comparative analysis of genomes are being used to detect signatures of natural selection at the gene and population level, as an attempt to understand the origin of primordial metabolism and its expansion. These studies, however, are still mainly centered on genes and the proteins they encode, somehow neglecting the small organic chemicals that support life processes. In this work, we selected steroids as an ancient family of metabolites widely distributed in all eukaryotes and applied unsupervised machine learning techniques to reveal the traits that natural selection has imprinted on molecular properties throughout the evolutionary process. Our results clearly show that sterols, the primal steroids that first appeared, have more conserved properties and that, from then on, more complex compounds with increasingly diverse properties have emerged, suggesting that chemical diversification parallels the expansion of biological complexity. In a wider context, these findings highlight the worth of chemoinformatic approaches to a better understanding the evolution of metabolism.

The ongoing global pandemic of infection disease COVID-19 caused by the 2019 novel coronavirus (SARS-COV-2, formerly 2019-nCoV) presents critical threats to public health and the economy. The genome of SARS-CoV-2 had been sequenced and structurally annotated, yet little is known of the intrinsic organization and evolution of the genome. To this end, we present a mathematical method for the genomic spectrum, a kind of barcode, of SARS-CoV-2 and common human coronaviruses. The genomic spectrum is constructed according to the periodic distributions of nucleotides and therefore reflects the unique characteristics of the genome. The results demonstrate that coronavirus SARS-CoV-2 exhibits predominant latent periodicity-2 regions of non-structural proteins 3, 4, 5, and 6. Further analysis of the latent periodicity-2 regions suggests that the dinucleotide imbalances are increased during evolution and may confer the evolutionary fitness of the virus. Especially, SARS-CoV-2 isolates have increased latent periodicity-2 and periodicity-3 during COVID-19 pandemic. The special strong periodicity-2 regions and the intensity of periodicity-2 in the SARS-CoV-2 whole genome may become diagnostic and pharmaceutical targets in monitoring and curing the COVID-19 disease.

Periodical cicadas, Magicicada spp., are a useful model system for understanding the population processes that influence range boundaries. Unlike most insects, these species typically exist at very high densities (occasionally >1000/ m2) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on plant roots. After the underground period, adults emerge from the ground to mate and oviposit over a period of just a few days. Collections of populations that are developmentally synchronized across large areas are known as "broods". There are usually sharp boundaries between spatially adjacent broods and regions of brood overlap are generally small. The exact mechanism behind this developmental synchronization and the sharp boundary between broods remain unknown: previous studies have focused on the impacts of predator-driven Allee-effects, competition among nymphs, and their impacts on the persistence of off-synchronized emergence events. Here, we present a nonlinear Leslie-type matrix model to additionally consider cicada movement between spatially separated broods, and examine its role in maintaining brood boundaries and within-brood developmental synchrony that is seen in nature. We successfully identify ranges of competition and dispersal that lead to stable coexistence of broods that differ between spatial patches.

Photosynthetic microorganisms are known to adjust their photosynthetic capacity according to light intensity. This so-called photoacclimation process is thought to maximize growth at equilibrium, but its dynamics under varying conditions remains less understood. To tackle this problem, microalgae growth and photoacclimation are represented by a (coarse-grained) resource allocation model. Using optimal control theory (the Pontryagin maximum principle) and numerical simulations, we determine the optimal strategy of resource allocation to maximize microalgal growth rate over a time horizon. We show that, after a transient, the optimal trajectory approaches the optimal steady state, a behavior known as the turnpike property. Then, a bi-level optimization problem is solved numerically to estimate model parameters from experimental data. The fitted trajectory represents well a Dunaliella tertiolecta culture facing a light down-shift. Finally, we study photoacclimation dynamics under day/night cycle. In the optimal trajectory, the synthesis of the photosynthetic apparatus surprisingly starts a few hours before dawn. This anticipatory behavior has actually been observed both in the laboratory and in the field. This shows the algal predictive capacity and the interest of our method which predicts this phenomenon.

We develop and analyze a deterministic ordinary differential equation mathematical model for the within-mosquito dynamics of the Plasmodium falciparum malaria parasite. Our model takes into account the action and effect of blood resident human-antibodies, ingested by the mosquito during a blood meal from humans, in inhibiting gamete fertilization. The model also captures subsequent developmental processes that lead to the different forms of the parasite within the mosquito. Continuous functions are used to model the switching transition from oocyst to sporozoites as well as human antibody density variations within the mosquito gut are proposed and used. In sum, our model integrates the developmental stages of the parasite within the mosquito such as gametogenesis, fertilization and sporogenesis culminating in the formation of sporozoites. Quantitative and qualitative analyses including a sensitivity analysis for influential parameters are performed. We quantify the average sporozoite load produced at the end of the within-mosquito malaria parasite's developmental stages. Our analysis shows that an increase in the efficiency of the ingested human antibodies in inhibiting fertilization within the mosquito's gut results in lowering the density of oocysts and hence sporozoites that are eventually produced by each mosquito vector. So, it is possible to control and limit oocysts development and hence sporozoites development within a mosquito by boosting the efficiency of antibodies as a pathway to the development of transmission-blocking vaccines which could potentially reduce oocysts prevalence among mosquitoes and hence reduce the transmission potential from mosquitoes to human.