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p53 regulates the cellular response to genotoxic damage and prevents carcinogenic events. Theoretical and experimental studies state that the p53-Mdm2 network constitutes the core module of regulatory interactions activated by cellular stress induced by a variety of signaling pathways. In this paper, a strategy to control the p53-Mdm2 network regulated by p14ARF is developed, based on the pinning control technique, which consists into applying local feedback controllers to a small number of nodes (pinned ones) in the network. Pinned nodes are selected on the basis of their importance level in a topological hierarchy, their degree of connectivity within the network, and the biological role they perform. In this paper, two cases are considered. For the first case, the oscillatory pattern under gamma-radiation is recovered; afterward, as the second case, increased expression of p53 level is taken into account. For both cases, the control law is applied to p14ARF (pinned node based on a virtual leader methodology), and overexpressed Mdm2-mediated p53 degradation condition is considered as carcinogenic initial behavior. The approach in this paper uses a computational algorithm, which opens an alternative path to understand the cellular responses to stress, doing it possible to model and control the gene regulatory network dynamics in two different biological contexts. As the main result of the proposed control technique, the two mentioned desired behaviors are obtained., (Copyright © 2020 Suarez, Vega, Sanchez, González-Santiago, Rodríguez-Jorge, Alanis, Chen and Hernandez-Vargas.)

Bacteria control the expression of specific genes by Quorum Sensing (QS). This works using small signaling molecules called Autoinducers (AIs), for example, the Autoinducer-2 (AI-2). In this work, we present a mathematical model that represents the AI-2 dynamics on Escherichia coli , which is linked to the cell growth and the lsr operon expression. The model is adjusted using experimental data. Our results suggest that the extracellular AI-2 activity level depends on the cell growth rate, and this activity depends on the cell exponential growth phase. The model was adapted to simulate the interference of QS mechanisms in a co-culture of two E. coli strains: a wild type strain and a knock out strain that detects AI-2 but does not produce it. Co-culture simulations unveiled two conditions to avoid the QS on the wild strain: when the knock out takes control of the growth medium and overcomes the wild strain, or when is pre-cultured to its mid-exponential phase and then added to the wild strain culture. Model simulations unveiled new insights about the interference of bacterial communication and offer new tools for QS control.

The recent outbreaks of Ebola virus (EBOV) infections have underlined the impact of the virus as a major threat for human health. Due to the high biosafety classification of EBOV (level 4), basic research is very limited. Therefore, the development of new avenues of thinking to advance quantitative comprehension of the virus and its interaction with the host cells is urgently needed to tackle this lethal disease. Mathematical modeling of the EBOV dynamics can be instrumental to interpret Ebola infection kinetics on quantitative grounds. To the best of our knowledge, a mathematical modeling approach to unravel the interaction between EBOV and the host cells is still missing. In this paper, a mathematical model based on differential equations is used to represent the basic interactions between EBOV and wild-type Vero cells in vitro. Parameter sets that represent infectivity of pathogens are estimated for EBOV infection and compared with influenza virus infection kinetics. The average infecting time of wild-type Vero cells by EBOV is slower than in influenza infection. Simulation results suggest that the slow infecting time of EBOV could be compensated by its efficient replication. This study reveals several identifiability problems and what kind of experiments are necessary to advance the quantification of EBOV infection. A first mathematical approach of EBOV dynamics and the estimation of standard parameters in viral infections kinetics is the key contribution of this work, paving the way for future modeling works on EBOV infection.