The role of noise in the tumor dynamics under chemotherapy treatment

Dynamical systems modeling tumor growth have been investigated to analyze the dynamics between tumor and healthy cells. Recent theoretical studies indicate that these interactions may lead to different dynamical outcomes under the effect of particular cancer therapies. In the present paper, we derive a system of nonlinear differential equations, in order to investigate solid tumors in vivo, taking into account the impact of chemotherapy on both tumor and healthy cells. We start by studying our model only in terms of deterministic dynamics under the variation of a drug concentration parameter. Later, with the introduction of noise, a stochastic model is used to analyze the impact of the unavoidable random fluctuations. As a result, new insights into noise-induced transitions are provided and illustrated in detail using techniques from dynamical systems and from the theory of stochastic processes.

Dynamical Systems Modeling of Bt Resistant Cornborer Population Dynamics

SummaryMathematical models provide insights for the design and optimization of strategies to control disease epidemics and evolution of pesticide resistance in crops. Here, we present a simple mathematical model to investigate the population dynamics of non-Bt resistant and Bt resistant cornborers in a field with refuge. In the presence of refuge, it is expected that the population of Bt resistant pests will decline due to the dilution effect (non-Bt resistant cornborers mate with Bt resistant pests). We have found that increasing the refuge size can be effective in reducing Bt resistant pests as long as there exists a relatively huge population of non-Bt resistant cornborers at the start of the simulation. This implies that refuge is useless in inhibiting the evolution of cornborers if a sufficient initial population of non-Bt resistant cornborers is absent.

Substrate complex competition is a regulatory motif that allows NFκB RelA to license but not amplify NFκB RelB

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context.