Rigorous results of limiting behaviors of total tumor size under cyclic intermittent therapy for the system of reversible phenotype-switchable tumor cells

We are keenly interested in finding the limiting behaviors of total tumor size when tumor cells are subject to the periodic repetition of therapy and rest periods, called intermittent cyclic therapy. We hypothesize that each tumor cell can take either therapy-sensitive or therapy-tolerant phenotype, its phenotype transition is mainly driven by the presence or absence of environmental stress, and such a transition is reversible. Even though those aforementioned hypotheses make the model system simple, most of prior papers attempted to numerically find the optimal therapeutic scheduling that minimizes total tumor size, and there is no rigorous proof of the limiting behaviors of total tumor size to my knowledge. Here we present such long-waited mathematically rigorous results. In the first part of the paper, we present the derivation of total tumor size reduction criterion and prove two theorems of two different limiting behaviors of total tumor size under two different therapy strategies, one leading to an asymptotic finite tumor size according to an iterated map method and anther leading to asymptotically diminishing of total tumor size. In the second part of the paper, we discuss the effects of the intratumoral competition between sensitive and tolerant phenotypes on the total tumor size reduction criterion

Bacteriophage-mediated competition in Bordetella bacteria

Apparent competition between species is believed to be one of the principle driving forces that structure ecological communities, although the precise mecha nisms have yet to be characterized. Here we develop a model system that isolates phage-mediated interactions by neutralizing resource competition using two genetically identical Bordetella bronchiseptica strains that differ only in that one is the carrier of a phage and the other is susceptible to the phage. We observe and quantify the competitive advantage of the bacterial strain bearing the prophage in both invading and in resisting invasion by bacteria susceptible to the phage, and use our measurements to develop a mathematical model of phage-mediated competition. The model predicts, and experimental evidence confirms, that the competitive advantage conferred by the phage depends only on the relative phage pathology and is independent of other phage and host parameters. This work combines experimental and mathematical approaches to the study of phage-driven competition, and provides an experimentally tested framework for evaluation of the effects of pathogens/parasites on interspecific competition.Comment: 10pages, 8 figure

Noise-induced oscillatory shuttling of NF-{\kappa}B in a two compartment IKK-NF-{\kappa}B-I{\kappa}B-A20 signaling model

NF-{\kappa}B is a pleiotropic protein whose nucleo-cytoplasmic trafficking is tightly regulated by multiple negative feedback loops embedded in the NF-{\kappa}B signaling network and contributes to diverse gene expression profiles important in immune cell differentiation, cell apoptosis, and innate immunity. The intracellular signaling processes and their control mechanisms, however, are susceptible to both extrinsic and intrinsic noise. In this article, we present numerical evidence for a universal dynamic behavior of NF-{\kappa}B, namely oscillatory nucleo-cytoplasmic shuttling, due to the fundamentally stochastic nature of the NF-{\kappa}B signaling network. We simulated the effect of extrinsic noise with a deterministic ODE model, using a statistical ensemble approach, generating many copies of the signaling network with different kinetic rates sampled from a biologically feasible parameter space. We modeled the effect of intrinsic noise by simulating the same networks stochastically using the Gillespie algorithm. The results demonstrate that extrinsic noise diversifies the shuttling patterns of NF-{\kappa}B response, whereas intrinsic noise induces oscillatory behavior in many of the otherwise non-oscillatory patterns. We identify two key model parameters which significantly affect the NF-{\kappa}B dynamic response and deduce a two-dimensional phase-diagram of the NF-{\kappa}B response as a function of these parameters. We conclude that if single-cell experiments are performed, a rich variety of NF-{\kappa}B response will be observed, even if population-level experiments, which average response over large numbers of cells, do not evidence oscillatory behavior.Comment: 49 pages, 12 figure

Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution $P(k)$,including scale-free(SF) networks with power law distributions $P(k)\sim k^{-\gamma}$. Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function $C(k)$ which reduces the infection transmission rate $\lambda$ across an edge going from a node with high connectivity $k$. A mean field approximation with the neglect of degree-degree correlation then leads to a finite threshold $\lambda_{c}>0$ for SF networks with $2<\gamma \leq 3$. We also find, in this approximation, the fraction of infected individuals among those with degree $k$ for $\lambda$ close to $\lambda_{c}$. We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree-degree correlations.Comment: 6 figure

Bidirectional two colored light emission from stress-activated ZnS-microparticles-embedded polydimethylsiloxane elastomer films

Bidirectional two-colored mechanoluminescent light emission has been demonstrated by unifying two polydimethylsiloxane elastomer layers functionalized with zinc sulfide doped with Cu (ZnS:Cu) or Cu and Mn (ZnS:Cu,Mn). The bilayered composite films are simply fabricated by dispensing uncured ZnS:Cu,Mn + PDMS onto previously spin-coated and ardened ZnS:Cu + PDMS film. The robust PDMS-PDMS bonding yields a ilm which can simultaneously emit light with color coordinates of (0.25, 0.56) and (0.50, 0.48), similar to the intrinsic colors of ZnS:Cu and ZnS:Cu,Mn, respectively. Composite films can emit light in upper and lower directions without fracture when it is stretched. © 2013 Optical Society of America.1

Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process

We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one- and two-dimensions. We consider in particular a situation in which space is divided into two regions: an oasis and a desert (low and high death rates). Carrying out computer simulations we find that the population in the (quasi) stationary state will be zero, localized, or delocalized, depending on the values of the drift and other parameters. The phase diagram is similar to that obtained by Nelson and coworkers from a deterministic, spatially continuous model of a bacterial population undergoing convection in a heterogeneous medium.Comment: 8 papes, 12 figure

Substrate thermal conductivity effect on heat dissipation and lifetime improvement of organic light-emitting diodes

We report substrate thermal conductivity effect on heat dissipation and lifetime improvement of organic light-emitting diodes (OLEDs). Heat dissipation behavior of top-emission OLEDs fabricated on silicon, glass, and planarized stainless steel substrates was measured by using an infrared camera. Peak temperature measured from the backside of each substrate was saturated to be 21.4, 64.5, and 40.5 °C, 180 s after the OLED was operated at luminance of 10 000 cd/m2 and 80% luminance lifetime was about 198, 31, and 96 h, respectively. Efficient heat dissipation through the highly thermally conductive substrates reduced temperature increase, resulting in much improved OLED lifetime.This work supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (Grant No. KRF-2008-331-D00216)