Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models

BACKGROUND: Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction. RESULTS: A complete parametric analysis of dynamic regimes of a conceptual model of anti-tumor virus therapy is presented. The role and limitations of mass-action kinetics are discussed. A functional response, which is a function of the ratio of uninfected to infected tumor cells, is proposed to describe the spread of the virus infection in the tumor. One of the main mathematical features of ratio-dependent models is that the origin is a complicated equilibrium point whose characteristics determine the main properties of the model. It is shown that, in a certain area of parameter values, the trajectories of the model form a family of homoclinics to the origin (so-called elliptic sector). Biologically, this means that both infected and uninfected tumor cells can be eliminated with time, and complete recovery is possible as a result of the virus therapy within the framework of deterministic models. CONCLUSION: Our model, in contrast to the previously published models of oncolytic virus-tumor interaction, exhibits all possible outcomes of oncolytic virus infection, i.e., no effect on the tumor, stabilization or reduction of the tumor load, and complete elimination of the tumor. The parameter values that result in tumor elimination, which is, obviously, the desired outcome, are compatible with some of the available experimental data. REVIEWERS: This article was reviewed by Mikhail Blagosklonny, David Krakauer, Erik Van Nimwegen, and Ned Wingreen

Gene family evolution: an in-depth theoretical and simulation analysis of non-linear birth-death-innovation models

BACKGROUND: The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome evolution. RESULTS: In this work, we extend our previous analysis of stochastic BDIMs. In addition to the previously examined rational BDIMs, we introduce potentially more realistic logistic BDIMs, in which birth/death rates are limited for the largest families, and show that their properties are similar to those of models that include no such limitation. We show that the mean time required for the formation of the largest gene families detected in eukaryotic genomes is limited by the mean number of duplications per gene and does not increase indefinitely with the model degree. Instead, this time reaches a minimum value, which corresponds to a non-linear rational BDIM with the degree of approximately 2.7. Even for this BDIM, the mean time of the largest family formation is orders of magnitude greater than any realistic estimates based on the timescale of life's evolution. We employed the embedding chains technique to estimate the expected number of elementary evolutionary events (gene duplications and deletions) preceding the formation of gene families of the observed size and found that the mean number of events exceeds the family size by orders of magnitude, suggesting a highly dynamic process of genome evolution. The variance of the time required for the formation of the largest families was found to be extremely large, with the coefficient of variation >> 1. This indicates that some gene families might grow much faster than the mean rate such that the minimal time required for family formation is more relevant for a realistic representation of genome evolution than the mean time. We determined this minimal time using Monte Carlo simulations of family growth from an ensemble of simultaneously evolving singletons. In these simulations, the time elapsed before the formation of the largest family was much shorter than the estimated mean time and was compatible with the timescale of evolution of eukaryotes. CONCLUSIONS: The analysis of stochastic BDIMs presented here shows that non-linear versions of such models can well approximate not only the size distribution of gene families but also the dynamics of their formation during genome evolution. The fact that only higher degree BDIMs are compatible with the observed characteristics of genome evolution suggests that the growth of gene families is self-accelerating, which might reflect differential selective pressure acting on different genes

An Atypical Cutaneous Reaction to Rivastigmine Transdermal Patch

Rivastigmine is a cholinesterase inhibitor which improves cognitive function and is currently being used in patients with mild to moderate Parkinson's and Alzheimer's dementia. This drug can be given orally or topically, as transdermal patch. The latter form is currently used for most excellent compliance and few side effects. The most common cutaneous side effects are irritative dermatitis. We report the second case of active sensitization by the rivastigmine-patch in a patient suffering from Alzheimer's dementia

Birth and death of protein domains: A simple model of evolution explains power law behavior

BACKGROUND: Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power law distributions has the potential of revealing non-trivial aspects of genome evolution. RESULTS: A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a birth, death and innovation model (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered in details and the distributions of the equilibrium frequencies of domain families of different size are determined for each case. We apply the BDIM formalism to the analysis of the domain family size distributions in prokaryotic and eukaryotic proteomes and show an excellent fit between these empirical data and a particular form of the model, the second-order balanced linear BDIM. Calculation of the parameters of these models suggests surprisingly high innovation rates, comparable to the total domain birth (duplication) and elimination rates, particularly for prokaryotic genomes. CONCLUSIONS: We show that a straightforward model of genome evolution, which does not explicitly include selection, is sufficient to explain the observed distributions of domain family sizes, in which power laws appear as asymptotic. However, for the model to be compatible with the data, there has to be a precise balance between domain birth, death and innovation rates, and this is likely to be maintained by selection. The developed approach is oriented at a mathematical description of evolution of domain composition of proteomes, but a simple reformulation could be applied to models of other evolving networks with preferential attachment

Forming of Competitive Advantages of Regional Agrarian and Industrial Complex as Mechanism of Ensuring Economic Safety

The Russian economy faced the problems of increase of efficiency of agrarian-industrial complex, its competitiveness, which directly affects the economic security of the country. The more developed the factors determining the competitiveness the more sustainable and viable economy is becoming before emerging internal and external threats. The paper discusses issues of mutual influence competitiveness and economic security. Special attention is paid to ensuring the competitiveness of the agro-industrial complex. The need to ensure food and economic security of the country and growth of socio-economic efficiency of agriculture highlight are the problems of increasing the competitiveness of Russian agriculture. Proposed a number of measures are suggested on financial and organizational procedures that will enhance the potential of the enterprises of agrarian and industrial complex for production of competitive products. DOI: 10.5901/mjss.2015.v6n3s7p21

Decomposition of Condensed Phase Energetic Materials: Interplay between Uni- and Bimolecular Mechanisms

Activation energy for the decomposition of explosives is a crucial parameter of performance. The dramatic suppression of activation energy in condensed phase decomposition of nitroaromatic explosives has been an unresolved issue for over a decade. We rationalize the reduction in activation energy as a result of a mechanistic change from unimolecular decomposition in the gas phase to a series of radical bimolecular reactions in the condensed phase. This is in contrast to other classes of explosives, such as nitramines and nitrate esters, whose decomposition proceeds via unimolecular reactions both in the gas and in the condensed phase. The thermal decomposition of a model nitroaromatic explosive, 2,4,6-trinitrotoluene (TNT), is presented as a prime example. Electronic structure and reactive molecular dynamics (ReaxFF-lg) calculations enable to directly probe the condensed phase chemistry under extreme conditions of temperature and pressure, identifying the key bimolecular radical reactions responsible for the low activation route. This study elucidates the origin of the difference between the activation energies in the gas phase (∼62 kcal/mol) and the condensed phase (∼35 kcal/mol) of TNT and identifies the corresponding universal principle. On the basis of these findings, the different reactivities of nitro-based organic explosives are rationalized as an interplay between uni- and bimolecular processes