Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies

Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death rates, effects of chemotherapies (both cytotoxic and cytostatic) and mutations. We extend previous work by demonstrating how qualitatively different actions of chemotherapeutic and cytostatic treatments may induce different levels of resistance. The mathematical interest of our study is in the formalism of constrained Hamilton-Jacobi equations in the framework of viscosity solutions. We derive the long-term temporal dynamics of the fittest traits in the regime of small mutations. In the context of adaptive cancer management, we also analyse whether an optimal drug level is better than the maximal tolerated dose

Generalized Gaussian Estimates for Elliptic Operators with Unbounded Coefficients on Domains

We consider second-order elliptic operators A in divergence form with coefficients belonging to Lloc∞(Ω), when Ω ⊆ ℝd is a sufficiently smooth (unbounded) domain. We prove that the realization of A in L2(Ω), with Neumann-type boundary conditions, generates a contractive, strongly continuous and analytic semigroup (T(t)) which has a kernel k satisfying generalized Gaussian estimates, written in terms of a distance function induced by the diffusion matrix and the potential term. Examples of operators where such a distance function is equivalent to the Euclidean one are also provided

On vector-valued Schrödinger operators with unbounded diffusion in Lp spaces

We prove generation results of analytic strongly continuous semigroups on Lp(Rd, Rm) (1 < p< ∞) for a class of vector-valued Schrödinger operators with unbounded coefficients. We also prove Gaussian type estimates for such semigroups

An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations

On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

Development of temporal auditory processing in childhood: Changes in efficiency rather than temporal-modulation selectivity

The ability to detect amplitude modulation (AM) is essential to distinguish the spectro-temporal features of speech from those of a competing masker. Previous work shows that AM sensitivity improves until 10 years of age. This may relate to the development of sensory factors (tuning of AM filters, susceptibility to AM masking) or to changes in processing efficiency (reduction in internal noise, optimization of decision strategies). To disentangle these hypotheses, three groups of children (5–11 years) and one of young adults completed psychophysical tasks measuring thresholds for detecting sinusoidal AM (with a rate of 4, 8, or 32 Hz) applied to carriers whose inherent modulations exerted different amounts of AM masking. Results showed that between 5 and 11 years, AM detection thresholds improved and that susceptibility to AM masking slightly increased. However, the effects of AM rate and carrier were not associated with age, suggesting that sensory factors are mature by 5 years. Subsequent modelling indicated that reducing internal noise by a factor 10 accounted for the observed developmental trends. Finally, children’s consonant identification thresholds in noise related to some extent to AM sensitivity. Increased efficiency in AM detection may support better use of temporal information in speech during childhood

Tritonia nilsodhneri marcus Ev., 1983 (Gastropoda, heterobranchia, tritoniidae): First records for the adriatic sea and new data on ecology and distribution of mediterranean populations

The nudibranch Tritonia nilsodhneri, usually feeding on a variety of gorgoniacean species, is known from different localities of the eastern Atlantic Ocean and the Mediterranean Sea. Knowledge of the host preferences of the Mediterranean populations is still scarce. Few records of this nudibranch have been reported from the eastern Mediterranean basin. With this report, the occurrence of T. nilsodhneri within the Mediterranean basin is extended to the Adriatic Sea. Furthermore, the list of the host species associated to the Mediterranean populations for feeding habits is increased from two up to five. Mediterranean specimens of T. nilsodhneri were observed for the first time feeding and spawning on Leptogorgia sarmentosa, Eunicella cavolini and E. labiata. Finally, these last two Gorgoniidae species are also reported here as a new host species for T. nilsodhneri

Traveling waves in a coarse-grained model of volume-filling cell invasion: Simulations and comparisons

Many reaction–diffusion models produce traveling wave solutions that can be interpreted as waves of invasion in biological scenarios such as wound healing or tumor growth. These partial differential equation models have since been adapted to describe the interactions between cells and extracellular matrix (ECM), using a variety of different underlying assumptions. In this work, we derive a system of reaction–diffusion equations, with cross-species density-dependent diffusion, by coarse-graining an agent-based, volume-filling model of cell invasion into ECM. We study the resulting traveling wave solutions both numerically and analytically across various parameter regimes. Subsequently, we perform a systematic comparison between the behaviors observed in this model and those predicted by simpler models in the literature that do not take into account volume-filling effects in the same way. Our study justifies the use of some of these simpler, more analytically tractable models in reproducing the qualitative properties of the solutions in some parameter regimes, but it also reveals some interesting properties arising from the introduction of cell and ECM volume-filling effects, where standard model simplifications might not be appropriate