The paper proposes a general framework allowing the analysis of wetting problems in thesituation when interfacial tensions depend on external fields. An equation predictingapparent contact angles of sessile droplets deposited on rough surfaces in the presence ofexternal fields is derived. The problem of wetting is discussed in the framework of thevariational approach. Derivation of a general equation generalizing the Cassie and Wenzelapproaches is presented. The effects related to the line tension which are important fornano-structured surfaces are considered.

Many cancer-associated genes and pathways remain to be identified in order to clarify themolecular mechanisms underlying cancer progression. In this area, genome-wideloss-of-function screens appear to be powerful biological tools, allowing the accumulationof large amounts of data. However, this approach currently lacks analytical tools toexploit the data with maximum efficiency, for which systems biology methods analyzingcomplex cellular networks may be extremely helpful. In this article we report such asystems biology strategy based on the construction of a Network for a biological processand specific for a given cell system (cell type). The networks are created fromgenome-wide loss-of-function screen datasets. We also propose tools to analyze networkproperties. As one of the tools, we suggest a mathematical model for discriminationbetween two distinct cell processes that may be affected by knocking down the activity ofa gene, i. e., a decreased cell number may be caused by arrested cell proliferation orenhanced cell death. Next we show how this discrimination between the two cell processeshelps to construct two corresponding subnetworks. Finally, we demonstrate an applicationof the proposed strategy to the identification and characterization of putative novelgenes and pathways significant for the control of lung cancer cell growth, based on theresults of a genome-wide proliferation/viability loss-of-function screen of human lungadenocarcinoma cells.

We obtain solvability conditions in H6(ℝ3) for asixth order partial differential equation which is the linearized Cahn-Hilliard problemusing the results derived for a Schrödinger type operator without Fredholm property in ourpreceding article [18].

Recent discovery of cancer stem cells in tumorigenic tissues has raised many questionsabout their nature, origin, function and their behavior in cell culture. Most of currentexperiments reporting a dynamics of cancer stem cell populations in culture show theeventual stability of the percentages of these cell populations in the whole population ofcancer cells, independently of the starting conditions. In this paper we propose amathematical model of cancer stem cell population behavior, based on specific features ofcancer stem cell divisions and including, as a mathematical formalization of cell-cellcommunications, an underlying field concept. We compare the qualitative behavior ofmathematical models of stem cells evolution, without and with an underlying signal. Inabsence of an underlying field, we propose a mathematical model described by a system ofordinary differential equations, while in presence of an underlying field it is describedby a system of delay differential equations, by admitting a delayed signal originated byexisting cells. Under realistic assumptions on the parameters, in both cases (ODE withoutunderlying field, and DDE with underlying field) we show in particular the stability ofpercentages, provided that the delay is sufficiently small. Further, for the DDE case (inpresence of an underlying field) we show the possible existence of, either damped orstanding, oscillations in the cell populations, in agreement with some existingmathematical literature. The outcomes of the analysis may offer to experimentalists a toolfor addressing the issue regarding the possible non-stem to stem cells transition, bydetermining conditions under which the stability of cancer stem cells population can beobtained only in the case in which such transition can occur. Further, the provideddescription of the variable corresponding to an underlying field may stimulate furtherexperiments for elucidating the nature of “instructive" signals for cell divisions,underlying a proper pattern of the biological system.

We present a model for describing the spread of an infectious disease with publicscreening measures to control the spread. We want to address the problem of determining anoptimal screening strategy for a disease characterized by appreciable duration of theinfectiveness period and by variability of the transmission risk. The specific disease wehave in mind is the HIV infection. However the model will apply to a disease for whichclass-age structure is significant and should not be disregarded.

Unveiling the mechanisms through which the somitogenesis regulatory network exertsspatiotemporal control of the somitic patterning has required a combination ofexperimental and mathematical modeling strategies. Significant progress has been made forthe zebrafish clockwork. However, due to its complexity, the clockwork of the amniotesegmentation regulatory network has not been fully elucidated. Here, we address thequestion of how oscillations are arrested in the amniote segmentation clock. We do this byconstructing a minimal model of the regulatory network, which privileges architecturalinformation over molecular details. With a suitable choice of parameters, our model isable to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways inpresomitic mesoderm (PSM) cells. By introducing positional information via a single Wnt3agradient, we show that oscillations are arrested following an infinite-period bifurcation.Notably: the oscillations increase their amplitude as cells approach the anterior PSM andremain in an upregulated state when arrested; the transition from the oscillatory regimeto the upregulated state exhibits hysteresis; and opposing Fgf8 and RA gradients along thePSM naturally arise in our simulations. We hypothesize that the interaction between alimit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch(originated by the Wnt-Notch positive cross-regulation) is responsible for the observedsegmentation patterning. Our results agree with previously unexplained experimentalobservations and suggest a simple plausible mechanism for spatiotemporal control ofsomitogenesis in amniotes.

Modification of behaviour in response to changes in the environment or ambientconditions, based on memory, is typical of the human and, possibly, many animalspecies.One obvious example of such adaptivity is, for instance, switching to a saferbehaviour when in danger, from either a predator or an infectious disease. In humansociety such switching to safe behaviour is particularly apparent during epidemics.Mathematically, such changes of behaviour in response to changes in the ambient conditionscan be described by models involving switching. In most cases, this switching is assumedto depend on the system state, and thus it disregards the history and, therefore, memory.Memory can be introduced into a mathematical model using a phenomenon known as hysteresis.We illustrate this idea using a simple SIR compartmental model that is applicable inepidemiology. Our goal is to show why and how hysteresis can arise in such a model, andhow it may be applied to describe a variety of memory effects. Our other objective is tointroduce a unified paradigm for mathematical modelling with memory effects inepidemiology and ecology. Our approach treats changing behaviour as an irreversible flowrelated to large ensembles of elementary exchange operations that recently has beensuccessfully applied in a number of other areas, such as terrestrial hydrology, andmacroeconomics. For the purposes of illustrating these ideas in an application to biology,we consider a rather simple case study and develop a model from first principles. Weaccompany the model with extensive numerical simulations which exhibit interestingqualitative effects.

The impacts of the two-beam interference heating on the number of core-shell and embeddednanoparticles and on nanostructure coarsening are studied numerically based on thenon-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20nm) metallic bilayers. The model incorporates thermocapillary forces and disjoiningpressures, and assumes dewetting from the optically transparent substrate atop of thereflective support layer, which results in the complicated dependence of lightreflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillaryeffect is due to the local thickness-dependent, steady-state temperature profile in theliquid, which is derived based on the mean substrate temperature estimated from theelaborate thermal model of transient heating and melting/freezing. Linear stabilityanalysis of the model equations set for Ag/Co bilayer predicts the dewetting length scalesin the qualitative agreement with experiment.

In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.

Recently, Wang and Xiao studied a four-dimensional competitive Lotka-Volterra systemwithin a deterministic environment in [11]. Withthe help of numerical example they showed the existence of a chaotic attractor through theperiod doubling route. In this paper, we are interested to study the dynamics of the samemodel in presence of environmental driving forces. To incorporate the environmentaldriving force into the deterministic system, we perturb the growth rates of each speciesby white noise terms. Then we prove that the unique positive global solution exists forthe noise added system and the general p-th order moment of it is boundedfor p ≥ 1, which ensures that the solution is stochasticallybounded. It is also shown that the solution of the stochastic system is stochasticallypermanent under some simple conditions. Finally , we demonstrate the noise inducedoscillation for the concerned model with the help of numerical example..

A decision analytical model is presented and analysed to assess the effectiveness andcost-effectiveness of routine vaccination against varicella and herpes-zoster, orshingles. These diseases have as common aetiological agent the varicella-zoster virus(VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity.The general concern is that universal varicella vaccination might lead to more cases ofzoster: with more vaccinated children exposure of the general population to varicellainfectives become smaller and thus a larger proportion of older people will have weakerimmunity to VZV, leading to more cases of reactivation of zoster. Our compartment modelshows that only two possible equilibria exist, one without varicella and the other onewhere varicella and zoster both thrive. Threshold quantities to distinguish these casesare derived. Cost estimates on a possible herd vaccination program are discussedindicating a possible tradeoff choice.

In this paper, we show finite time blow-up of solutions of the p−waveequation in ℝN, with critical Sobolev exponent. Our workextends a result by Galaktionov and Pohozaev [4]

Treating cancer patients with metastatic disease remains an ultimate challenge inclinical oncology. Because invasive cancer precludes or limits the use of surgery,metastatic setting is often associated with (poor) survival, rather than sustainedremission, in patients with common cancers like lung, digestive or breast carcinomas.Mathematical modeling may help us better identify non detectable metastatic status to inturn optimize treatment for patients with metastatic disease. In this paper we present afamily of models for the metastatic growth. They are based on four principles : to be assimple as possible, involving the least possible number of parameters, the maininformations are obtained from the primary tumor and being able to recover the variety ofphenomena observed by the clinicians. Several simulations of therapeutic strategies arepresented illustrating possible applications of modeling to the clinic.

Flow cytometric analysis using intracellular dyes such as CFSE is a powerful experimentaltool which can be used in conjunction with mathematical modeling to quantify the dynamicbehavior of a population of lymphocytes. In this survey we begin by providing an overviewof the mathematically relevant aspects of the data collection procedure. We then presentan overview of the large body of mathematical models, along with their assumptions anduses, which have been proposed to describe the dynamics of proliferating cell populations.While much of this body of work has been aimed at modeling the generation structure (cellsper generation) of the proliferating population, several recent models have considered themore fundamental task of modeling CFSE histogram data directly. Such models are analyzedand recent results are discussed. Finally, directions for future research aresuggested.

Progression along the successive phases of the mammalian cell cycle is driven by anetwork of cyclin-dependent kinases (Cdks). This network is regulated by a variety ofnegative and positive feedback loops. We previously proposed a detailed, 39-variable modelfor the Cdk network and showed that it is capable of temporal self-organization in theform of sustained oscillations, which correspond to the repetitive, transient, sequentialactivation of the cyclin- Cdk complexes that govern the successive phases of the cellcycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci 106, 21643-8]. Here we compare thedynamical behavior of three models of different complexity for the Cdk network driving themammalian cell cycle. The first is the detailed model that counts 39 variables and isbased on Michaelis-Menten kinetics for the enzymatic steps. From this detailed model, webuild a version based only on mass-action kinetics, which counts 80 variables. In thisversion we do not need to assume that enzymes are present in much smaller amounts thattheir substrates, which is not necessarily the case in the cell cycle. We show that thesetwo versions of the model for the Cdk network yield similar results. In particular theypredict sustained oscillations of the limit cycle type. We show that the model for the Cdknetwork can be reduced to a version containing only 5 variables, which is more amenable tostochastic simulations. This skeleton version retains the dynamic properties of the morecomplex versions of the model for the Cdk network in regard to Cdk oscillations. Theregulatory wiring of the Cdk network therefore governs its dynamic behavior, regardless ofthe degree of molecular detail. We discuss the relative advantages of each version of themodel, all of which support the view that the mammalian cell cycle behaves as a limitcycle oscillator.

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenicmechanisms are manifold and mediated through a range of positive and negative feedbackregulations of immune and physiological processes engaged in virus-host interactions. Thefundamental questions towards understanding the pathogenesis of HIV infection are nowshifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finallydisrupted? (ii) can one modify the dynamic equilibrium for host benefit? (iii) can onepredict the outcome of a system perturbation via antiviral drugs or drugs modulating thehost immune response dynamics? Answering these questions requires a majorinterdisciplinary effort, and in particular, the development of novel mathematicalapproaches for a coherent quantitative description and prediction of intra-patient HIVevolution, the immunological responses to HIV infection, and the systems level homeostaticregulation of specific effector and regulatory lymphocyte populations in correlation withdisease status. Here we summarized fundamental biological features of HIV infection andcurrent mathematical modelling attempts to understand HIV pathogenesis.

The matrix KdV equation with a negative dispersion term is considered in the right upperquarter–plane. The evolution law is derived for the Weyl function of a correspondingauxiliary linear system. Using the low energy asymptotics of the Weyl functions, theunboundedness of solutions is obtained for some classes of the initial–boundaryconditions.

Contact behavior plays an important role in influenza transmission. In the progression ofinfluenza spread, human population reduces mobility to decrease infection risks. In thispaper, a mathematical model is proposed to include adaptive mobility. It is shown that themobility response does not affect the basic reproduction number that characterizes theinvasion threshold, but reduces dramatically infection peaks, or removes the peaks.Numerical calculations indicate that the mobility response can provide a very goodprotection to susceptible individuals, and a combination of mobility response andtreatment is an effective way to control influenza outbreak.

In this paper we present a theory describing the diffusion limited evaporation of sessilewater droplets in presence of contact angle hysteresis. Theory describes two stages ofevaporation process: (I) evaporation with a constant radius of the droplet base; and (II)evaporation with constant contact angle. During stage (I) the contact angle decreases fromstatic advancing contact angle to static receding contact angle, during stage (II) thecontact angle remains equal to the static receding contact angle. Universal dependencesare deduced for both evaporation stages. Obtained universal curves are validated againstavailable in the literature experimental data.

Motivated by recent experiments on the electro-hydrodynamic instability of spin-castpolymer films, we study the undulation instability of a thin viscoelastic polymer filmunder in-plane stress and in the presence of either a close by contactor or an electricfield, both inducing a normal stress on the film surface. We find that the in-plane stressaffects both the typical timescale of the instability and the unstable wavelengths. Thefilm stability is also sensitive to the boundary conditions used at the film-substrateinterface. We have considered two conditions, either rigidly attaching the film to thesubstrate or allowing for slip.