Dynamical properties of model gene networks and implications for the inverse problem

We study the inverse problem, or the "reverse-engineering" problem, for two abstract models of gene expression dynamics, discrete-time Boolean networks and continuous-time switching networks. Formally, the inverse problem is similar for both types of networks. For each gene, its regulators and its Boolean dynamics function must be identified. However, differences in the dynamical properties of these two types of networks affect the amount of data that is necessary for solving the inverse problem. We derive estimates for the average amounts of time series data required to solve the inverse problem for randomly generated Boolean and continuous-time switching networks. We also derive a lower bound on the amount of data needed that holds for both types of networks. We find that the amount of data required is logarithmic in the number of genes for Boolean networks, matching the general lower bound and previous theory, but are superlinear in the number of genes for continuous-time switching networks. We also find that the amount of data needed scales as 2(K), where K is the number of regulators per gene, rather than 2(2K), as previous theory suggests.     

Ameboid cell motility: a model and inverse problem, with an application to live cell imaging data

In this article a mathematical model for ameboid cell movement is developed using a spring-dashpot system with Newtonian dynamics. The model is based on the facts that the cytoskeleton plays a primary role for cell motility and that the cytoplasm is viscoelastic. Based on the model, the inverse problem can be posed: if a structure like a spring-dashpot system is embedded into the living cell, what kind of characteristic properties must the structure have in order to reproduce a given movement of the cell? This inverse problem is the primary topic of this paper. On one side the model mimics some features of the movement, and on the other side, the solution to the inverse problem provides model parameters that give some insight, principally into the mechanical aspect, but also, through qualitative reasoning, into chemical and biophysical aspects of the cell. Moreover, this analysis can be done locally or globally and in different media by using the simplest possible information: positions of the cell and nuclear membranes. It is shown that the model and solution to the inverse problem for simulated data sets are highly accurate. An application to a set of live cell imaging data obtained from random movements of a human brain tumor cell (U87-MG human glioblastoma cell line) then provides an example of the efficiency of the model, through the solution of its inverse problem, as a way of understanding experimental data.     

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations

In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L_p×L_p for p∈(1, ∞). Due to the lack of compactness on L₁ spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.     

Positive solutions of an elliptic system arising from a model in evolutionary ecology

We give sufficient and almost necessary conditions for the existence of positive solutions to an elliptic system satisfying various Dirichlet boundary conditions. The elliptic system consists of the steady-state equations of a parabolic system used to model the growth and spread of a particular gene and population living in a bounded region. The model takes into account the fact that the fitness of the individuals in the population may depend on the population size. Some non-existence results are also included.Research partially supported by NSF grant no. DMS-8801968     

The relative importance of olfaction and vision in a diurnal and a nocturnal hawkmoth

Nectar-feeding animals can use vision and olfaction to find rewarding flowers and different species may give different weight to the two sensory modalities. We have studied how a diurnal or nocturnal lifestyle affects the weight given to vision and olfaction. We tested naïve hawkmoths of two species in a wind tunnel, presenting an odour source and a visual stimulus. Although the two species belong to the same subfamily of sphingids, the Macroglossinae, their behaviour was quite different. The nocturnal Deilephila elpenor responded preferably to the odour while the diurnal Macroglossum stellatarum strongly favoured the visual stimulus. Since a nocturnal lifestyle is ancestral for sphingids, the diurnal species, M. stellatarum, has evolved from nocturnal moths that primarily used olfaction. During bright daylight visual cues may have became more important than odour.     

The use of inverse sine transformations in the analysis of non-metric cranial data

In recent years osteologists have frequently used non-metric (dichotomous) cranial data to measure biological distance between skeletal samples of Homo sapiens. Applying methods used earlier by biologists, these workers begin by attempting to stabilize the variance of the measures used by transforming the observed trait frequencies using some type of inverse sine transformation. The frequently used Grewal-Smith transformation doesn't work well for small samples of the size often considered by osteologists. As a consequence the mean measure of divergence between populations determined by this method is strongly influenced by a bias which depends on sample size. This paper compares several transformations in terms of how close the actual variance of the transformed frequency corresponds to its nominal value. It is suggested that the traditional (Grewal-Smith) inverse sine transformation not be used, and several alternatives are considered.     

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts.     

Approximate expressions of the bifurcating periodic solutions in a neuron model with delay-dependent parameters by perturbation approach

This paper is interested in gaining insights of approximate expressions of the bifurcating periodic solutions in a neuron model. This model shares the property of involving delay-dependent parameters. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work so harder. Most existing methods for studying the nonlinear dynamics fail when applied to such a class of delay models. Although Xu et al. (Phys Lett A 354:126–136, 2006) studied stability switches, Hopf bifurcation and chaos of the neuron model with delay-dependent parameters, the dynamics of this model are still largely undetermined. In this paper, a detailed analysis on approximation to the bifurcating periodic solutions is given by means of the perturbation approach. Moreover, some examples are provided for comparing approximations with numerical solutions of the bifurcating periodic solutions. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only.     

A singular dispersion relation arising in a caricature of a model for morphogenesis

In 1983 Oster et al. proposed a model for morphogenesis consisting of a system of partial differential equations in which the dispersion relation for the problem linearised about the zero solution has a singularity. That is, the initial growth rate of a small perturbation of wave number k from the zero solution tends to positive or negative infinity as k tends to some critical value k _c from above or below respectively. We consider here as a caricature of the model a single partial differential equation with a similar dispersion relation in a bounded one-dimensional domain. The wave number, or equivalently the domain size, may be thought of as a bifurcation parameter. For the Neumann problem a phenomenon arises in which, as the domain size l increases past a critical value l _l ,the linear stability of the n-th mode jumps from one solution to a remote solution. That is, for l _n the trivial solution is unstable and a certain non-trivial solution is stable to perturbations of mode n, whereas for l>l _n the opposite is true. For the Dirichlet or the Robin problem a linear stability change in the trivial solution occurs, but no corresponding change in any other solution has been found. The corresponding initial boundary value problems are then considered. An asymptotic analysis is performed in the weakly nonlinear limit in the particular case in which only one mode is unstable and gives an asymptotic solution for two classes of nonlinearity, one symmetric and the other asymmetric about u=0. A development of the method of harmonic balance is then used to obtain approximate solutions in the strongly nonlinear case and when more than one mode may be unstable.     

Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect.We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation.     

On the interchain associations in aqueous solutions of a succinoglycan polysaccharide

Formation of interchain associations between succinoglycan chains have been studied by comparing weight average molecular weight, intrinsic viscosity of succinoglycan as a function of the conditions to prepare the solutions (polymer concentration, the heating temperature adopted compared with T_m). The different solutions obtained were characterized by their Newtonian viscosity, the storage and loss moduli and their sensitivity to the temperature. It was found that interchain associations, first stabilized mainly during the disorder-order transition convert to more stable associations by aging at temperatures below but not too far from T_m. These associations appear from succinoglycan solutions characterized by an overlap parameter higher than about 8 and modify only very slightly the conformational transition parameters obtained from microcalorimetry measurements.     

Estimation of tumor characteristics in a breast tissue with known skin surface temperature

Presence of a tumor and its characteristics like location, size and properties are estimated. Estimation is based on the measurement of the skin surface temperature of the breast. Consideration is given to a 2-D breast tissue infected with a tumor. Heat transfer in the breast tissue modeled using the Pennes bioheat equation is solved by the finite volume method. Skin surface temperature profile of the breast is characteristic of the tumor location, its size and grade. In the inverse analysis, the objective function is minimized using the genetic algorithm. Exact estimation is obtained if one parameter is estimated at a time. However, the accuracies are acceptable even when blood perfusion rate, location and size are estimated simultaneously.     

Numerical analysis for determination of the presence of a tumor and estimation of its size and location in a tissue

This article deals with the numerical analysis to ascertain the presence of a tumor and to estimate its size and location in a tissue. Heat transfer in the tissue is modeled using the Pennes bioheat transfer equation, and is solved using the finite volume method. Consideration is given to 1-D brain and breast tissues. Temperature distributions in the tissues are specific to the tumor grades, its locations and sizes, and these are different than that of a normal tissue. With temperature distribution known a priori, estimations of the position and the size of a tumor are done using the inverse analysis. The proposed approach gives a correct estimation of the presence of a tumor and its location and size.     

The occurrence of ochratoxin A in dust collected from a problem household

Accumulated dust samples were collected from the heating ducts in a household where signs resembling ochratoxin poisoning in animals occurred. Several Penicillium spp. and Aspergillus ochraceous had been identified previously from air samples taken from this house. A composite sample from six collected samples was examined by HPLC, and it was determined that 58 ppb of ochratoxin A was present in this sample. A second set of six samples was collected and determinations were made by HPLC of the ochratoxin content in each sample. All samples, including one sample of dirt from a crawl space, yielded at least a trace of ochratoxin A; however, one sample of dust collected from the heating ducts yielded over 1500 ppb of ochratoxin A, and another sample of dust from a different heating duct yielded 306 ppb of ochratoxin A. Ochratoxin A was confirmed in all samples by LC-MS, and ochratoxin was evident in the samples by TLC analysis. This is believed to be the first report of finding ochratoxin inhouse dust. This revised version was published online in June 2006 with corrections to the Cover Date.     

Estimating mean response as a function of treatment duration in an observational study, where duration may be informatively censored

After a treatment is found to be effective in a clinical study, attention often focuses on the effect of treatment duration on outcome. Such an analysis facilitates recommendations on the most beneficial treatment duration. In many studies, the treatment duration, within certain limits, is left to the discretion of the investigators. It is often the case that treatment must be terminated prematurely due to an adverse event, in which case a recommended treatment duration is part of a policy that treats patients for a specified length of time or until a treatment-censoring event occurs, whichever comes first. Evaluating mean response for a particular treatment-duration policy from observational data is difficult due to censoring and the fact that it may not be reasonable to assume patients are prognostically similar across all treatment strategies. We propose an estimator for mean response as a function of treatment-duration policy under these conditions. The method uses potential outcomes and embodies assumptions that allow consistent estimation of the mean response. The estimator is evaluated through simulation studies and demonstrated by application to the ESPRIT infusion trial coordinated at Duke University Medical Center.     

A problem in multivariate analysis of codon usage data and a possible solution

Multivariate analyses are often used to identify major trends of variation in synonymous codon usage among genes. These analyses need to be performed on properly normalized codon usage data to avoid biases masking this synonymous variation, i.e., gene length, amino acid usage, and codon degeneracy; however, previous studies have failed to do so. In this paper, we demonstrate that the use of alternative normalized data (called 'relative adaptiveness' in the literature) can avoid all these biases and furthermore, can identify more trends of variation among genes, including GC-ending codon usage, GT-ending codon usage, and gene expression level.     

SANS/SAXS study of the BSA solvation properties in aqueous urea solutions via a global fit approach

We report on the solvation properties and intermolecular interactions of a model protein (bovine serum albumine, BSA) in urea aqueous solutions, as obtained by combining small-angle neutron and X-ray scattering experiments. According to a global fit strategy, all the whole set of scattering curves are analysed by considering a unique model which includes the BSA structure, the protein-protein interactions and the thermodynamic exchange process of water/urea molecules at the protein solvent interface. As a main result, the equilibrium constant that accounts for the difference in composition between the bulk solvent and the protein solvation layer is derived. Results confirm that urea preferentially sticks to the protein surface, inducing a noticeable change in both the repulsive and the attractive interaction potentials.