A study of the viscoelastic effect in a bone remodeling model

The present paper addresses the following question can a simple regulatory bone remodeling model predict effects of viscosity on the trabecular morphology? For that, we propose an extension of a previous bone remodeling model by taking into account the viscosity properties of the tissue. Zener’s law is used to describe the mechanical behavior of the bone and a specific law of the apparent bone density rate is proposed. Based on stability analysis, numerical simulations are then performed to investigate the viscosity role on simulations of the bone remodeling process. We show that the viscous contribution affects the evolution of the apparent bone density, by slowing down the adaptation process, which seems to be confirmed by simulations with real data obtained from rat tibia.     

Using string kernel to predict signal peptide cleavage site based on subsite coupling model

Summary. Owing to the importance of signal peptides for studying the molecular mechanisms of genetic diseases, reprogramming cells for gene therapy, and finding new drugs for healing a specific defect, it is in great demand to develop a fast and accurate method to identify the signal peptides. Introduction of the so-called {−3,−1, +1} coupling model (Chou, K. C.: Protein Engineering, 2001, 14–2, 75–79) has made it possible to take into account the coupling effect among some key subsites and hence can significantly enhance the prediction quality of peptide cleavage site. Based on the subsite coupling model, a kind of string kernels for protein sequence is introduced. Integrating the biologically relevant prior knowledge, the constructed string kernels can thus be used by any kernel-based method. A Support vector machines (SVM) is thus built to predict the cleavage site of signal peptides from the protein sequences. The current approach is compared with the classical weight matrix method. At small false positive ratios, our method outperforms the classical weight matrix method, indicating the current approach may at least serve as a powerful complemental tool to other existing methods for predicting the signal peptide cleavage site. The software that generated the results reported in this paper is available upon requirement, and will appear at http://www.pami.sjtu.edu.cn/wm. An erratum to this article is available at .     

Identifiability of a stochastic model for cell debris in flow cytometry

 One of the most important problems in recovering DNA distribution from flow cytometric DNA measurements is the presence of background noise. In this paper, we analyse a probabilistic model recently proposed for background debris distribution and based on a specific probabilistic mechanism for the DNA fragmentation process of the cell nucleus. In particular, we carry out some sufficient conditions to uniquely identify the original DNA distribution from the flow cytometric data. Received: 15 June 1997 / Revised version: 18 November 1997     

A theoretical approach to G-protein modulation of cellular responsiveness

 Structure and function of cells often depend critically on molecular signals arriving at their surface. There are universal mechanisms of signal transduction and signal processing across cell membranes. In this paper the mechanisms involving guanine-nucleotide regulatory proteins (“G-proteins”) and certain receptor-kinases are considered. On the basis of recent findings in molecular biology a mathematical model is developed taking into account all essential components in the biochemical network between first and second messenger. There are two coupled feedback loops inherent in this process. The model finally consists of three nonlinear equations, which are obtained from a system of originally ten equations by using conservation laws and quasi-steady state conditions. The second part of the paper contains a mathematical analysis of the model. Solutions describing the temporal development of the involved biochemical species are shown to be bounded, more specifically to remain, independent of the size of the input signal, in a bounded domain of the state space. For the situation of stationary input signals existence, uniqueness and asymptotic stability of steady states are derived. We also demonstrate biologically relevant stimulus-response properties like monotonicity and saturation effects. For temporally non-constant input signals we show numerically that the model is able to produce phenomena of hypersensitivity and desensitization which are important characteristics of cellular responsiveness. Received 18 March 1996; received in revised form 15 April 1996     

Multiparametric bifurcations for a model in epidemiology

 In the present paper we make a bifurcation analysis of an SIRS epidemiological model depending on all parameters. In particular we are interested in codimension-2 bifurcations. Received 8 April 1994; received in revised form 29 June 1995     

Polymorphism, distribution, and segregation of AFLP markers in a doubled haploid rice population

We exploited the newly developed amplified fragment length polymorphism (AFLP) technique to study the polymorphism, distribution and inheritance of AFLP markers with a doubled haploid rice population derived from ‘IR64’/‘Azucena’. Using only 20 pairs of primer combinations, we detected 945 AFLP bands of which 208 were polymorphic. All 208 AFLP markers were mapped and distributed over all 12 chromosomes. When these were compared with RFLP markers already mapped in the population, we found the AFLP markers to be highly polymorphic in rice and to follow Mendelian segregation. As linkage map of rice can be generated rapidly with AFLP markers they will be very useful for marker-assisted backcrossing. Received: 11 April 1996 / Accepted: 14 June 1996     

Ultrastructural and lanthanum tracer examination of rapidly resorbing rat alveolar bone suggests that osteoclasts internalize dying bone cells

Glutaraldehyde-formaldehyde fixed undecalcified alveolar bone from 7-day-old rats was prepared for light and electron microscopy. Colloidal lanthanum was used as an ultrastructural tracer, and both random and semi-serial sections were examined. Lanthanum penetrated the infoldings of the ruffled border and some nearby vacuoles and vesicles. The majority of vacuoles and vesicles were lanthanum-free. Some osteoclast profiles contained a large vacuole with a cell enclosed in its interior. The enclosed cell exhibited an irregular nucleus containing condensed peripheral chromatin, intact cytoplasmic organelles, conspicuous rough endoplasmic reticulum and large blebs on the cell surface. These features are characteristic of osteoblasts or bone-lining cells or immature osteocytes which may be undergoing apoptosis or necrosis. The observation of remnants of cellular structures within internalized osteoclast vacuoles, together with the above results, suggests that osteoclasts engulf and probably degrade dying osteoblasts/bone-lining cells or immature osteocytes. Received: 29 April 1997 / Accepted: 20 February 1998     

A generalized transport model for biased cell migration in an anisotropic environment

 A generalized transport model is derived for cell migration in an anisotropic environment and is applied to the specific cases of biased cell migration in a gradient of a stimulus (taxis; e.g., chemotaxis or haptotaxis) or along an axis of anisotropy (e.g., contact guidance). The model accounts for spatial or directional dependence of cell speed and cell turning behavior to predict a constitutive cell flux equation with drift velocity and diffusivity tensor (termed random motility tensor) that are explicit functions of the parameters of the underlying random walk model. This model provides the connection between cell locomotion and the resulting persistent random walk behavior to the observed cell migration on longer time scales, thus it provides a framework for interpreting cell migration data in terms of underlying motility mechanisms. Received: 8 April 1999     

An in vivo model of a mechanically-induced bone marrow lesion

Bone marrow lesions (BMLs) are radiologic abnormalities in magnetic resonance images of subchondral bone that are correlated with osteoarthritis. Little is known about the physiologic processes within a BML, although BMLs are associated with mechanical stress, bone tissue microdamage and increased bone remodeling. Here we establish a rabbit model to study the pathophysiology of BMLs. We hypothesized that in vivo loads that generate microdamage in cancellous bone would also create BMLs and increase bone remodeling. In vivo cyclic loading (0.2–2.0 MPa in compression for 10,000 cycles at 2 Hz) was applied to epiphyseal cancellous bone in the distal femurs of New Zealand white rabbits (n = 3, right limb loaded, left limb controls experienced surgery but no loading). Magnetic resonance images were collected using short tau inversion recovery (STIR) and T1 weighted sequences at 1 and 2 weeks after surgery/loading and histological analysis of the BML was performed after euthanasia to examine tissue microdamage and remodeling. Loaded limbs displayed BMLs while control limbs showed only a small BML-like signal caused by surgery. Histological analysis of the BML at 2 weeks after loading showed increased tissue microdamage (p = 0.03) and bone resorption (p = 0.01) as compared to controls. The model described here displays the hallmarks of load-induced BMLs, supporting the use of the model to examine changes in bone during the development, progression and treatment of BMLs.     

A theoretical three-dimensional model for lactoperoxidase and eosinophil peroxidase,built on the scaffold of the myeloperoxidase X-ray structure

 Lactoperoxidase (LPO), eosinophil peroxidase (EPO) and myeloperoxidase (MPO) belong to the class of haloperoxidases, a group of mammalian enzymes able to catalyze the peroxidative oxidation of halides and pseudohalides, such as thiocyanate. They all play a key role in the development of antibacterial activity. The homology in their functional role is emphasized by the striking similarity of their primary structures. A theoretical model for the three-dimensional structure of LPO and EPO has been developed on the basis of the X-ray structure of MPO, a high degree of similarity having been found in their sequences. Evidence supporting the hypothesis of an ester linkage between heme and apoprotein in LPO and EPO, originally proposed by Hultquist and Morrison is discussed. Received: 2 May 1996 / Accepted: 25 July 1996     

A mathematical model for drug administration by using the phagocytosis of red blood cells

 A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem. Received 15 December 1994; received in revised form 20 July 1995     

Extinction of top-predator in a three-level food-chain model

 In this paper we extend the Lyapunov functions, constructed by A. Ardito and P. Ricciardi for predator–prey system [1], to the three level food chain models. We first consider a general three-level food-chain model. A criterion for the extinction of top predator will be given. Then we restrict our attentions to the case in which the prey is of logistic growth and predators have Holling’s type II functional responses. Received: 10 October 1997     

Protected polymorphism in the two-locus haploid model with unpredictable fitnesses

 In an unpredictable environment, the distributions of alleles from which polymorphism can be maintained forever belong to a certain set, the C-viability kernel. Such a set is calculated in the two-locus haploid model, as well as the corresponding fitnesses at any time which make this maintenance possible. The dependence of the C-viability kernel on the set U of admissible fitnesses and on the recombination rate r is studied. Notably, the C-viability kernel varies rapidly in the neighborhood of equal fitness of AB and ab; it becomes empty when ab has a fitness below a certain function, which is delineated, of the recombination rate. The properties of the two-locus model under constraints, out of equilibrium and with unpredictable selection are thus presented. Received: 20 May 1999     

A mathematical model to describe the dynamic response of a spruce tree to the wind

 A mathematical, computer-based, dynamic sway model of a Sitka spruce (Picea sitchensis) tree was developed and tested against measurements of the movement of a tree within a forest. The model tree was divided into segments each with a stiffness, mass and damping parameter. Equations were formulated to describe the response of every segment which together form a system of coupled differential equations. These were solved with the aid of matrices and from the resulting modes, the transfer function of the tree was found and used to calculate the movement of the tree in the wind. Comparison of the modelled movement of a tree in response to the measured wind speed above a forest canopy gave good agreement with the measured movement of the top of the tree but less satisfactory agreement close to the base. The comparison also pointed to the complexity of tree response to the wind and inadequacies in the model. In particular, the branches need to be treated as coupled cantilevers attached to the stem rather than simply as masses lumped together. Received: 18 February 1997 / Accepted: 16 December 1997     

A stochastic model of brain cell differentiation in tissue culture

 The timing of cell differentiation can be controlled both by cell-intrinsic mechanisms and by cell-extrinsic signals. Oligodendrocyte type-2 astrocyte progenitor cells are known to be the precursor cells that give rise to oligodendrocytes. When stimulated to divide by purifed cortical astrocytes or by platelet-derived growth factor, these progenitor cells generate oligodendrocytes in vitro with a timing like that observed in vivo. The most widely accepted model of this process assumes a cell-intrinsic biological clock that resides in the progenitor cell. The intrinsic clock model originally proposed in 1986 remains as the dominant theoretical concept for the analysis of timed differentiation in this cell lineage. However, the results of a recent experimental study (Ibarrola et al., Developmental Biology, vol. 180, 1–21, 1996) are most consistent with the hypothesis that the propensity of a clone of dividing O-2A progenitor cells initially to generate at least one oligodendrocyte may be regulated by cell-intrinsic mechanisms, but that environmental signals regulate the extent of further oligodendrocyte generation. We propose a stochastic model of cell differentiation in culture to accommodate the most recent experimental findings. Our model is an age-dependent branching stochastic process with two types of cells. The model makes it possible to derive analytical expressions for the expected number of progenitor cells and of oligodendrocytes as functions of time. The model parameters were estimated by fitting these functions through data on the average (sample mean) number of both types of cells per colony at different time intervals from start of experiment. Using this method we provide a biologically meaningful interpretation of the observed pattern of oligodendrocyte generation in vitro and its modification in the presence of thyroid hormone. Received: 18 April 1997 / Revised version: 30 November 1997     

Modeling aggregation and growth processes in an algal population model: analysis and computations

 Aggregation, the formation of large particles through multiple collision of smaller ones is a highly visible phenomena in oceanic waters which can control material flux to the deep sea. Oceanic aggregates more than 1 cm in diameter have been observed and are frequently described to consist of phytoplankton cells as well as other organic matter such as fecel pellets and mucus nets from pteropods. Division of live phytoplankton cells within an aggregate can also increase the size of aggregate (assuming some daughter cells stay in the aggregate) and hence could be a significant factor in speeding up the formation process of larger aggregate. Due to the difficulty of modeling cell division within aggregates, few efforts have been made in this direction. In this paper, we propose a size structured approach that includes growth of aggregate size due to both cell division and aggregation. We first examine some basic mathematical issues associated with the development of a numerical simulation of the resulting algal aggregation model. The numerical algorithm is then used to examine the basic model behavior and present a comparison between aggregate distribution with and without division in aggregates. Results indicate that the inclusion of a growth term in aggregates, due to cell division, results in higher densities of larger aggregates; hence it has the impact to speed clearance of organic matter from the surface layer of the ocean. Received 1 July 1994; received in revised form 23 February 1996     

The periodically forced Droop model for phytoplankton growth in a chemostat

 It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population, to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone growth rate and monotone uptake rate, the latter possibly depending on the cell quota. Received 10 October 1995; received in revised form 26 March 1996     

Larval density and developmental instability in the acoustically orienting parasitoid Homotrixa alleni.

The relationship between developmental stress caused by intraspecific larval density and fluctuating asymmetry (FA) was examined in the tachinid parasitoid Homotrixa alleni. Individuals reared in larger clutches were significantly smaller in body size when they emerged as adults. As predicted, smaller individuals were shown to have significantly higher levels of FA in their tibiae. This negative relationship was consistent across each pair of tibia and the magnitude of FA was also significantly correlated between tibiae. The exact nature of the observed relationship between larval density and FA in H. alleni remains speculative. Received: 20 December 1999 / Received in revised form: 17 February 2000 / Accepted: 17 February 2000     

Homoclinic chaos in a model of natural selection

 We modify a simple mathematical model for natural selection originally formulated by Robert M. May in 1983 by permitting one homozygote to have a larger selective advantage when rare than the other, and show that the new model exhibits dynamical chaos. We determine an open region of parameter space associated with homoclinic points, and prove that there are infinite sequences of period-doubling bifurcations along selected paths through parameter space. We also discuss the possibility of chaos arising from imbalance in the homozygote fitnesses in more realistic biological situations, beyond the constraints of the model. Received 3 February 1995; received in revised form 1 November 1995