Abstract：
:In contrast to their name, biofilms are not always flat and homogeneous but instead often exhibit complex structural heterogeneity. It has been suggested that nonhomogeneous geometry is selected in order to increase biofilm growth rate. A previous study (Dockery and Klapper (2002) SIAM J. Appl. Math., 62, 853-869) of a model biofilm system in a static bulk fluid demonstrated that under some circumstances a flat biofilm-bulk fluid interface is linearly unstable to perturbation due to growth induced forces. Computations indicated that subsequent nonlinear evolution results in fingers and mushrooms of biofilm similar to structures observed in actual biofilms. However, the important complementary issue of biological functionality was not considered. Here a weakly nonlinear analysis of the simple growing biofilm layer model in Dockery and Klapper (2002, SIAM J. Appl. Math., 62, 853-869) is presented. It is argued that, at least in the case of biofilms free of external mechanical stress, overall growth is in fact generally inhibited by the presence of growing perturbations in the linear stage. Hence a more complex explanation of function is necessary.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Klapper Idoi
10.1016/j.bulm.2003.11.008subject
Has Abstractpub_date
2004-07-01 00:00:00pages
809-24issue
4eissn
0092-8240issn
1522-9602pii
S0092824003001393journal_volume
66pub_type
杂志文章abstract：:In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocrine and paracrine growth factors in tumor growth. Bull. math. Biol. 53, 639-656). The target population, a generic tumor, was modeled as a single, homogeneous population using the ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02460696
更新日期：1993-09-01 00:00:00
abstract：:Bursting electrical activity is ubiquitous in excitable cells such as neurons and many endocrine cells. The technique of fast/slow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9559-7
更新日期：2011-06-01 00:00:00
abstract：:A method for obtaining delay histograms for the time course of neurotransmitter release is presented. The delay histogram is derived from the measured psc (or the sum of several psc's) and the mpsc (obtained experimentally or otherwise) by means of a simple, quick, mathematical procedure. The procedure may be automate...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458628
更新日期：1991-01-01 00:00:00
abstract：:We investigate the existence of oscillatory dynamics and multiple steady-state flow rates in a network with a simple topology and in vivo microvascular blood flow constitutive laws. Unlike many previous analytic studies, we employ the most biologically relevant models of the physical properties of whole blood. Through...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0089-1
更新日期：2015-07-01 00:00:00
abstract：:Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protei...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0438-y
更新日期：2018-07-01 00:00:00
abstract：:We explore the dynamics of invasive weeds by partial differential equation (PDE) modelling and applying dynamical system and phase portrait techniques. We begin by applying the method of characteristics to a preexisting PDE model of the spreading of T. fluminensis, an invasive weed which has been responsible for nativ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00825-9
更新日期：2021-01-07 00:00:00
abstract：:Continuing the discussion of how children can modify and regularize linguistic inputs from adults, we present a new interpretation of existing algorithms to model and investigate the process of a learner learning from an inconsistent source. On the basis of this approach is a (possibly nonlinear) function (the update ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0250-0
更新日期：2017-03-01 00:00:00
abstract：:The coordinated beating of motile cilia is responsible for ovum transport in the oviduct, transport of mucus in the respiratory tract, and is the basis of motility in many single-celled organisms. The beating of a single motile cilium is achieved by the ATP-driven activation cycles of thousands of dynein molecular mot...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-008-9296-3
更新日期：2008-05-01 00:00:00
abstract：:This work aims to examine the global behavior of a Gause type predator-prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9577-5
更新日期：2011-06-01 00:00:00
abstract：:A semi-empirical model applicable to the flow of blood and other particulate suspensions through narrow tubes has been developed. It envisages a central core of blood surrounded by a wall layer of reduced hematocrit. With the help of this model the wall layer thickness and extent of plug flow may be calculated using p...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02459514
更新日期：1975-10-01 00:00:00
abstract：:Evidence suggests that many G protein-coupled receptors (GPCRs) are bound together forming dimers. The implications of dimerisation for cellular signalling outcomes, and ultimately drug discovery and therapeutics, remain unclear. Consideration of ligand binding and signalling via receptor dimers is therefore required ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0387-x
更新日期：2019-09-01 00:00:00
abstract：:Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimension...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00807-x
更新日期：2020-09-26 00:00:00
abstract：:Distinct electrophysiological phenotypes are exhibited by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0516-1
更新日期：2019-01-01 00:00:00
abstract：:Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent ac...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458276
更新日期：1994-09-01 00:00:00
abstract：:Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0205-x
更新日期：2016-09-01 00:00:00
abstract：:Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open mathematical problem. One successful strategy consists of analyzing small networks ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-00555-z
更新日期：2019-04-01 00:00:00
abstract：:Human rabies is one of the major public health problems in China with an average of 1977 cases per year. It is estimated that 95% of these human rabies cases are due to dog bites. In recent years, the number of wildlife-associated human rabies cases has increased, particularly in the southeast and northeast regions of...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-00537-1
更新日期：2019-04-01 00:00:00
abstract：:The apoptotic caspase-3/8 feedback loop describes the core of the extrinsic pro-apoptotic signaling pathway, an essential part of apoptosis. Latter is a prototype of the programmed cell death, which enables organisms to remove damaged or infected cells. The reaction network of the caspase-3/8 feedback loop in a single...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9892-8
更新日期：2013-11-01 00:00:00
abstract：:Theoretical and empirical arguments are used to support the growth kinetics of disseminated tumors. Employing viable hypotheses, it is established that Gompertzian growth of disseminated cancer cells can be derived from a number of theoretical considerations. Empirical methods are used to validate and confirm the theo...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.1999.0165
更新日期：2000-05-01 00:00:00
abstract：:A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Spontaneously acquired drug resistance is accounted for, as well as the evolution in time of normal cells. In addition, optimization of conflicting objectives forms the aim of the chemotherapeutic...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458426
更新日期：1997-07-01 00:00:00
abstract：:We study crossflow filtration mechanisms in suspension-feeding fishes using computational fluid dynamics to model fluid flow and food particle movement in the vicinity of the gill rakers. During industrial and biological crossflow filtration, particles are retained when they remain suspended in the mainstream flow tra...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9709-6
更新日期：2012-04-01 00:00:00
abstract：:The virulent effects of a pathogen on host fecundity and mortality (both intrinsic and extrinsic mortality due to predation) often increase with the age of infection. Age of infection often is also correlated with parasite fitness, in terms of the number of both infective propagules produced and the between-host trans...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0141-9
更新日期：2016-02-01 00:00:00
abstract：:In a companion paper (Lof et al., in Bull. Math. Biol., 2008), we describe a spatio-temporal model for insect behavior. This model includes chemical information for finding resources and conspecifics. As a model species, we used Drosophila melanogaster, because its behavior is documented comparatively well. We divide ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-008-9329-y
更新日期：2008-10-01 00:00:00
abstract：:A protein fold can be viewed as a self-avoiding walk in certain lattice model, and its contact map is a graph that represents the patterns of contacts in the fold. Goldman, Istrail, and Papadimitriou showed that a contact map in the 2D square lattice can be decomposed into at most two stacks and one queue. In the term...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0212-y
更新日期：2017-01-01 00:00:00
abstract：:While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9521-8
更新日期：2010-11-01 00:00:00
abstract：:Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the un...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-008-9382-6
更新日期：2009-05-01 00:00:00
abstract：:We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotic...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0426-2
更新日期：2019-11-01 00:00:00
abstract：:The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binar...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9859-9
更新日期：2013-09-01 00:00:00
abstract：:In this paper we develop and extend a previous model of cell deformations, initially proposed to describe the dynamical behaviour of round-shaped cells such as keratinocytes or leukocytes, in order to take into account cell pseudopodial dynamics with large amplitude membrane deformations such as those observed in fibr...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/j.bulm.2003.11.004
更新日期：2004-09-01 00:00:00
abstract：:The culmination of the morphogenesis of the cellular slime mould Dictyostelium discoideum involves complex cell movements which transform a mound of cells into a globule of spores on a slender stalk. We show that cyclic AMP signalling and differential adhesion, combined with cell differentiation and slime production, ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2001.0277
更新日期：2002-03-01 00:00:00
