Abstract：
:Cell cycle times are vital parameters in cancer research, and short cell cycle times are often related to poor survival of cancer patients. A method for experimental estimation of cell cycle times, or doubling times of cultured cancer cell populations, based on addition of paclitaxel (an inhibitor of cell division) has been proposed in literature. We use a mathematical model to investigate relationships between essential parameters of the cell division cycle following inhibition of cell division. The reduction in the number of cells engaged in DNA replication reaches a plateau as the concentration of paclitaxel is increased; this can be determined experimentally. From our model we have derived a plateau log reduction formula for proliferating cells and established that there are linear relationships between the plateau log reduction values and the reciprocal of doubling times (i.e. growth rates of the populations). We have therefore provided theoretical justification of an important experimental technique to determine cell doubling times. Furthermore, we have applied Monte Carlo experiments to justify the suggested linear relationships used to estimate doubling time from 5-day cell culture assays. We show that our results are applicable to cancer cell populations with cell loss present.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Daukste L,Basse B,Baguley BC,Wall DJdoi
10.1007/s11538-012-9764-7subject
Has Abstractpub_date
2012-10-01 00:00:00pages
2510-34issue
10eissn
0092-8240issn
1522-9602journal_volume
74pub_type
杂志文章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：:A coupled model is presented for simulating physical and biological dynamics in fresh water lakes. The physical model rests upon the assumption that the turbulent kinetic energy in a water column of the lake is fully contained in a mixed layer of variable depth. Below this layer the mechanical energy content is assume...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.1998.0075
更新日期：1999-03-01 00:00:00
abstract：:Understanding the life-history complex of eusociality has remained an enduring problem in evolutionary ecology, partially because natural selection models have considered traits in relative isolation. I aim for a more inclusive model that uses ecological interactions to predict the evolutionary existence of sexual rep...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9112-x
更新日期：2007-05-01 00:00:00
abstract：:In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and e...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0255-8
更新日期：2017-04-01 00:00:00
abstract：:We present a new symmetric model of the idiotypic immune network. The model specifies clones of B-lymphocytes and incorporates: (1) influx and decay of cells; (2) symmetric stimulatory and inhibitory idiotypic interactions; (3) an explicit affinity parameter (matrix); (4) external (i.e. non-idiotypic) antigens. Suppre...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458444
更新日期：1989-01-01 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：: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：:Trichloroethylene (TCE) is an industrial chemical and an environmental contaminant. TCE and its metabolites may be carcinogenic and affect human health. Physiologically based pharmacokinetic (PBPK) models that differ in compartmentalization are developed for TCE metabolism in humans, and the focus of this investigatio...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-007-9233-x
更新日期：2007-11-01 00:00:00
abstract：:Logical modeling of biological regulatory networks gives rise to a representation of the system's dynamics as a so-called state transition graph. Analysis of such a graph in its entirety allows for a comprehensive understanding of the functionalities and behavior of the modeled system. However, the size of the vertex ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-012-9782-5
更新日期：2013-06-01 00:00:00
abstract：:Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluo...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9524-5
更新日期：2011-01-01 00:00:00
abstract：:This study investigates fluid flow and elastic deformation in tissues that are drained by the primary lymphatic system. A model is formulated based on the Rossi hypothesis that states that the primary lymphatic valves, which are formed by overlapping endothelial cells around the circumferential lining of lymphatic cap...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0078-4
更新日期：2015-06-01 00:00:00
abstract：:It has been recently observed that the dynamical properties of mass action systems arising from many models of biochemical reaction networks can be characterized by considering the corresponding properties of a related generalized mass action system. The correspondence process known as network translation in particula...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0077-5
更新日期：2015-06-01 00:00:00
abstract：:In order to understand the role of space in ecological communities where each species produces a certain type of resource and has varying abilities to exploit the resources produced by its own species and by the other species, we carry out a comparative study of an interacting particle system and its mean-field approx...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9649-1
更新日期：2012-01-01 00:00:00
abstract：:The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar-von Caemmerer-Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordi...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00676-z
更新日期：2019-12-23 00:00:00
abstract：:Biological invasion is an important area of research in mathematical biology and more so if it concerns species which are vectors for diseases threatening the public health of large populations. That is certainly the case for Aedes aegypti and the dengue epidemics in South America. Without the prospect of an effective...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/j.bulm.2004.08.005
更新日期：2005-05-01 00:00:00
abstract：:In this paper we attack the problem of understanding the localization of the main structures involved in the motor circadian rhythm of crayfish by analysing its ontogeny. We present experimental results giving the properties of this rhythm in young and adult crayfish. Then we construct a mathematical model (based on a...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.2001.0227
更新日期：2001-03-01 00:00:00
abstract：:Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like signaling and heat shock response pathways. Following thermal stress, expression levels of small heat shock protein-16.2 show a spatial patterning across the 20 intestinal cells that reside along the length of the worm. Here, we present a hypo...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0482-7
更新日期：2018-10-01 00:00:00
abstract：:The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor media...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02459482
更新日期：1996-07-01 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：:In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth o...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00656-3
更新日期：2019-10-01 00:00:00
abstract：:Tandem repeats play many important roles in biological research. However, accurate characterization of their properties is limited by the inability to easily detect them. For this reason, much work has been devoted to developing detection algorithms. A widely used algorithm for detecting tandem repeats is the "tandem ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9146-0
更新日期：2006-11-01 00:00:00
abstract：:We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00666-1
更新日期：2019-12-01 00:00:00
abstract：:Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, i...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9580-x
更新日期：2011-03-01 00:00:00
abstract：:We formulate a mathematical model for food collection and production of workers and nymphs in 2 species of mound building termites. We maximise the number of nymphs (reproductives) produced by each colony over its lifetime with respect to the proportion of eggs that hatch as nymphs as opposed to workers. The results p...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-007-9248-3
更新日期：2008-01-01 00:00:00
abstract：:Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation of bone-marrow-derived endothelial progenitor cells (E...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-007-9253-6
更新日期：2007-11-01 00:00:00
abstract：:This study is concerned with reconciling theoretical modelling of the fluid flow in the airway surface liquid with experimental visualisation of tracer transport in human airway epithelial cultures. The airways are covered by a dense mat of cilia of length approximately 6 microm beating in a watery periciliary liquid ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-006-9163-z
更新日期：2007-04-01 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
abstract：:In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three sp...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/S0092-8240(03)00041-7
更新日期：2003-09-01 00:00:00
abstract：:The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed Ross-Macdonald model. Then we ca...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-007-9292-z
更新日期：2008-05-01 00:00:00
abstract：:A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting B cell clones is presented. For each clone the population dynamics of proliferating B cells, non-proliferating B cells and free antibodies are considered. An effective response function, whic...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02460702
更新日期：1993-11-01 00:00:00
