Abstract：
:Cancer is a complex phenomenon, and the sheer variation in behaviour across different types renders it difficult to ascertain underlying biological mechanisms. Experimental approaches frequently yield conflicting results for myriad reasons, and mathematical modelling of cancer is a vital tool to explore what we cannot readily measure, and ultimately improve treatment and prognosis. Like experiments, models are underpinned by certain biological assumptions, variation of which can lead to divergent predictions. An outstanding and important question concerns contact inhibition of proliferation (CIP), the observation that proliferation ceases when cells are spatially confined by their neighbours. CIP is a characteristic of many healthy adult tissues, but it remains unclear to which extent it holds in solid tumours, which exhibit regions of hyper-proliferation, and apparent breakdown of CIP. What precisely occurs in tumour tissue remains an open question, which mathematical modelling can help shed light on. In this perspective piece, we explore the implications of different hypotheses and available experimental evidence to elucidate the implications of these scenarios. We also outline how erroneous conclusions about the nature of tumour growth may be arrived at by looking selectively at biological data in isolation, and how this might be circumvented.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Grimes DR,Fletcher AGdoi
10.1007/s11538-019-00677-ysubject
Has Abstractpub_date
2020-01-22 00:00:00pages
20issue
2eissn
0092-8240issn
1522-9602pii
10.1007/s11538-019-00677-yjournal_volume
82pub_type
杂志文章abstract：:Classical evolutionary game theory (EGT) focuses on competition among phenotypes while assuming asexual transmission of these phenotypes to the next generation. However, phenotypic selection and sexual recombination are not necessarily mutually reinforcing in populations with sexual reproduction. In particular, it has...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00705-2
更新日期：2020-02-06 00:00:00
abstract：:A dynamic model for cell differentiation, where cells with internal chemical reaction dynamics interact with each other and replicate was studied. It led to spontaneous differentiation of cells and determination, as discussed in the isologous diversification. The following features of the differentiation were obtained...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.1997.0034
更新日期：1998-07-01 00:00:00
abstract：:Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time a...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-013-9824-7
更新日期：2013-04-01 00:00:00
abstract：:Synaptic spines grow as a consequence of the formation of F-actin filaments at the spine head. The dynamics of F-actin in the spine head upon excitation of N-methy-D-aspartate (NMDA) receptors has recently been investigated experimentally, but there is no quantitative account of how these dynamic changes occur upon ac...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9614-4
更新日期：2011-09-01 00:00:00
abstract：:Viruses that infect bacteria, i.e., bacteriophage or 'phage,' are increasingly considered as treatment options for the control and clearance of bacterial infections, particularly as compassionate use therapy for multi-drug-resistant infections. In practice, clinical use of phage often involves the application of multi...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-020-00751-w
更新日期：2020-06-12 00:00:00
abstract：:Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature, dense and fibrous extracellular matrix, irregular cellular architecture, ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0402-x
更新日期：2019-09-01 00:00:00
abstract：:We address the problem of using nonlinear models to design experiments to characterize the dynamics of cellular processes by using the approach of the Maximally Informative Next Experiment (MINE), which was introduced in W. Dong et al. (PLoS ONE 3(8):e3105, 2008) and independently in M.M. Donahue et al. (IET Syst. Bio...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-014-9935-9
更新日期：2014-03-01 00:00:00
abstract：:It is well established that in problems featuring slow passage through a Hopf bifurcation (dynamic Hopf bifurcation) the transition to large-amplitude oscillations may not occur until the slowly changing parameter considerably exceeds the value predicted from the static Hopf bifurcation analysis (temporal delay effect...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-017-0366-2
更新日期：2018-01-01 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：:A mathematical model (Kliemann, W. 1987. Bull. math. Biol. 49, 135-152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistic for chi 2-test was developed for the branching pattern of dendritic trees and for...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458630
更新日期：1991-01-01 00:00:00
abstract：:A mathematical model for the plant-pollinator-robber interaction is studied to understand the factors leading to the widespread occurrence and stability of such interactions. In the interaction, a flowering plant provides resource for its pollinator and the pollinator has both positive and negative effects on the plan...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-012-9750-0
更新日期：2012-09-01 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：:The surface protein B7-H1, also called PD-L1 and CD274, is found on carcinomas of the lung, ovary, colon, and melanomas but not on most normal tissues. B7-H1 has been experimentally determined to be an antiapoptotic receptor on cancer cells, where B7-H1-positive cancer cells have been shown to be immune resistant, and...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-011-9665-1
更新日期：2012-01-01 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：: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：:Human T-cell lymphotropic virus type I (HTLV-I) infection in humans causes a chronic infection of CD4+ T cells, and is associated with various disease outcomes, among them with the development of adult T-cell leukemia (ATL). The T-cell dynamics after HTLV-I infection can be described in a mathematical model with coupl...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1006/bulm.1999.0117
更新日期：1999-09-01 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：:We study the global stability of a class of models for in-vivo virus dynamics that take into account the Cytotoxic T Lymphocyte immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally a...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-010-9543-2
更新日期：2011-03-01 00:00:00
abstract：:Dengue is a growing public health problem in tropical and subtropical cities. It is transmitted by mosquitoes, and the main strategy for epidemic prevention and control is insecticide fumigation. Effective management is, however, proving elusive. People's day-to-day movement about the city is believed to be an importa...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0209-6
更新日期：2016-10-01 00:00:00
abstract：:Collective dynamics of migrating cell populations drive key processes in tissue formation and maintenance under normal and diseased conditions. Collective cell behavior at the tissue level is typically characterized by considering cell density patterns such as clusters and moving cell fronts. However, there are also i...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-015-0079-3
更新日期：2015-04-01 00:00:00
abstract：:Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of a Tetrahymena pyriformis-Escherichia coli community. In this study ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458309
更新日期：1996-03-01 00:00:00
abstract：:An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chem...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0428-0
更新日期：2019-08-01 00:00:00
abstract：:Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-016-0181-1
更新日期：2016-06-01 00:00:00
abstract：:When two strings of symbols are aligned it is important to know whether the observed number of matches is better than that expected between two independent sequences with the same frequency of symbols. When strings are of different lengths, nulls need to be inserted in order to align the sequences. One approach is to ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/BF02458576
更新日期：1990-01-01 00:00:00
abstract：:The apparent synchronisation of spatially discrete populations is a well documented phenomenon. However, it is not clear what the governing mechanisms are for this synchrony, and whether they are robust over a range of environmental conditions and patch specific population dynamic behaviours. In this paper, we explore...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1016/j.bulm.2004.05.006
更新日期：2004-11-01 00:00:00
abstract：:Farmers frequently decide where to locate the colonies of their domesticated eusocial bees, especially given the following mutually exclusive scenarios: (i) there are limited nectar and pollen sources within the vicinity of the apiary that cause competition among foragers; and (ii) there are fewer pollinators compared...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-014-9943-9
更新日期：2014-05-01 00:00:00
abstract：:Recent discoveries in ecological stoichiometry have indicated that food quality in terms of the phosphorus/carbon (P/C) ratio affects consumers whether the imbalance involves insufficient or excess nutrients. This phenomenon is called the "stoichiometric P/C knife-edge." In this study, we develop and analyze a produce...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-019-00629-6
更新日期：2019-07-01 00:00:00
abstract：:National Bureau of Statistics of China reports that the incidence of schistosomiasis has been increasing in recent years. To study dynamic behaviors of schistosomiasis transmission, based on practical experience of staff in Anhui Institute of Schistosomiasis, a mathematical schistosomiasis model with reinfection of re...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-018-0474-7
更新日期：2018-09-01 00:00:00
abstract：:We develop a model for describing the dynamics of imatinib-treated chronic myelogenous leukemia. Our model is based on replacing the recent agent-based model of Roeder et al. (Nat. Med. 12(10):1181-1184, 2006) by a system of deterministic difference equations. These difference equations describe the time-evolution of ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章
doi：10.1007/s11538-007-9276-z
更新日期：2008-04-01 00:00:00
abstract：:Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we ...
journal_title：Bulletin of mathematical biology
pub_type： 杂志文章,评审
doi：10.1006/bulm.1999.0155
更新日期：2000-03-01 00:00:00
