Abstract:
:Metabolic flux analysis using carbon labeling experiments (CLEs) is an important tool in metabolic engineering where the intracellular fluxes have to be computed from the measured extracellular fluxes and the partially measured distribution of 13C labeling within the intracellular metabolite pools. The relation between unknown fluxes and measurements is described by an isotopomer labeling system (ILS) (see Part I [Math. Biosci. 169 (2001) 173]). Part II deals with the structural flux identifiability of measured ILSs in the steady state. The central question is whether the measured data contains sufficient information to determine the unknown intracellular fluxes. This question has to be decided a priori, i.e. before the CLE is carried out. In structural identifiability analysis the measurements are assumed to be noise-free. A general theory of structural flux identifiability for measured ILSs is presented and several algorithms are developed to solve the identifiability problem. In the particular case of maximal measurement information, a symbolical algorithm is presented that decides the identifiability question by means of linear methods. Several upper bounds of the number of identifiable fluxes are derived, and the influence of the chosen inputs is evaluated. By introducing integer arithmetic this algorithm can even be applied to large networks. For the general case of arbitrary measurement information, identifiability is decided by a local criterion. A new algorithm based on integer arithmetic enables an a priori local identifiability analysis to be performed for networks of arbitrary size. All algorithms have been implemented and flux identifiability is investigated for the network of the central metabolic pathways of a microorganism. Moreover, several small examples are worked out to illustrate the influence of input metabolite labeling and the paradox of information loss due to network simplification.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Isermann N,Wiechert Wdoi
10.1016/s0025-5564(02)00222-5subject
Has Abstractpub_date
2003-06-01 00:00:00pages
175-214issue
2eissn
0025-5564issn
1879-3134pii
S0025556402002225journal_volume
183pub_type
杂志文章abstract::Let S be a set of n objects. A binary tree of S is a binary tree whose leaves are labeled without repetition from S. The operation of pruning a tree T is that of removing some leaves from T and suppressing all inner vertices of degree 2 which are formed by this deletion. Given two trees T and U, an agreement tree is a...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(94)90012-4
更新日期:1994-10-01 00:00:00
abstract::Microorganisms exhibit varied regulatory strategies such as direct regulation, symmetric anticipatory regulation, asymmetric anticipatory regulation, etc. Current mathematical modeling frameworks for the growth of microorganisms either do not incorporate regulation or assume that the microorganisms utilize the direct ...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2013.11.005
更新日期:2014-02-01 00:00:00
abstract::A mathematical model for the growth of a population of fish in the larval stage is proposed. The emphasis is put on the first part of the larval stage, when the larvae are still passive. It is assumed that during this stage, the larvae move with the phytoplankton on which they feed and share their food equally, leadin...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(98)00008-x
更新日期:1998-06-01 00:00:00
abstract::Cancer virotherapy represents a dynamical system that requires mathematical modeling for complete understanding of the outcomes. The combination of virotherapy with radiation (radiovirotherapy) has been recently shown to successfully eliminate tumors when virotherapy alone failed. However, it introduces a new level of...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2005.11.001
更新日期:2006-01-01 00:00:00
abstract::The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of respon...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(92)90052-x
更新日期:1992-04-01 00:00:00
abstract::Human solid tumors are believed to be caused by a sequence of genetic abnormalities arising in the tumor cells. The understanding of these sequences is extremely important for improving cancer treatment. Models for the occurrence of the abnormalities include linear structure and a recently proposed tree-based structur...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(02)00086-x
更新日期:2002-04-01 00:00:00
abstract::A two-state variable model in which saturable binding takes place is studied. Two mathematical representations of the same model are considered, one a standard chemical kinetics type of polynomial system, the other a reduced model formed from the original system via a pseudo-steady-state approximation. For a particula...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(95)00064-x
更新日期:1996-04-01 00:00:00
abstract::The modified SIS epidemiological model considers the usual direct transmission (short cycle) and indirect transmission (long cycle) of typhoid fever. Thresholds are determined, and the equilibrium points are shown to be globally stable. Local stability of the equilibrium points is shown in the corresponding model with...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(89)90081-3
更新日期:1989-09-01 00:00:00
abstract::Three-species food-chain models, in which the prey population exhibits group defense, are considered. Using the carrying capacity of the environment as the bifurcation parameter, it is shown that the model without delay undergoes a sequence of Hopf bifurcations. In the model with delay it is shown that using a delay a...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(92)90079-c
更新日期:1992-09-01 00:00:00
abstract::The goal of this article is to formulate and analyze the simplest logistic pair-formation model and to contrast its dynamics to that of the corresponding Malthusian pair-formation model, that is, a generalization of the Kendall-Keyfitz model. The Malthusian pair-formation model supports a unique nontrivial stable expo...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(94)00077-d
更新日期:1995-07-01 00:00:00
abstract::Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting stat...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2011.03.003
更新日期:2011-06-01 00:00:00
abstract::This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to pred...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2017.08.009
更新日期:2017-11-01 00:00:00
abstract::This paper considers the geometry of plants with golden spiral phyllotaxis, i.e. growing leaf by leaf on a spiral with golden divergence angle, via the simplest mathematical model, a cylinder with regular arrangement of points on its surface. As is well-known, Fibonacci numbers appear by means of the order of parastic...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2018.05.003
更新日期:2018-07-01 00:00:00
abstract::This paper is concerned with the development of a stochastic path of prostate-specific antigen (PSA) level after radiation treatment for prostate cancer. PSA is a biomarker for prostate cancer, higher levels of which indicate the seriousness of the cancer progression. Following the deterministic modeling of the data b...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(02)00215-8
更新日期:2003-04-01 00:00:00
abstract::We study spatial stochastic epidemic models called households models. The households models have more than two states at each vertex of a graph in contrast to the contact process. We show that, in the households models on trees, two thresholds of infection rates characterize epidemics. The global critical infection ra...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2008.02.004
更新日期:2008-05-01 00:00:00
abstract::We consider a host-parasitoid system with individuals moving on a square grid of patches. We study the effects of increasing movement frequency of hosts and parasitoids on the spatial dynamics of the system. We show that there exists a threshold value of movement frequency above which spatial synchrony occurs and the ...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2006.03.019
更新日期:2006-10-01 00:00:00
abstract::The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e., available for ligand binding) or inactive. An active receptor turns inactive upon binding a ligand, and it can reap...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(90)90122-f
更新日期:1990-03-01 00:00:00
abstract::Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, it is also useful to consider a dual type of statistical consistency where we increase the number of species, rather ...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2010.07.002
更新日期:2010-10-01 00:00:00
abstract::Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act wi...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(92)90006-i
更新日期:1992-02-01 00:00:00
abstract::The reaction-diffusion equation is one of the possible ways for modeling animal movement, where the reactive part stands for the population growth and the diffusive part for random dispersal of the population. However, a reaction-diffusion model may not represent all aspects of the spatial dynamics, because of the exi...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2020.108346
更新日期:2020-06-01 00:00:00
abstract::In this paper we study the dynamics of two competing species when one of them is subject to a disease. In order to keep the model simple, we present it under the strong assumption that the disease cannot cross the species barrier. We answer several important questions about the long term behavior of the environment. I...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(01)00081-5
更新日期:2001-12-01 00:00:00
abstract::The Yule process generates a class of binary trees which is fundamental to population genetic models and other applications in evolutionary biology. In this paper, we introduce a family of sub-classes of ranked trees, called Ω-trees, which are characterized by imbalance of internal nodes. The degree of imbalance is de...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2013.08.008
更新日期:2013-11-01 00:00:00
abstract::In this paper, we first propose a prey-predator model with prey-stage structure and diffusion. Then we discuss the following three problems: (1) stability of non-negative constant steady states for the reduced ODE system and the corresponding reaction diffusion system with homogeneous Neumann boundary conditions; (2) ...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2007.08.008
更新日期:2008-04-01 00:00:00
abstract::In the present paper, we propose and analyze an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2016.08.014
更新日期:2016-11-01 00:00:00
abstract::On the basis of this study, it is concluded that within physiological limits the minimum value for the mean capture time of LDL receptors by coated pits must be induced fundamentally by an optimal characterization of their insertion rate function. The corresponding steady-state surface aggregation patterns for the unb...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(99)00043-7
更新日期:1999-11-01 00:00:00
abstract::Threshold parameters of epidemic models play a central role in the assessment of proposed control strategies for infectious diseases. They have been determined for numerous standard epidemic models. This paper points out, with several examples, that threshold parameters depend on the social setting of the community an...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(94)00061-4
更新日期:1995-10-01 00:00:00
abstract::A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The da...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/s0025-5564(02)00178-5
更新日期:2003-03-01 00:00:00
abstract::Calculations of the oxygen distribution in resting and contracting skeletal muscle are presented, based on a mathematical model and experimental data obtained on the hamster cremaster muscle [Klitzman et al., Microvasc. Res. 25:108-131 (1983)]. The model considers a slab of tissue penetrated by a regular square array ...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(86)90164-1
更新日期:1986-09-01 00:00:00
abstract::Many microbial ecosystems can be seen as microbial 'food chains' where the different reaction steps can be seen as such: the waste products of the organisms at a given reaction step are consumed by organisms at the next reaction step. In the present paper we study a model of a two-step biological reaction with feedbac...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/j.mbs.2016.02.008
更新日期:2016-05-01 00:00:00
abstract::Invariants are functions of the probabilities of state configurations among lineages, with expected values equal to zero under certain phylogenies. For two-state sequences, the existence of certain quadratic invariants requires a symmetric substitution model. For sequences with more than two states, the necessary cond...
journal_title:Mathematical biosciences
pub_type: 杂志文章
doi:10.1016/0025-5564(91)90083-u
更新日期:1991-07-01 00:00:00