373 research outputs found
Joining and decomposing reaction networks
In systems and synthetic biology, much research has focused on the behavior
and design of single pathways, while, more recently, experimental efforts have
focused on how cross-talk (coupling two or more pathways) or inhibiting
molecular function (isolating one part of the pathway) affects systems-level
behavior. However, the theory for tackling these larger systems in general has
lagged behind. Here, we analyze how joining networks (e.g., cross-talk) or
decomposing networks (e.g., inhibition or knock-outs) affects three properties
that reaction networks may possess---identifiability (recoverability of
parameter values from data), steady-state invariants (relationships among
species concentrations at steady state, used in model selection), and
multistationarity (capacity for multiple steady states, which correspond to
multiple cell decisions). Specifically, we prove results that clarify, for a
network obtained by joining two smaller networks, how properties of the smaller
networks can be inferred from or can imply similar properties of the original
network. Our proofs use techniques from computational algebraic geometry,
including elimination theory and differential algebra.Comment: 44 pages; extensive revision in response to referee comment
A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone
Recommended standardized procedures for determining exhaled lower respiratory
nitric oxide and nasal nitric oxide have been developed by task forces of the
European Respiratory Society and the American Thoracic Society. These
recommendations have paved the way for the measurement of nitric oxide to
become a diagnostic tool for specific clinical applications. It would be
desirable to develop similar guidelines for the sampling of other trace gases
in exhaled breath, especially volatile organic compounds (VOCs) which reflect
ongoing metabolism. The concentrations of water-soluble, blood-borne substances
in exhaled breath are influenced by: (i) breathing patterns affecting gas
exchange in the conducting airways; (ii) the concentrations in the
tracheo-bronchial lining fluid; (iii) the alveolar and systemic concentrations
of the compound. The classical Farhi equation takes only the alveolar
concentrations into account. Real-time measurements of acetone in end-tidal
breath under an ergometer challenge show characteristics which cannot be
explained within the Farhi setting. Here we develop a compartment model that
reliably captures these profiles and is capable of relating breath to the
systemic concentrations of acetone. By comparison with experimental data it is
inferred that the major part of variability in breath acetone concentrations
(e.g., in response to moderate exercise or altered breathing patterns) can be
attributed to airway gas exchange, with minimal changes of the underlying blood
and tissue concentrations. Moreover, it is deduced that measured end-tidal
breath concentrations of acetone determined during resting conditions and free
breathing will be rather poor indicators for endogenous levels. Particularly,
the current formulation includes the classical Farhi and the Scheid series
inhomogeneity model as special limiting cases.Comment: 38 page
Inference of complex biological networks: distinguishability issues and optimization-based solutions
<p>Abstract</p> <p>Background</p> <p>The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation.</p> <p>Results</p> <p>We claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP), therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining 'true' reaction structures are generally not enough without additional prior information.</p> <p>Conclusions</p> <p>The inference of biological networks can be an extremely challenging problem even in the utopian case of perfect experimental information. Unfortunately, the practical situation is often more complex than that, since the measurements are typically incomplete, noisy and sometimes dynamically not rich enough, introducing further obstacles to the structure/parameter estimation process. In this paper, we show how the structural uniqueness and identifiability of the models can be guaranteed by carefully adding extra constraints, and that these important properties can be checked through appropriate computation methods.</p
Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model
Modeling viral dynamics in HIV/AIDS studies has resulted in a deep
understanding of pathogenesis of HIV infection from which novel antiviral
treatment guidance and strategies have been derived. Viral dynamics models
based on nonlinear differential equations have been proposed and well developed
over the past few decades. However, it is quite challenging to use experimental
or clinical data to estimate the unknown parameters (both constant and
time-varying parameters) in complex nonlinear differential equation models.
Therefore, investigators usually fix some parameter values, from the literature
or by experience, to obtain only parameter estimates of interest from clinical
or experimental data. However, when such prior information is not available, it
is desirable to determine all the parameter estimates from data. In this paper
we intend to combine the newly developed approaches, a multi-stage
smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares
(SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear
differential equation model. In particular, to the best of our knowledge, this
is the first attempt to propose a comparatively thorough procedure, accounting
for both efficiency and accuracy, to rigorously estimate all key kinetic
parameters in a nonlinear differential equation model of HIV dynamics from
clinical data. These parameters include the proliferation rate and death rate
of uninfected HIV-targeted cells, the average number of virions produced by an
infected cell, and the infection rate which is related to the antiviral
treatment effect and is time-varying. To validate the estimation methods, we
verified the identifiability of the HIV viral dynamic model and performed
simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Identifiable reparametrizations of linear compartment models
Identifiability concerns finding which unknown parameters of a model can be
quantified from given input-output data. Many linear ODE models, used in
systems biology and pharmacokinetics, are unidentifiable, which means that
parameters can take on an infinite number of values and yet yield the same
input-output data. We use commutative algebra and graph theory to study a
particular class of unidentifiable models and find conditions to obtain
identifiable scaling reparametrizations of these models. Our main result is
that the existence of an identifiable scaling reparametrization is equivalent
to the existence of a scaling reparametrization by monomial functions. We also
provide partial results beginning to classify graphs which possess an
identifiable scaling reparametrization.Comment: 5 figure
- …