1,005 research outputs found
The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies
This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics
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
Carbon transit through degradation networks
The decay of organic matter in natural ecosystems is controlled by a network of biologically, physically, and chemically driven processes. Decomposing organic matter is often described as a continuum that transforms and degrades over a wide range of rates, but it is difficult to quantify this heterogeneity in models. Most models of carbon degradation consider a network of only a few organic matter states that transform homogeneously at a single rate. These models may fail to capture the range of residence times of carbon in the soil organic matter continuum. Here we assume that organic matter is distributed among a continuous network of states that transform with stochastic, heterogeneous kinetics. We pose and solve an inverse problem in order to identify the rates of carbon exiting the underlying degradation network (exit rates) and apply this approach to plant matter decay throughout North America. This approach provides estimates of carbon retention in the network without knowing the details of underlying state transformations. We find that the exit rates are approximately lognormal, suggesting that carbon flow through a complex degradation network can be described with just a few parameters. These results indicate that the serial and feedback processes in natural degradation networks can be well approximated by a continuum of parallel decay rates.National Science Foundation (U.S.) (Grant EAR-0420592)United States. National Aeronautics and Space Administration (Grant NNA08CN84A
Decentralized control of compartmental networks with H∞ tracking performance
published_or_final_versio
Identifiability of large nonlinear biochemical networks
Dynamic models formulated as a set of ordinary differential equations provide a detailed description of the time-evolution of a system. Such models of (bio)chemical reaction networks have contributed to important advances in biotechnology and biomedical applications, and their impact is foreseen to increase in the near future. Hence, the task of dynamic model building has attracted much attention from scientists working at the intersection of biochemistry, systems theory, mathematics, and computer science, among other disciplines-an area sometimes called systems biology. Before a model can be effectively used, the values of its unknown parameters have to be estimated from experimental data. A necessary condition for parameter estimation is identifiability, the property that, for a certain output, there exists a unique (or finite) set of parameter values that produces it. Identifiability can be analysed from two complementary points of view: structural (which searches for symmetries in the model equations that may prevent parameters from being uniquely determined) or practical (which focuses on the limitations introduced by the quantity and quality of the data available for parameter estimation). Both types of analyses are often difficult for nonlinear models, and their complexity increases rapidly with the problem size. Hence, assessing the identifiability of realistic dynamic models of biochemical networks remains a challenging task. Despite the fact that many methods have been developed for this purpose, it is still an open problem and an active area of research. Here we review the theory and tools available for the study of identifiability, and discuss some closely related concepts such as sensitivity to parameter perturbations, observability, distinguishability, and optimal experimental design, among others.This work was funded by the Galician government (Xunta de Galiza) through the I2C postdoctoral program (fellowship ED481B2014/133-0), and by the Spanish Ministry of Economy and Competitiveness (grant DPI2013-47100-C2-2-P)
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