123,158 research outputs found
Optimal Rate of Direct Estimators in Systems of Ordinary Differential Equations Linear in Functions of the Parameters
Many processes in biology, chemistry, physics, medicine, and engineering are
modeled by a system of differential equations. Such a system is usually
characterized via unknown parameters and estimating their 'true' value is thus
required. In this paper we focus on the quite common systems for which the
derivatives of the states may be written as sums of products of a function of
the states and a function of the parameters.
For such a system linear in functions of the unknown parameters we present a
necessary and sufficient condition for identifiability of the parameters. We
develop an estimation approach that bypasses the heavy computational burden of
numerical integration and avoids the estimation of system states derivatives,
drawbacks from which many classic estimation methods suffer. We also suggest an
experimental design for which smoothing can be circumvented. The optimal rate
of the proposed estimators, i.e., their -consistency, is proved and
simulation results illustrate their excellent finite sample performance and
compare it to other estimation approaches
Optimal experimental design for mathematical models of haematopoiesis.
The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters
Trajectory Synthesis for Fisher Information Maximization
Estimation of model parameters in a dynamic system can be significantly
improved with the choice of experimental trajectory. For general, nonlinear
dynamic systems, finding globally "best" trajectories is typically not
feasible; however, given an initial estimate of the model parameters and an
initial trajectory, we present a continuous-time optimization method that
produces a locally optimal trajectory for parameter estimation in the presence
of measurement noise. The optimization algorithm is formulated to find system
trajectories that improve a norm on the Fisher information matrix. A
double-pendulum cart apparatus is used to numerically and experimentally
validate this technique. In simulation, the optimized trajectory increases the
minimum eigenvalue of the Fisher information matrix by three orders of
magnitude compared to the initial trajectory. Experimental results show that
this optimized trajectory translates to an order of magnitude improvement in
the parameter estimate error in practice.Comment: 12 page
Using numerical plant models and phenotypic correlation space to design achievable ideotypes
Numerical plant models can predict the outcome of plant traits modifications
resulting from genetic variations, on plant performance, by simulating
physiological processes and their interaction with the environment.
Optimization methods complement those models to design ideotypes, i.e. ideal
values of a set of plant traits resulting in optimal adaptation for given
combinations of environment and management, mainly through the maximization of
a performance criteria (e.g. yield, light interception). As use of simulation
models gains momentum in plant breeding, numerical experiments must be
carefully engineered to provide accurate and attainable results, rooting them
in biological reality. Here, we propose a multi-objective optimization
formulation that includes a metric of performance, returned by the numerical
model, and a metric of feasibility, accounting for correlations between traits
based on field observations. We applied this approach to two contrasting
models: a process-based crop model of sunflower and a functional-structural
plant model of apple trees. In both cases, the method successfully
characterized key plant traits and identified a continuum of optimal solutions,
ranging from the most feasible to the most efficient. The present study thus
provides successful proof of concept for this enhanced modeling approach, which
identified paths for desirable trait modification, including direction and
intensity.Comment: 25 pages, 5 figures, 2017, Plant, Cell and Environmen
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
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