103,095 research outputs found
The impact of temporal sampling resolution on parameter inference for biological transport models
Imaging data has become widely available to study biological systems at
various scales, for example the motile behaviour of bacteria or the transport
of mRNA, and it has the potential to transform our understanding of key
transport mechanisms. Often these imaging studies require us to compare
biological species or mutants, and to do this we need to quantitatively
characterise their behaviour. Mathematical models offer a quantitative
description of a system that enables us to perform this comparison, but to
relate these mechanistic mathematical models to imaging data, we need to
estimate the parameters of the models. In this work, we study the impact of
collecting data at different temporal resolutions on parameter inference for
biological transport models by performing exact inference for simple velocity
jump process models in a Bayesian framework. This issue is prominent in a host
of studies because the majority of imaging technologies place constraints on
the frequency with which images can be collected, and the discrete nature of
observations can introduce errors into parameter estimates. In this work, we
avoid such errors by formulating the velocity jump process model within a
hidden states framework. This allows us to obtain estimates of the
reorientation rate and noise amplitude for noisy observations of a simple
velocity jump process. We demonstrate the sensitivity of these estimates to
temporal variations in the sampling resolution and extent of measurement noise.
We use our methodology to provide experimental guidelines for researchers
aiming to characterise motile behaviour that can be described by a velocity
jump process. In particular, we consider how experimental constraints resulting
in a trade-off between temporal sampling resolution and observation noise may
affect parameter estimates.Comment: Published in PLOS Computational Biolog
Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
In many chemical and biological applications, systems of differential
equations containing unknown parameters are used to explain empirical
observations and experimental data. The DEs are typically nonlinear and
difficult to analyze, requiring numerical methods to approximate the solutions.
Compounding this difficulty are the unknown parameters in the DE system, which
must be given specific numerical values in order for simulations to be run.
Estrogen receptor protein dimerization is used as an example to demonstrate
model construction, reduction, simulation, and parameter estimation.
Mathematical, computational, and statistical methods are applied to empirical
data to deduce kinetic parameter estimates and guide decisions regarding future
experiments and modeling. The process demonstrated serves as a pedagogical
example of quantitative methods being used to extract parameter values from
biochemical data models.Comment: 23 pages, 9 figures, to be published in SIAM Revie
Stock assessment of protogynous fish: evaluating measures of spawning biomass used to estimate biological reference points
In stock assessments, recruitment is typically modeled as a function of females only. For protogynous stocks, however, disproportionate fishing on males increases the possibility of reduced fertilization rates. To incorporate the importance of males in protogynous stocks, assessment models have been used to predict recruitment not just from female spawning biomass (Sf), but also from that of males (Sm) or both sexes (Sb). We conducted a simulation study to evaluate the ability of these three measures to estimate biological reference points used in fishery management. Of the three, Sf provides best estimates if the potential for decreased fertilization is weak, whereas Sm is best only if the potential is very strong. In general, Sb estimates the true reference points most closely, which indicates that if the potential for decreased fertilization is moderate or unknown, Sb should be used in assessments of protogynous stocks. Moreover, for a broad range of scenarios, relative errors from Sf and Sb occur in opposite directions, indicating that estimates from these measures could be used to bound uncertainty
Quantitative model for inferring dynamic regulation of the tumour suppressor gene p53
Background: The availability of various "omics" datasets creates a prospect of performing the study of genome-wide genetic regulatory networks. However, one of the major challenges of using mathematical models to infer genetic regulation from microarray datasets is the lack of information for protein concentrations and activities. Most of the previous researches were based on an assumption that the mRNA levels of a gene are consistent with its protein activities, though it is not always the case. Therefore, a more sophisticated modelling framework together with the corresponding inference methods is needed to accurately estimate genetic regulation from "omics" datasets.
Results: This work developed a novel approach, which is based on a nonlinear mathematical model, to infer genetic regulation from microarray gene expression data. By using the p53 network as a test system, we used the nonlinear model to estimate the activities of transcription factor (TF) p53 from the expression levels of its target genes, and to identify the activation/inhibition status of p53 to its target genes. The predicted top 317 putative p53 target genes were supported by DNA sequence analysis. A comparison between our prediction and the other published predictions of p53 targets suggests that most of putative p53 targets may share a common depleted or enriched sequence signal on their upstream non-coding region.
Conclusions: The proposed quantitative model can not only be used to infer the regulatory relationship between TF and its down-stream genes, but also be applied to estimate the protein activities of TF from the expression levels of its target genes
Parameter Estimation and Uncertainty Quantication for an Epidemic Model
We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )—an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications of correlation for parameter identifiability are discussed. Uncertainty estimates and sensitivity analysis are used to investigate how the frequency at which data is sampled affects the estimation process and how the accuracy and uncertainty of estimates improves as data is collected over the course of an outbreak. We assess the informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneficial to the estimation process. This technique can be used to design data sampling schemes in more general contexts
Estimation of kinetic rates of MAP kinase activation from experimental data
Mathematical model is an important tool in systems biology to study the dynamics of biological systems inside the cell. One of the significant challenges in systems biology is the lack of kinetic rates that should be measured in experiments or estimated from experimental data. This work addresses this issue by using a genetic algorithm to estimate reaction rates related to the phosphorylation and dephosphorylation of MAP kinase (ERK) in the mitogen-activated protein (MAP) kinase pathway from biological measurements. In addition, we discuss the robustness of the mathematical model with regards to the variation of kinetic rates together with external noise due to environmental fluctuations. This has been proposed as an additional criterion to choose the estimate from the candidate parameter sets that are obtained from different implementations of the genetic algorithm
Information Content in Data Sets for a Nucleated-Polymerization Model
We illustrate the use of tools (asymptotic theories of standard error
quantification using appropriate statistical models, bootstrapping, model
comparison techniques) in addition to sensitivity that may be employed to
determine the information content in data sets. We do this in the context of
recent models [23] for nucleated polymerization in proteins, about which very
little is known regarding the underlying mechanisms; thus the methodology we
develop here may be of great help to experimentalists
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