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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Published on: April 27, 2021

Identifying a static nonlinear structure in a biological system using noisy, sparse data.

Joshua R Porter1, John S Burg, Peter J Espenshade

  • 1Department of Electrical & Computer Engineering, Johns Hopkins University, 105 Barton Hall, 3400 N. Charles Street, Baltimore, MD 21218, USA. josh.porter@jhu.edu

Journal of Theoretical Biology
|February 8, 2012
PubMed
Summary

This study introduces a new method to model unknown parts of biological systems using noisy data. The technique improves noise reduction and accurately models static nonlinearities, aiding in system identification.

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Area of Science:

  • Systems biology
  • Biophysics
  • Computational biology

Background:

  • Investigating complex biological systems often requires modeling unknown components when direct experimentation is not feasible.
  • Challenges arise from noisy and sparsely sampled measurements, common in cellular-level biological studies.

Purpose of the Study:

  • To develop a procedure for identifying static nonlinearities within biological systems using noisy, sparse input-output measurements.
  • To enhance noise reduction techniques for more accurate biological system modeling.

Main Methods:

  • Introduced weighted-sum predictability for improved noise reduction compared to traditional loading controls.
  • Normalized measurements to their weighted sum and interpolated data to obtain continuous signals.
  • Directly solved for the input-output characteristics of the static nonlinearity.

Main Results:

  • Successfully applied the procedure to model ergosterol sensing by Sre1 and Scp1 proteins in fission yeast.
  • Simulations using the identified model produced results consistent with experimental observations.
  • Demonstrated improved noise reduction through weighted-sum normalization.

Conclusions:

  • The presented structure identification procedure offers a novel tool for characterizing and modeling biological systems.
  • The method is effective even with noisy and sparse biological measurements.
  • Weighted-sum predictability provides a robust approach for handling noise in biological data analysis.