Bubble model analysis on the cell formation of a green alga

2020 ◽  
Vol 13 (05) ◽  
pp. 2050032
Author(s):  
Yuandi Wang ◽  
Nanjun Yan ◽  
Zhigang Zhou ◽  
Kai Zeng
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Cell Walls ◽  
Morphological Evolution ◽  
Cell Formation ◽  
Biological Mechanisms ◽  
Double Bubble ◽  
Complex Process ◽  
Differential Equation Models ◽  
Experimental Data Analysis

Mathematical simulation for cell and division, a complex process resulting from a series of major morphological evolution and biological mechanisms, is shown by using variational principle. Groups of differential equation systems with boundary conditions for the cell walls satisfying come out from analysis on minimally total length. Double bubble model for cell geometric formation is found and a mechanism for tri-bubble model is also investigated here. An interesting fact is that every angle between any two tangent lines at the same intersections of cell edges for both double bubble and tri-bubble is equal to [Formula: see text]. In addition to the derivation of these differential equation models, these theories are also applied to the specific experimental data analysis, and it is found that the model is very consistent with the experimental results.

scholarly journals Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture

2021 ◽  
Author(s):  
Benjamin P Holder ◽  
Catherine A. A. Beauchemin
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Influenza Infection ◽  
Biologically Relevant ◽  
Differential Equation Models ◽  
Viral Yield ◽  
Infection Parameters ◽  
Delay Differential

Background For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. Results We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. Conclusions By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.

scholarly journals Fides: Reliable Trust-Region Optimization for Parameter Estimation of Ordinary Differential Equation Models

2021 ◽  
Author(s):  
Fabian Froehlich ◽  
Peter Karl Sorger
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Ordinary Differential Equation ◽  
Model Calibration ◽  
Trust Region ◽  
Mass Action ◽  
Approximation Schemes ◽  
Benchmark Problems ◽  
Mass Action Kinetics ◽  
Differential Equation Models

Motivation: Because they effectively represent mass action kinetics, ordinary differential equation models are widely used to describe biochemical processes. Optimization-based calibration of these models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a prerequisite for many subsequent analysis steps, including uncertainty analysis, model selection and biological interpretation. Although multiple hypothesis have been advanced to explain why optimization based calibration of biochemical models is challenging, there are few comprehensive studies that test these hypothesis and tools for performing such studies are also lacking. Results: We implemented an established trust-region method as a modular python framework (fides) to enable structured comparison of different approaches to ODE model calibration involving Hessian approximation schemes and trust-region subproblem solvers. We evaluate fides on a set of benchmark problems that include experimental data. We find a high variability in optimizer performance among different implementations of the same algorithm, with fides performing more reliably that other implementations investigated. Our investigation of possible sources of poor optimizer performance identify shortcomings in the widely used Gauss-Newton approximation. We address these shortcomings by proposing a novel hybrid Hessian approximation scheme that enhances optimizer performance.

scholarly journals Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture

2021 ◽  
Author(s):  
Benjamin P Holder ◽  
Catherine A. A. Beauchemin
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Influenza Infection ◽  
Biologically Relevant ◽  
Differential Equation Models ◽  
Viral Yield ◽  
Infection Parameters ◽  
Delay Differential

Background For a typical influenza infection in vivo, viral titers over time are characterized by 1–2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. Results We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. Conclusions By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.

scholarly journals Integrating experimental data to calibrate quantitative cancer models

2015 ◽  
Author(s):  
Heiko Enderling
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Cell Cycle ◽  
Cell Proliferation ◽  
Cancer Cells ◽  
Unknown Parameters ◽  
Agent Based ◽  
Cancer Models ◽  
Differential Equation Models ◽  
Model Dynamics

For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. Experimental data can be utilized to calibrate model dynamics rates or rate constants. Proper integration of experimental data, however, depends on the chosen theoretical framework. Using live imaging of cell proliferation as an example, we show how to derive cell cycle distributions in agent-based models and averaged proliferation rates in differential equation models. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.

Overview of Gene Regulatory Network Inference Based on Differential Equation Models

2020 ◽  
Vol 21 (11) ◽  
pp. 1054-1059
Author(s):  
Bin Yang ◽  
Yuehui Chen
Keyword(s):  
Differential Equation ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Network Inference ◽  
New Drugs ◽  
Gene Regulatory Network Inference ◽  
Ode Models ◽  
Differential Equation Models ◽  
Linear Ode ◽  
Gene Regulatory

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.

scholarly journals Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ahmed A. Mahmoud ◽  
Sarat C. Dass ◽  
Mohana S. Muthuvalu ◽  
Vijanth S. Asirvadam
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Delay Differential Equation ◽  
Information Matrix ◽  
Likelihood Inference ◽  
Multiple Delays ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Delay Differential ◽  
Initial Starting

This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.

THE “KVAZAR” PACKAGE FOR PATTERN RECOGNITION AND ITS APPLICATIONS

1993 ◽  
Vol 03 (04) ◽  
pp. 439-444 ◽  
Author(s):  
VLADIMIR S. KAZANTSEV
Keyword(s):  
Experimental Data ◽  
Pattern Recognition ◽  
Data Analysis ◽  
Linear Inequalities ◽  
Processing Data ◽  
Experimental Data Analysis ◽  
Ibm Pc

The package of applied programs named KVAZAR has been elaborated to be used for classification, diagnostic, predicative, experimental data analysis problems. The package may be used in medicine, biology, geology, economics, engineering and some other problems. The algorithmical base of the package is the method of pattern recognition, based on the linear inequalities and committee constructions. Other algorithms are used too. The package KVAZAR is intended to be used with IBM PC AT/XT. The range of processing data is bounded by 40,000 numbers.

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