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08:31
Kinematic Analysis of Cell Division and Expansion: Quantifying the Cellular Basis of Growth and Sampling Developmental Zones in Zea mays Leaves
Published on: December 2, 2016
Estimating the division rate for the growth-fragmentation equation.
1INRIA Paris-Rocquencourt, EPI BANG, Domaine de Voluceau, 78153, Le Chesnay Cedex, France. marie.doumic@inria.fr
Journal of Mathematical Biology
|June 7, 2012
Summary
This study develops methods to determine fragmentation rates in growth-fragmentation equations using asymptotic solutions. This is crucial for understanding complex biological processes when direct observation is challenging.
Area of Science:
- Mathematical Biology
- Theoretical Ecology
- Biophysics
Background:
- Growth-fragmentation equations model dynamic processes like cell division and protein polymerization.
- Direct observation of these systems is often difficult, necessitating indirect methods for parameter recovery.
- Previous work focused on specific cases, like the cell division equation.
Purpose of the Study:
- To develop theoretical and numerical methods for recovering fragmentation rates in general growth-fragmentation equations.
- To utilize time-asymptotic solutions for parameter estimation.
- To handle general fragmentation kernels and growth rates.
Main Methods:
- Analysis of time-asymptotic behavior of growth-fragmentation equations.
- Development of inverse problem methodologies.
- Application of theoretical and numerical techniques.
Main Results:
- Established theoretical results for recovering fragmentation rates from asymptotic solutions.
- Presented numerical methods applicable to general growth-fragmentation models.
- Demonstrated the feasibility of parameter estimation under broad conditions.
Conclusions:
- The study provides a general framework for inferring fragmentation rates from indirect observations.
- The developed methods offer valuable tools for analyzing complex biological dynamics.
- Further research is needed to address remaining challenges in parameter recovery.
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