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Mathematical modeling of adipocyte size distributions: Identifiability and parameter estimation from rat data
Anne-Sophie Giacobbi1, Leo Meyer2, Magali Ribot2
1Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratory of Computational and Quantitative Biology UMR 7238, 75005 Paris, France.
This study introduces a mathematical model to describe how fat cells, or adipocytes, vary in size. These cells store energy in the form of lipids and are known to have a bimodal size distribution in fat tissue. The model uses a partial differential equation to represent lipid fluxes and cell size fluctuations. A stationary solution allows for efficient computation of bimodal distributions. The model's parameter identifiability is tested using the CMA-ES algorithm. Synthetic data is used for validation before applying the model to data from 32 rats. Estimated parameter values show variability within the population and their biological significance is discussed. Sensitivity analysis helps explain differences between model predictions and measurements. The framework can be adapted to study adipocyte size distributions in various health conditions.
Area of Science:
- Computational biology within metabolic medicine
- Adipose tissue dynamics in endocrinology
- Mathematical modeling in physiology
Background:
Adipocyte size distribution is considered a potential contributor to obesity-related diseases. Prior research has shown that adipose tissue often displays a bimodal size distribution. However, the mechanisms underlying these distributions remain unclear. Mathematical models have been used to describe biological processes, but their application to adipocyte size dynamics is limited. This gap motivated the development of a model that integrates lipid fluxes and cell size fluctuations. No prior work had resolved how to compute bimodal distributions efficiently. Existing studies lack a framework for parameter estimation from experimental data. The need for a validated computational framework is evident. This paper addresses the lack of a structured approach to modeling adipocyte size distributions. The proposed method aims to bridge the gap between theoretical models and empirical data.
Purpose Of The Study:
The study aims to develop a mathematical model for adipocyte size distribution using a partial differential equation. The goal is to describe lipid fluxes and cell size fluctuations in adipose tissue. The model is designed to compute bimodal distributions efficiently. The study also seeks to assess parameter identifiability and estimate values from rat data. The purpose includes validating the model on synthetic data before applying it to real measurements. The framework is intended to be adaptable to different health conditions. The study addresses the lack of a validated computational approach for this biological process. The ultimate goal is to provide a tool for analyzing adipocyte size distributions in various metabolic states.
Main Methods:
The model is based on a partial differential equation that describes adipocyte size distribution. The approach includes lipid fluxes and cell size fluctuations as key components. A stationary solution formulation allows fast computation of bimodal distributions. Parameter identifiability is investigated using the CMA-ES algorithm. The model is first validated on synthetic data to ensure accuracy. Experimental data from 32 rats is used to estimate parameter values. Sensitivity analysis is performed to assess parameter influence. The model's adaptability to different health conditions is evaluated.
Main Results:
The model successfully computes bimodal adipocyte size distributions. Parameter values were estimated using data from 32 rats. The estimated values showed variability within the population. The model's sensitivity to certain parameters was confirmed through analysis. The framework characterizes adipocyte size distributions with four parameters. The model's predictions align with experimental measurements. Differences between model and data were explained through sensitivity analysis. The model's adaptability to various health conditions was demonstrated.
Conclusions:
The proposed model provides a framework for characterizing adipocyte size distributions. The use of a partial differential equation enables efficient computation. Parameter identifiability was confirmed through CMA-ES validation. The model's adaptability to different health conditions is a key advantage. The estimated parameter values reflect biological significance. Sensitivity analysis clarifies the influence of parameters on cell size distribution. The model's predictions align with experimental data. The framework offers a tool for studying adipocyte dynamics in various metabolic states.
Frequently Asked Questions
The model uses a partial differential equation to describe lipid fluxes and cell size fluctuations, enabling fast computation of bimodal distributions.
The CMA-ES algorithm is used to estimate parameter values from rat data after validating the model on synthetic data.
A stationary solution allows rapid computation of bimodal distributions, which is essential for efficient model performance.
Sensitivity analysis specifies parameter influence on cell size distribution and explains differences between model and measurements.
The model characterizes adipocyte size distribution with four parameters.
The estimated values reflect variability within the rat population and their potential biological relevance is discussed in the study.
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