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Abstract BackgroundThe biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems. ResultsIn this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models. ConclusionWe developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.
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This content will become publicly available on April 2, 2026
Investigating the Impact of Measurement Variance on Gene Circuit Model Parameterization
Summary Ordinary differential equation (ODE)-based modeling is a powerful tool in the design and characterization of synthetic gene circuits. Despite its popularity, identifying the model parameters based off experimental measurement is a nontrivial task. In this study, we leverage cell-free experimental measurement of two RNA-based regulators to investigate the impact and the incorporation of measurement variance in the pair-wise squared error objective function used for ODE-model parameterization. Our findings suggest that while unweighted objective function and weighting by the inverse variance can provide reasonably accurate parameter estimation, weighing the objective function with the inverse stabilized variance could further improve the parameterization, by also capturing the system variance with a mitigated prediction variance.
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- Award ID(s):
- 2223720
- PAR ID:
- 10639307
- Publisher / Repository:
- bioRxiv
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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