Quantitative Assessment of Biological Dynamics with Aggregate Data.

Area of Science:

• Computational Biology
• Statistical Modeling
• Microbial Ecology

Background:

• Parameter estimation in ordinary differential equation (ODE) models is crucial for understanding biological systems.
• Traditional methods often require detailed time-series data, which may not always be available.
• Aggregate data, like sample means and standard deviations, are common but challenging to utilize for parameter estimation.

Purpose of the Study:

• To develop and apply a Bayesian learning framework for parameter estimation in ODE models using indirect aggregate data.
• To introduce novel computational schemes, including modified Hamiltonian Monte Carlo and an elliptical slice sampler, tailored for summary statistics and biological models.
• To benchmark the framework's performance against synthetic and real microbial growth data.

Main Methods:

• Development of a comprehensive Bayesian framework for parameter estimation.
• Implementation of specialized Markov chain Monte Carlo (MCMC) computational schemes.
• Adaptation of Hamiltonian Monte Carlo for summary statistics and development of an elliptical slice sampler for biological models.
• Benchmarking with synthetic microbial growth data and validation with real Prochlorococcus growth curve data.

Main Results:

• The developed learning framework effectively utilizes aggregate data for parameter estimation in ODE models.
• The specialized MCMC methods demonstrated robustness in handling constraints from summary statistics.
• Performance evaluation showed that the Bayesian framework outperforms traditional least-squares fitting methods.
• Successful application to both synthetic and real microbial growth data, including Prochlorococcus species.

Conclusions:

• The proposed Bayesian learning framework provides a robust approach for parameter estimation when only aggregate data are available.
• The novel computational methods enhance the ability to perform data assimilation in ODE models.
• This framework offers a valuable tool for analyzing experimental and historical biological data, improving model-based predictions.