Berkeley Madonna

Berkeley Madonna is a general purpose differential equations solver designed for modeling and analysis of dynamical systems. It targets a broad range of users including academic researchers, educators, and professionals across fields such as life sciences, pharmacology, space science, and conservation biology.

Version 10 is the current release, offering 64-bit architecture that is 2–5 times faster than previous versions and capable of handling large, memory-intensive models. It is compatible with macOS Catalina and later (including Apple M1/M2 chips) as well as current and planned Windows operating systems. Version 10 is a free upgrade for all version 9 users.

Core Modeling Approach

• Uses a graphical interface that allows users to construct models using symbols rather than writing equations manually.
• Icons selected from a toolbar automatically generate the underlying equations.
• Clicking Run immediately solves the equations and plots the results.
• Supports ordinary differential equations (ODEs), difference equations, and discrete simulations.
• Offers multiple integration schemes for solving equations.

Visualization and Analysis Tools

• Results are automatically graphed upon execution.
• Sliders allow users to interactively explore the effect of changing parameter values in real time.
• Parameter plot tool provides graphical insight into parameter relationships.
• Fast Fourier Transform (FFT) button offers additional analytical visualization.
• Curve fitting interface enables extraction of parameter estimates from experimental data.
• Batch runs allow plotting of results across a sweep of parameter values.

Documented Use Cases

• Cellular pH regulation research at UC Berkeley, studying how cellular compartments maintain distinct pH values.
• Battery performance prediction for the Mars Express spacecraft at the European Space Agency.
• Modeling gene expression during HIV infection at UCSF and the Gladstone Institute's Center for Cell Circuitry.
• Population modeling for green sea turtle conservation at Conservation International.
• Construction of physiologically based pharmacokinetic (PBPK) models, as described in a published version 10 tutorial paper.

Licensing Tiers

• Education license for educational use.
• Academic license for academic research.
• Professional license for commercial or professional applications.

Berkeley Madonna is developed with cross-platform compatibility in mind, supporting both macOS and Windows environments. A peer-reviewed tutorial paper describing version 10 features and a PBPK modeling workflow is available for free download from the Berkeley Madonna website.