Other modelling approaches

Deterministic models: All the modelling frameworks introduced in this tutorial are deterministic, meaning that they predict a system’s behaviour without accounting for randomness or uncertainty in the modelled process. In this tutorial we solely focused on deterministic models.

Stochastic models: In contrast to the deterministic models, this model incorporate randomness, recognising that biological processes are often influenced by unpredictable or unknown factors. Examples of such factors include the probability of two molecules colliding or the probability of getting infected when meeting an infected person. Examples of stochastic models are Markov Chains or stochastic differential equations. A brief introduction to stochastic models in systems biology can be found in an overview article Stochastic approaches in systems biology (Ullah M, Wolkenhauer O, 2010).

Spatial models: In this tutorial we also focused on homogeneous environments, where we assume that there are no spatial gradients in the amounts of the model elements in the unit of environment that is represented by the model. Spatial models can account for such gradients.

Constraint-based models: These models describe what a biological system can do, rather than how it changes over time. Instead of tracking concentrations or rates as we did with ODEs or difference equations, these models define rules that the system must follow — for example, how much of each molecule goes in and out of a cell, or limits on how fast a reaction can happen. A common example for this is modelling metabolism: we can use constraint-based models to predict which combinations of reactions can work together to let a cell grow, given the nutrients available or how to tune metabolism to increase the yield of a specific metabolite. These models are especially useful when we know the mechanism but we don’t know the exact details of how fast each model component is produced and consumed. For a more detailed discussion, check out these articles: Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis (Volkova S et al, 2020) and Constraint-based models predict metabolic and associated cellular functions (Bordbar A, Monk J, and King Z et al, 2014).

There are also modelling approaches that do not necessarily aim to describe mechanistically what is happening in the system, such as classical statistical models (for example linear regressions) or machine learning. Machine learning models can be a powerful approach when mechanisms are not clear or of interest, and machine learning algorithms can also be used to fit mechanistic models (Noordijk B et al, 2024).