In silico

In order to better understand the dynamical processes that are crucial for the proper functioning of living systems, we make use of models,  usually in the form of interpretable mathematical differential equations. Models not only allow us to describe the things that can be observed in a given experiment. If carefully formulated, they can predict behavior that is still unknown, allowing us to study the system without additional experiments. Broadly speaking, we use two main methods of obtaining models:


Two concepts of modeling interpretable models in the form of differential equations: Model- and data-driven.

The model-driven approach is focused on formulating a suitable model from expertise and scientific intuition based on interpretation of experimental data. After recognizing patterns in the measured data, an expert in his or her field suggests a model from their knowledge and intuition. This approach has been the backbone of natural sciences over the last centuries, however in times of Big Data recognizing patterns in data becomes increasingly difficult and modeling approaches can be prone to the scientist’s bias.


The data-driven approach, in contrast, focuses more on identifying patterns directly from data and letting an algorithm determine the correct structure of the model itself. This way of modeling, commonly also referred to as machine learning, is able to reduce the bias towards certain modeling principles and identify patterns in large data sets. In order to make these models interpretable either regression-based (white box) or methods mixing neural networks and regression algorithms are used (gray box). Nevertheless, data-driven approaches usually require a careful setup and very large, high-quality data sets.

In our group, we are using both approaches to uncover and develop models that are able to describe the underlying dynamics of biological systems. Furthermore, we not only want to model the system, but also understand its dynamical behavior by applying tools of mathematical analysis from the field of nonlinear and complex systems. Applying the powerful tool of bifurcation analysis not only allows us to validate existing experimental measurements, but also extrapolate and identify potentially unknown behavior. This knowledge allows us to design new experiments to validate our models. 

Using dynamical analysis of models, we can extrapolate from current experiments (blue) and predict new, unknown behavior (white) which can be test experimentally.

Selected publications


Prokop, B.; Frolov, N.; Gelens, L.

Enhancing model identification with SINDy via nullcline reconstruction Forthcoming

In: Chaos: An Interdisciplinary Journal of Nonlinear Science, Forthcoming.

Links | BibTeX


Prokop, B.; Gelens, L.

From biological data to oscillator models using SINDy

In: iScience, vol. 27, no. 4, pp. 109316, 2024, ISSN: 2589-0042.

Links | BibTeX


Puls*, O.; Ruiz-Reynés*, D.; Tavella, F.; Jin, M.; Kim, Y.; Gelens*, L.; Yang*, Q.

Mitotic waves in frog egg extracts: Transition from phase waves to trigger waves

2024, visited: 23.01.2024.

Links | BibTeX


Parra-Rivas*, P.; Ruiz-Reynés*, D.; Gelens, L.

Cell cycle oscillations driven by two interlinked bistable switches

In: Molecular Biology of the Cell, vol. 34, no. 6, pp. ar56, 2023.

Links | BibTeX


Kamenz, J.; Gelens, L.; Ferrell, J. E. Jr.

Bistable, Biphasic Regulation of PP2A-B55 Accounts for the Dynamics of Mitotic Substrate Phosphorylation

In: Current Biology, vol. 31, no. 4, pp. 794-808.e6, 2021, ISSN: 0960-9822.

Links | BibTeX


Rombouts, J.; Gelens, L.

Dynamic Bistable Switches Enhance Robustness and Accuracy of Cell Cycle Transitions

In: PLOS Computational Biology, vol. 17, no. 1, pp. e1008231, 2021, ISSN: 1553-7358.

Links | BibTeX


Nolet, F. E. *; Vandervelde, A. *; Vanderbeke, A. *; Pineros, L. *; Chang, J. B.; Gelens, L.

Nuclei determine the spatial origin of mitotic waves

In: eLife, vol. 9, pp. e52868, 2020, ISSN: 2050-084X.

Links | BibTeX


Rombouts, J.; Vandervelde, A.; Gelens, L.

Delay models for the early embryonic cell cycle oscillator

In: PLoS One, vol. 13, no. 3, pp. 1-21, 2018.

Links | BibTeX


Anderson*, G. A.; Gelens*, L.; Baker, J.; Ferrell, J. E. Jr.

Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of Xenopus laevis Development

In: Cell Reports, vol. 21, iss. 1, pp. 37–46, 2017, (featured on the cover).

Links | BibTeX