We typically work with ordinary differential equation (ODE) models of molecular processes derived from mass action kinetics as they provide efficient means to encode our knowledge of biological system, allow us to make sense of dynamically resolved perturbation data and have direct biophysical interpretation. ODE models are well-established means to describe molecular process, but have not caught up with the advent of structural methods such as cryogenic electron microscopy, single molecule fluorescence resonance energy transfer or AlphaFold. These structural methods provide an unprecedentedly detailed (dynamic) picture of molecular mechanisms that is not faithfully represented by ODE models of molecular processes, impeding interpretability and potentially diminishing predictive power. Similarly, omics methods such as mass-spectromotry and single-cell RNA sequencing offer a systems level perspective of the cell identity and its cell-to-cell variability, but this has not been connected to variability in the dynamics response of molecular processes.

Our vision is to build models that bridge the structural, molecular, and systems level, encoding what we know about molecular processes in mathematical models and inferring what we do not know using machine learning. We apply these models to interesting biological problems, including the prediction of sensitivity to anti-cancer drugs, anticipation of cell fate decisions and design of synthetic molecular switches.

Pathways and Systems Dynamics

Cell plasticity enables undifferentiated cells to follow developmental programs and cancer cells to adopt drug-resistant cell states [Gerosa *et. al* 2020, Fröhlich *et. al* 2022]. Methods such as RNA-velocity can reconstruct the vector field underlying such system-level dynamics, but does not identify the underlying molecular mechanisms. We want to build models that connect the vector field of system dynamics to mathematical models of molecular processes and thereby make differentiation trajectories programmable through targeted drugs and cytokine stimulation.

Software for Mathematical Modeling

Building and training mathematical models is an error prone and computationally demanding process. We are interested in building software that automates this process and developing more scalable methods. This includes the simulation engine AMICI, the calibration toolbox pyPESTO, the optimizer fides and the problem specification standard PEtab. We are continuously improving and extending these tools to push the envelope of biologocal problem complexity we can practically consider.

System State to Molecular Processes

How and which extracellular cues are processed in any individual cell depends on its molecular make-up, including the expression level of proteins. In the past, we have exploited this relationship by contextualize mathematical models of signal transduction using omics data [Fröhlich *et. al* 2018]. However, this approach relies on many assumptions and requires large models that are hard to build, interpret and train. We are interested in applying machine learning to contextualize mathematical models of molecular processes using omics and imaging data and apply them for the data-driven prediction of drug sensitivity and cytokine responsiveness.

Structure Dynamics to Molecular Processes

The composition and architecture of molecular processes is defined at the level of protein structure, which dictates which proteins interact with each other, how these interactions are coupled and how they are influenced by post-translational modifications. Structure-based models of molecular processes are formulated based on thermodynamic principles and incorporate information about the energetic landscape of protein conformations and interactions in model equations. We have used such models to describe rewiring and drug resistance in cancer cells [Gerosa *et. al* 2020, Fröhlich *et. al* 2022]. In the future, we want to apply machine learning to structure-based models to learn how coarse-grained, context-dependent regulatory rules emerge from fine-grained interactions. Moreover, we will apply these models to design synthetic molecular circuits and predict drug interactions.