Connecting theory and experiment in cell and tissue mechanics

Understanding the basic principles of living systems is an inherently multi-disciplinary endeavour. Modern cell biology uses experimental methods that build on advances from diverse fields such as physics, chemistry and genetics. For quantitative data analysis, approaches in bioinformatics, image analysis and machine learning have become indispensable (Driscoll and Zaritsky, 2021). To understand and conceptualize experimental observations, approaches from theoretical physics and mathematical biology are becoming increasingly important (Beta et al., 2023). Describing biological systems using the language of physics has a long history, arguably starting from early work such as D'Arcy Thompson's 1917 work on explaining cell and tissue morphology using the physics of foams and stating that “…the morphologist is, ipso facto, a student of physical science”, as well as Erwin Schrödinger's 1944 book What is Life? (Schrödinger, 1944; Thompson, 1917). These early works made the important point that despite their complexity and intricate behaviours, living systems are fundamentally constrained by the laws of physics and in many cases exploit physical phenomena to perform biological functions.

Building quantitative theoretical models of biological processes, and constraining these models with data, is a key avenue towards understanding the role of physical phenomena in biological systems. With modern imaging and sequencing methods, the complexity, dimensionality and accuracy of quantitative experimental data sets is rapidly increasing. To make sense of these ‘big data’, theoretical models are increasingly integrated in early stages of experimental projects. Indeed, physical modelling can often provide simplified benchmarks to interpret data as it comes in, help generate new hypotheses and design experiments, and provide principled frameworks to perform data-driven model inference. This means that rather than being separate endeavours, experiment and theory increasingly interact in real time. Integrating both approaches requires collaborations between groups with different backgrounds and perspectives, such as experimental cell biology and theoretical physics.

These collaborations can be difficult to establish and pursue, which was reflected by the numerous challenges raised in a discussion panel at the recent February 2023 Workshop on Collective Cell Migration organized by The Company of Biologists (see https://www.biologists.com/workshops/february-2023/). Some of the key conceptual issues discussed were finding a common language to communicate between experimentalists and theorists and across fields, determining which type of modelling approach is appropriate for the specific biological question at hand, and learning to step out of one's own area of expertise in a collaboration. A central challenge was meeting both the desire of the experimentalist for details and the preference of the theorist for overly simplistic models. Furthermore, a commonly encountered issue was deciding which experiments should be performed to test a given physical model, within realistic limitations of time and cost. We therefore need to achieve mutual understanding of the available modelling and experimental approaches and their feasibility, and of how to best pair specific modelling strategies with a given experimental approach.

Here, we provide a perspective on how to navigate these challenges from the viewpoint of both a theorist and an experimentalist. We give an overview of some of the core biophysical modelling concepts, experimental methods that connect to these models and how to combine them. First, we will discuss different conceptual classes of modelling approaches, including bottom-up, data-driven and normative models. Then, using the example of cell migration, we discuss specific physical modelling approaches for cell and tissue biology datasets, and what type of predictions we can expect from these models. Finally, we will discuss available quantitative experimental techniques across biological scales that enable direct connections to physical models in molecular-, cell- and tissue-level contexts.

The aim of developing physical models of biological systems is to turn our intuition for how a biological system might work into a mathematical formulation that makes testable, quantitative predictions, and provides new heuristics and explanations. Physical models of biological systems connect our knowledge of the physics of the underlying processes to experimental biological observations. The choice of modelling approach depends on the scientific question, the biological system and the type of experimental data that the model should be compared to. In this section, we will first summarize three conceptual classes of modelling philosophies that have been applied across scales of biological systems, before discussing specific types of physical models in the next section.

First, the most common philosophy of modelling is to build bottom-up hypothesis-driven physical models (Fig. 1A). Here, one hypothesizes what the underlying biophysical processes are that might determine an observed behaviour, typically by selecting the most likely, or simplest, candidate mechanism before moving to more-complex scenarios. Bottom-up models can help cell biologists by clearly stating and mathematically formalizing the key assumptions of the model, allowing exploration of the implications of these assumptions in an unbiased way. One such bottom-up model is the molecular clutch model, which describes how actin polymerization, retrograde flow and adhesion dynamics interact to facilitate cell locomotion (Chan and Odde, 2008). This model makes clear assumptions on how these functional modules interplay to give rise to cell motion: the balance of polymerization and retrograde flow push forward the cell membrane, and the retrograde flow clutches to the substrate through the cell adhesions. A key question is then what range of migration behaviours can be explained by this simple picture. Remarkably, variants of this model were able to capture stick-slip motion in one-dimensional migration (Ron et al., 2020; Sens, 2020) and durotaxis in stiffness gradients (Sunyer et al., 2016). Bottom-up approaches therefore allow for connecting underlying mechanisms to large-scale behaviours and can play a key role in generating hypotheses for new experiments.

A second modelling approach is to train data-driven top-down models using experimental data (Fig. 1B). In this case, we assume a general class of models of the plausible mechanisms involved in the system. This is followed by model selection and parameter inference directly from the experimental data. The aim is to arrive at a model which can make predictions for new experiments that were not used to train the model. Such inverse approaches are more common in fields that generate standardized datasets, such as chromosome structure (Imakaev et al., 2015) or single-cell RNA sequencing data (Qiu et al., 2022). Recently, high-throughput imaging at the cell and tissue scale has started to give rise to large data sets on cell motility and morphology that can be used for model inference. An example of a tissue-scale top-down model is tension inference, which uses the local angles of cell–cell contacts to infer the mechanical state of the tissue. The inferred mechanical states can then be matched to physical models of tissues, such as vertex or foam models (Roffay et al., 2021). Such models are based on a mathematical formulation of the elastic energy of the tissue, which is assumed to be minimized for tissues at mechanical equilibrium (Alt et al., 2017; Fletcher et al., 2014). Measurement and segmentation of cell shape features can then constrain the parameters of these models, allowing predictions of tissue dynamics and morphological transitions. Furthermore, data-driven approaches have been used to infer models for the dynamics of migrating cells (Brückner et al., 2019; Selmeczi et al., 2008), the way different proteins contribute to traction force generation (Schmitt et al., 2023 preprint) and the interactions between multiple cells (Brückner et al., 2020; LaChance et al., 2022). To deal with the increasing complexity of experimental data sets, physics-constrained machine learning models are a promising avenue. In this case, parameters are inferred using neural network approaches that take into account physical principles of the system (Cichos et al., 2020; Colen et al., 2021). In summary, data-driven models allow an unbiased approach towards modelling complex systems, and can provide constraints for more detailed, mechanistic bottom-up approaches.

A third, less common, class of models are normative theories (Fig. 1C). Here, the idea is to postulate the biological function that a system performs, and to formalize this as a mathematical optimization problem, which can then make predictions for experimental observations. Normative theories are more prevalent in neuroscience, but have also been applied to cell- and tissue-level processes, such as chemotaxis (Mattingly et al., 2021) and developmental signalling networks (Pezzotta and Briscoe, 2023; Sokolowski et al., 2023). For example, a normative theory approach for optimization of positional information in a morphogen gradient has been used to predict gene expression patterns in the early fly embryo (Sokolowski et al., 2023). Beyond predicting optimal states of biological systems, normative theories have been combined with data-driven approaches to quantify how close a biological data set is to a putative optimal state (Młynarski et al., 2021).

Importantly, for any given biological process, any of these three theoretical approaches could be applied, and might yield insights on different aspects of the same problem. For example, with migrating cells, we could build a bottom-up model predicting trajectory dynamics, we could infer a model directly from such dynamics, or we could postulate the biological function of the process – such as efficient chemotaxis – and then predict how this could be done optimally. There are important considerations when choosing which type of approach to pursue. Bottom-up approaches require significant previous knowledge of what mechanisms might be relevant, data-driven top-down approaches necessitate large amounts of input data, and normative approaches require a generic formulation of the function of the process. However, for all these approaches, a key starting point is a physical model for the process, which can then be constrained and parametrized. In the next section, we will therefore discuss the specific types of physical models that could be integrated into one of these three modelling approaches.

Models cannot capture all the complexity of a biological system and therefore rely on simplifying assumptions. An important first step is to ensure that the model is simple enough such that its assumptions and parameters can be tested and constrained by the available experimental data. Thus, communication early in a collaboration about what type of experimental observations and datasets will be generated is crucial. This is clear in top-down approaches, where experimental data is directly used to constrain a model. However, it is equally applicable in bottom-up modelling, where it is important to discuss the implications and limitations of the key modelling assumptions, and to potentially revise these over the course of the project.

A classic example that demonstrates how simplifying assumptions aid in building models is the flocking behaviour of a cell assembly, the behaviour in which individual cells align their direction of motion to migrate collectively. To model this at the tissue scale, one can consider the polarity dynamics of each cell as a simple ‘energy’ potential that breaks symmetry to generate active motion, rather than simulating the diffusion and interactions of polarity molecules within each cell (Marchetti et al., 2013). However, when considering a single cell, a model of diffusible polarity cues should be able to reproduce the effective potential description in the tissue-scale model, thus connecting different levels of complexity. In physics, this is known as ‘coarse graining’, a key concept that describes how ‘zooming out’ in terms of complexity allows construction of models of effective variables that describe the system dynamics at each level of complexity.

To illustrate the general principles of how model and data complexity correspond, we highlight some of the key model types for cell and tissue dynamics, and the type of data that could be used to constrain them. Note that the optimal level of detail for both models and experimental measurements depends on the biological question asked. For instance, for the question of how single migrating cells navigate on or through substrates over long periods of time, a key experiment is to record their cell trajectory (Fig. 2A). To model such cell trajectories, the most coarse-grained (meaning least detailed) approach is to use active particles with polarity dynamics (Fig. 2B) (Romanczuk et al., 2012). Based on this, one could ask how cell polarities couple to the environment (Brückner et al., 2022). To connect large-scale behaviours to subcellular and molecular processes, the more detailed molecular clutch model (Chan and Odde, 2008) links adhesion dynamics, actin flows and traction forces to the diffusion of polarity molecules (Maiuri et al., 2015; Ron et al., 2020; Sens, 2020). At yet higher level of detail, phase field models capture the full 2D shape dynamics of migrating cells, and have been used to capture both single-cell and cell cluster migration (Camley et al., 2014; Kockelkoren et al., 2003; Marth and Voigt, 2014; Shao et al., 2012; Ziebert et al., 2011).

At the tissue level, interacting active particle models are used to model the collective dynamics of groups of cells (Alert and Trepat, 2020). Alternatively, collective flows can be modelled by active hydrodynamics, describing the cell collective as an effective fluid which can generate active stresses, with polar or nematic order parameters (Fig. 2A,B) (Jülicher et al., 2018). Importantly, such effective descriptions can still make predictions for how collective cell behaviours change in response to molecular perturbations. An example of this is the self-organized mechanical patterning of avian skin explants, which was captured using an active hydrodynamic model of the actin cortex (Palmquist et al., 2022). This model showed that mechanical patterning is a consequence of a positive feedback loop of active force generation and active flows, which was tested using experimental perturbations of the cell contractility and friction with the substrate.

To predict more detailed features such as cell and tissue morphology, vertex and active foam models are common choices (Fig. 2B). For instance, to understand how active force generation determines crypt budding in the intestinal epithelium, coupling a mechanical vertex model with segmentation of tissue shape revealed that out of a class of multiple possible mechanical mechanisms, a mechanism relying on spontaneous curvatures differences along the crypt–villus axis controls budding morphogenesis (Yang et al., 2021). For some biological questions, the cellular signalling state, such as the activity of extracellular signal-regulated kinase (ERK) proteins or of mechanosensors such as Yap1 (Low et al., 2014; Panciera et al., 2017), becomes relevant. In these scenarios, the model can be extended to mechano-chemical models that connect mechanical and chemical signalling degrees of freedom (Fig. 2A,B) (Bailles et al., 2022). For instance, mechano-chemical active matter and vertex models have been used to explain the emergence of ERK waves in expanding cell monolayers (Boocock et al., 2023, 2020).

Most of the studies discussed above take a bottom-up approach to modelling, or combine elements of bottom-up and data-driven modelling. Across these approaches, matching model complexity to the type of experimental data and biological question allows us to use experimental data to constrain models step-by-step and to make predictions that are directly testable in new experiments. Here, a key challenge is to balance model and data complexity such that there is no model overfitting, which occurs when a model excessively conforms to a specific data set, impairing its ability to generalize to new data (Lever et al., 2016). A recurring challenge in model complexity is integrating minimal physical models, which use a small number of parameters, and ‘big data’ approaches that often rely on machine learning. While minimal models often have better interpretability, big data approaches can have better predictive power and allow integration of large multimodal data sets. A promising avenue is to combine these opposite approaches by linking bottom-up approaches with data-driven top-down approaches.

Importantly, having a model that makes wrong predictions can be very useful – if the model is developed in a principled way, understanding whether and why a certain set of assumptions does not capture the experiment can help rule out hypotheses and generate new ones. Furthermore, models can make important contributions to understanding experimental results even if their predictions are qualitative rather than quantitative. For example, predicting the qualitative change of a behaviour in a mutant or perturbation experiment can potentially be a strong test of the predictive power of a model. Thus, a benchmark of a successful model is not only the level of molecular detail it describes, but also its power in making testable predictions and being generalizable across biological systems.

In the previous sections, we discussed different approaches of developing biophysical models, and how these models provide new insights into biological phenomena. Next, we will discuss strategies for using experimental readouts to constrain bottom-up models or as input into data-driven top-down approaches. These readouts can range from ‘omics’ data, protein localization and shape features of filaments, cells and tissues, to mechanical force measurements. Finding the most appropriate technique or measurement type to provide input data is one of the first steps for developing the model. Importantly, the chosen technique should reliably measure the heterogeneities of the system at a level well above the measurement noise of the method.

Newly developed technologies such as ‘omics’ approaches and high-throughput multiplexed imaging have moved the field towards automated and quantitative data analysis, yielding less biased, more reproducible and larger datasets. Although the emergence of these ‘big data’ approaches holds great promise, it also necessitates improvements in data handling and storage standards, such as standardized file formats, efficient data life cycles and high-performance analysis pipelines. A major effort in the bioimaging community has been the standardization of file formats and image analysis pipelines (Box 1) (Moore et al., 2023). Such frameworks will be beneficial for model input owing to higher resolution sampling of the heterogeneities of the system, increased statistical power and ability to measure multiscale data.

To gain high-resolution qualitative and quantitative measurements from raw imaging data, three main steps are required – segmentation, tracking and feature extraction (Fig. 3A). As a first step, the object of interest needs to be identified based on the pixel information of the image. Although in some cases, simple thresholding based on intensity might yield reliable object segmentation, in other cases, more sophisticated approaches, such as the use of deep neural networks, is required (Fig. 3A, Box 1). For instance, during early zebrafish development, actomyosin flow within the yolk syncytial layer has been shown to contribute to epithelial spreading (Behrndt et al., 2012). A model of thin-film active fluid accurately predicted the experimentally measured tension distributions and actomyosin flow velocity patterns assessed via particle image velocimetry (Box 1), which helped identify a previously unknown mechanism of flow-friction-mediated epithelial spreading. In addition, actin filaments can also be tracked by generating kymographs and detecting filaments using deep learning (Jakobs et al., 2019). For instance, by inputting measurements of centrifugal F-actin flows (Fig. 3A) and turnover into an active gel model, it has been shown that differential myosin contractility drives E-Cadherin redistribution in zebrafish ectoderm progenitor cells, which is critical for cell–cell contact formation and maturation (Arslan et al., 2023 preprint).

Beyond particle flows, tension measurements on the subcellular scale provide important readouts for model input. Several techniques to measure mechanical forces are available (Fig. 3B, Table 1) and depending on the experimental question and the model, different readouts for tension are required. For example, during early Caenorhabditis elegans zygote polarization, anisotropies in cortical tension were identified by performing laser ablations of the actomyosin cortex in different orientations and within different spatial regions (Mayer et al., 2010). By modelling the actomyosin cortex as thin-film active fluid, together with measuring cortical tension and actomyosin flow rates, the authors have demonstrated that polarization of the C. elegans zygote is driven by an actomyosin contractility gradient and a high viscosity of the cortex. These results contrasted with previously proposed mechanisms of polarization, such as gradients of cortical tension, and showed that alternative mechanisms can drive polarizations in vivo. Studies such as this exemplify that connecting experimental observations with physical modelling can provide new conceptual strategies in biological processes.

In summary, data on filament flows and subcellular force distributions have provided useful and important parameters for model input and led to new insights into biological processes such as morphogenesis, cell contact formation and early polarization events after fertilization.

When reading out cell-scale properties in 3D, additional challenges arise including high-quality cell segmentation and reliable tracking (Box 1). Combining cell tracks with cell segmentations provides multidimensional data over time, for instance allowing tracking of long-term morphogenetic events such as organoid growth (Fig. 3A) (De Medeiros et al., 2022). Such a live-cell tracking approach has been combined with stochastic population dynamics modelling to understand the lineage dynamics of dividing intestinal stem cells, revealing that proliferation and differentiation dynamics are tightly controlled during tissue growth (Huelsz-Prince et al., 2022).

Measuring mechanical forces at the cellular scale can also provide critical information about biological processes such as morphogenesis. Cells have been described to exhibit liquid-like properties (Steinberg, 1962; Townes and Holtfreter, 1955), such as surface tension, which is the tendency to minimize the exposed surface. Techniques such as micropipette aspiration can be used to measure surface tension. For example, modelling the 8- to 16-cell mouse blastocyst via a mesh-based mechanical cell surface model successfully predicted the localization of cells either at inner or outer positions based on the difference in surface tensions as measured via micropipette aspiration (Maître et al., 2016). By testing the model predictions, the authors identified that tension heterogeneities between cells are the basis of sorting cells to inner positions (inner cell mass) or outer positions (trophectoderm) in the mouse blastocyst.

Importantly, cell surface tension is the combination of cortical tension and membrane tension. In order to understand the specific contribution of membrane tension, optical tweezers (Fig. 3B) or fluorescent probes, such as FLIPPER probes (Soleimanpour et al., 2016), can be used. Differential cell membrane tensions have been linked to cell fate changes in mouse embryonic stem cells (De Belly et al., 2020) and lineage segregation in early mouse embryos (Yanagida et al., 2022). For instance, a 3D computational cell sorting model has been generated to predict the sorting outcomes during lineage segregation of epiblast and primitive endoderm. Although cell surface tensions could not explain segregation, a vertex model combined with dynamic cell membrane properties (e.g. cell surface fluctuations and membrane tension) accurately predicted sorting of cell progenitors (Yanagida et al., 2022). These examples show that biophysical modelling approaches are powerful tools that can help identify minimal requirements for a biological process and underscore the necessity of highly precise and dynamical measurements for model development.

Taken together, cell-scale measurements, such as cell tracking, fluorescent marker intensity and shape measurements, or surface and membrane tension readouts, are critical to constrain models and provide a better understanding of cell dynamics in contexts such as intestinal tissue homeostasis or lineage segregation during early development.

Increasing the length scale to tissue level allows assessment of the properties of multicellular systems and their interactions with the external environment such as the lumen or the extracellular matrix.

There is increasing evidence that luminal pressures and hydraulic oscillations contribute to biological processes such as cell fate patterning in mice (Chan et al., 2019) and in hydra (Ferenc et al., 2021). To understand how hydraulics controls the size and shape of the early mammalian embryo, a physical model of the spherical trophectoderm cell layer was developed that describes the trophectoderm as a spherical shell subject to osmotic and hydrostatic pressures (Chan et al., 2019). By measuring luminal pressure (via micropressure probes; Fig. 3B) as well as cavity radius and shell thickness, the model was constrained to experimental data and successfully predicted the hydraulic oscillations of the mouse blastocyst, revealing, for instance, how the oscillatory dynamics depend on the leakiness of cell–cell junctions.

Another important tissue–environment interaction is between tissue and the extracellular matrix. This interaction is critical during migration, when cells actively propel themselves forward by pulling on the underlying substrate. Interestingly, expanding cell monolayers exhibit mechanical waves, characterized by strain rates, that travel from the leading edge through the entire monolayer and back again (Serra-Picamal et al., 2012). Although stresses transmitted within the monolayer are maximal at the centre of the monolayer, the traction forces exerted onto the substrate are highest at the leading edge, suggesting force transmission through the tissue. Using a one-dimensional mechanical model dependent on elastic cell–cell and frictional cell–substrate forces measured via traction force microscopy (Fig. 3B), the authors identified that wave propagation through the tissue is well explained by sequential reinforcing and fluidizing of the cytoskeleton within cells (Serra-Picamal et al., 2012).

In multicellular systems, cells communicate with their neighbours to generate collective processes, such as tissue folding and spatially patterned cell differentiation (Zinner et al., 2020). To understand the mechanistic details of such emergent biological processes, it is crucial to perform measurements across scales – from molecular, to cellular and to tissue scale.

For instance, by combining cell-level and tissue-level measurements with theoretical modelling, it has been demonstrated that spatiotemporal changes in tissue viscosity ensure proper tissue morphogenesis during early zebrafish development (Petridou et al., 2021, 2019). Interestingly, abrupt changes in tissue viscosity are explained by a rigidity phase transition, meaning that minimal changes in cell connectivity will trigger large changes in tissue rigidity (Petridou et al., 2021). Combining percolation theory, which describes how the rigidity of a network depends on its connectivity, with readouts of cellular connectivity and viscosity (using micropipette aspiration, Fig. 3B) provided a powerful approach to identify a phase transition during early zebrafish morphogenesis. Beyond rigidity percolation, concepts from physics including jamming and unjamming transitions have been useful in describing tissue state transitions (Atia et al., 2021). For instance, during body axis elongation in zebrafish, cells undergo a jamming transition, where mesodermal progenitor cells exhibit fluid-like behaviour (measured via oil microdroplets, Fig. 3B) and become solid-like in the presomitic mesoderm (Mongera et al., 2018). Taken together, cell- and tissue-level measurements combined with physical concepts provide a powerful approach that can help rationalize non-intuitive biological phenomena such as abrupt changes in material properties.

Another example on how multiscale measurements inform modelling is self-organized intestinal organoid morphogenesis. To investigate the morphogenesis of mouse intestinal organoids, a spatially patterned mechanical 3D vertex model was used (Yang et al., 2021). The authors combined different types of tension measurement techniques, such as pipette aspiration and laser cuts (Fig. 3B), with epithelial thickness and lumen measurements and identified that differential spontaneous curvatures drive morphogenesis (Yang et al., 2021). This example demonstrates that combining multiscale measurements for model input, such as apical tension (cell level) with epithelial thickness and lumen volume (tissue level) allows for better understanding of self-organizing systems with emergent properties.

Finally, the advances in the fields of ‘omics’ and ‘big data’ offer great opportunities for unbiased and systems-level dissection of biological processes. For downstream analysis of high-content imaging data, approaches from the field of ‘omics’ have been adapted and proved very powerful. One example is the identification of symmetry breaking in intestinal organoid formation through generating single-organoid trajectories with changes in signalling and cell fate markers based on a combination of high-content, multiplexed and light-sheet imaging (Serra et al., 2019). Another study in ascidians (sea squirts), combining high-throughput single-cell genomics with light-sheet imaging and modelling, has shown that contact area-dependent cell communication can explain cell fate determination, providing an alternative explanation for fate acquisition to classical morphogen gradients (Guignard et al., 2020). Such interdisciplinary approaches open new avenues to draw trajectories of morphogenetic events while monitoring multiple different signalling markers in real time.

In the future, it will be very tempting to start thinking of integrating data from ‘omics’ approaches (single-cell RNA and ATAC sequencing) with high-content imaging of immunostained markers and live-cell or tissue imaging, in order to generate dynamical trajectories of biological processes that span temporal and spatial scales. Taken together, multiscale analyses will provide high quantitative and qualitative data for model input to gain new insights into emergent behaviours during self-organization observed in development and regeneration.

Understanding biological systems has become an increasingly interdisciplinary endeavour, with experimentalists and theorists joining forces to uncover the basic principles governing molecular, cell and tissue behaviour. Living systems are fundamentally constrained by the laws of physics and in many cases exploit physical phenomena to perform biological functions. Thus, advances in our understanding of biological systems increasingly rely on models based on principles from theoretical physics. In turn, the development of physical models of biological systems has also led to theoretical advances, especially in the physics of nonequilibrium phenomena, active matter and soft materials. These are still relatively new fields in theoretical physics, with many key open questions that were only identified thanks to the push to apply physics to living systems.

Developing experiments and theory in close collaboration is a very promising approach in quantitative cell biology, yet comes with key challenges, including finding a common language to communicate across fields and determining the appropriate type of modelling approach for the specific biological question and system. To help overcome these obstacles, we have provided a perspective on the different classes of modelling approaches, discussed examples of specific physical models for various types of biological datasets, and explored the types of experimental techniques available to test model predictions in the context of subcellular, cellular and tissue mechanics.

Beyond these conceptual and scientific challenges, there are also practical and administrative difficulties, which were put forward at The Company of Biologists workshop on Collective Cell Migration. These include finding a suitable collaborator, introducing modelling too late in the project, differing priorities and interests, as well as authorship and time commitment issues. To facilitate finding a suitable collaborator, a key step is to identify the type of model required to address the biological question of the project. Here, we emphasized the importance of matching the complexity and level of coarse graining of a model to the available data. Furthermore, seeking theoretical collaborators from the onset of the project could help to better conceptualize the problem and provide predictions early on, allowing theoreticians to update the model as new data come in. To ensure priorities and interests align, regular communication and setting of expectations upfront are possible solutions. Eventually, the goal should be to build long-term relationships and mutual respect that can last beyond a single project or paper. To provide a formal framework and fund interdisciplinary projects, researchers could aim to apply for collaborative grants which fund both parties. Furthermore, cross-disciplinary training at both graduate and post-graduate levels is key to ensure that graduate students and postdocs have the necessary background to effectively communicate across the disciplines. This will allow for fruitful collaborations in which both the details of the modelling approach but also details about the biological system can be appreciated and better incorporated. Finally, pairing up graduate students and postdocs with similar timelines can furthermore avoid time-commitment issues.

Although cross-disciplinary collaborations are challenging, they hold great promise – modelling biological systems can provide principled frameworks to test hypotheses or infer hidden features in complex data sets. These frameworks can then help to identify conserved patterns and strategies across different biological phenomena with the goal of reaching generalizable theories and models. Modelling can also provide a basis to integrate distinct types of data across scales, such as gene expression and morphological data sets. Thus, strong connections between biological data and theory will be critical to ensuring the new era of ‘big data’ leads to new conceptual insights into biological processes, rather than simply ever more accurate quantifications, with the ultimate goal being to develop predictive rather than descriptive pictures of biological processes. These advances might play a crucial role in future developments that rely on quantitative predictions, such as synthetic biology and bottom-up bioengineering, as well as medical and pharmacological applications.

We thank Prisca Liberali and Edouard Hannezo for many inspiring discussions; Mehmet Can Uçar, Nicoletta I Petridou and Qiutan Yang for a critical reading of the manuscript, and Claudia Flandoli for the artwork in Figs 2 and 3. We would also like to thank The Company of Biologists for the opportunity to attend the 2023 workshop on Collective Cell Migration, and all workshop participants for discussions.