New model extracts stiffness and fluidity from AFM data in minutes, enabling fast, accurate mechanical characterization of living cells at single-cell resolution.
(Nanowerk Spotlight) Cells are not just biochemical machines. They are also physical structures, shaped and influenced by forces. When a cell divides, moves, or responds to stress, its mechanical properties shift. These changes, whether subtle or pronounced, can carry essential biological meaning. Cancer cells often become softer as they progress toward malignancy. Stem cells tend to stiffen as they specialize. Neurons alter their stiffness during growth and connection. The mechanical behavior of a cell is not a side detail, it is often a marker of identity, function, and health.
To study these properties at the nanoscale, researchers often rely on atomic force microscopy. This technique uses an ultra-sharp probe to press into the surface of a living cell while measuring how much it deforms. From this data, scientists can infer how stiff or fluid-like the cell is. These measurements reveal how cells resist or yield to mechanical stress, a property known as viscoelasticity.
How atomic force microscopy measures cell mechanics. An ultra-sharp probe presses into a living cell, recording how the cell surface bends and pushes back. These interactions are captured as curves showing the relationship between applied force and indentation depth. Traditionally, researchers fit these curves to mechanical models to extract properties such as stiffness and fluidity—a process that is slow and error-prone. The new machine learning approach learns directly from the shape of these curves, predicting mechanical properties in minutes instead of hours. (Image: Reprinted from DOI:10.1002/aisy.202400867, CC BY) (click on image to enlarge)
Yet the usefulness of this tool has been constrained by one persistent problem. Each measurement produces a curve that must be interpreted through a set of mechanical equations. Extracting meaningful information from these curves requires fitting them to mathematical models. This process is slow, difficult to automate, and sensitive to experimental noise. Even a single high-resolution scan can take several hours to process.
Technical improvements in probe design and scanning speed have helped reduce acquisition time, but the real bottleneck remains in the data processing. Some research teams have explored using machine learning to classify cells based on their physical features or to enhance contrast in the resulting images. These approaches improve efficiency but stop short of addressing the core issue. The fundamental step of converting raw measurement curves into physical properties still relies on traditional fitting methods, which are not scalable and are often unreliable.
That is the challenge taken up in a new paper published in Advanced Intelligent Systems (“High‐Throughput Nanorheology of Living Cells Powered by Supervised Machine Learning”). Jaime R. Tejedor and Ricardo Garcia describe a supervised machine learning approach that replaces model fitting with fast and accurate prediction. Their method processes force measurement data directly, extracting key mechanical parameters of living cells in a fraction of the time previously required. In doing so, it offers a practical path toward high-throughput mechanical characterization at the single-cell level, with implications for both fundamental biology and applied biomedical research.
Their method bypasses the conventional fitting of force–distance curves to mechanical models. Instead, it uses a supervised machine learning regressor trained entirely on synthetic data to extract two key parameters: the modulus, which quantifies stiffness, and the fluidity coefficient, which reflects how much the cell behaves like a viscous fluid rather than a solid. This replacement of model fitting with direct prediction reduces computational complexity and improves robustness. It also removes the need for manual parameter selection, which has traditionally introduced subjectivity and variability into analysis workflows.
The model learns to interpret the indentation history encoded in atomic force microscopy curves. This is essential because viscoelastic behavior is time-dependent: the mechanical response of a cell to force depends not only on how much it is deformed, but also on how quickly and for how long. The authors address this by treating the indentation as a continuous function rather than a series of discrete values. They use functional data analysis to represent indentation profiles and encode the full deformation process. This allows the model to incorporate both the shape and timing of indentation events.
The regressor architecture consists of two neural networks. The first predicts the fluidity coefficient from a force–distance curve and associated experimental parameters. Its output is passed to a second network, which predicts the modulus. This nested structure separates the inference of these two interrelated properties and reduces interference between them. Both networks use dimensionless quantities to ensure general applicability across different instruments and measurement conditions.
The model was trained on 100,000 synthetic force–distance curves generated from a contact mechanics model that incorporates single power-law rheology and bottom-effect corrections. These curves simulate a wide range of conditions, including extreme cases that cover the entire expected range of mechanical responses in mammalian cells.
Model performance was first assessed on a synthetic test set. Predictions for both the modulus and the fluidity coefficient closely matched the true values used to generate the test data. Relative error remained below 1% across the full range of input conditions. The same model was then used to analyze experimental datasets from two mammalian cell types with distinct biological and mechanical profiles: HeLa cells and NIH 3T3 fibroblasts.
HeLa cells, derived from cervical cancer tissue, are generally stiffer and less deformable. Fibroblasts, which contribute to the structural framework of connective tissue, are softer and more fluid-like.
Force–distance curves for both cell types were obtained independently from previous experiments and not tailored to the model. The regressor reproduced known relationships between modulus and indentation speed. For both HeLa and fibroblast cells, higher indentation speeds resulted in lower apparent stiffness and increased fluidity. These trends match expectations for viscoelastic materials. Predictions also agreed with traditional fitting results. For HeLa cells, the mean error in modulus prediction was 2.8%, and for the fluidity coefficient it was 1.2%. For fibroblasts, both parameters were predicted with errors under 4%. The same trained model was applied to both datasets without modification, indicating that it generalizes well across biologically distinct samples.
The model also captured the inverse relationship between stiffness and fluidity. As cells became softer, they exhibited more fluid-like behavior. This pattern has been observed in previous studies, though its biological basis remains uncertain. The regressor reproduced this trend across the full dataset, further validating its consistency with known mechanical behavior. Here, the authors caution that while the trend is robust, the underlying mechanism is still unresolved—highlighting an open question in cell mechanics.
To assess practical utility, the authors applied the regressor to a high-resolution force-volume dataset acquired from a live HeLa cell. The dataset consisted of 262,000 individual force–distance curves. The model processed the full set in 39 minutes and 50 seconds. For comparison, conventional model fitting required nearly nine hours to complete the same task. Most of that time was spent on modulus extraction.
By contrast, the machine learning approach reduced parameter inference time by a factor of fifty. In practical terms, this means what once took nearly a full workday can now be completed within the span of a lunch break. This transforms the scale at which AFM data can realistically be used.
The resulting mechanical maps preserved spatial resolution and contrast. They revealed nanoscale features such as variations in stiffness across the cytoplasm and nucleus, as well as fine structural details associated with the actin filament network. These features were consistent with those identified through standard model fitting. The ability to generate such maps in under an hour without loss of accuracy has immediate implications for studies requiring large datasets or time-sensitive analysis. This shift makes it feasible to study thousands of cells in a single project, opening the door to applications like rapid drug screening or clinical diagnostics that demand high throughput.
The regressor was designed to be broadly applicable. It requires no experimental data for training and relies entirely on theoretically generated curves. This removes dependence on specific instruments, cell types, or imaging conditions. All variables involved in training and prediction are nondimensionalized, which enables generalization without retraining. The architecture also avoids errors introduced by irregular indentation profiles, such as those caused by scanner nonlinearity or signal noise. Functional data analysis allows the model to process both ideal and non-ideal indentation signals with equal reliability.
The approach offers a way to scale AFM-based nanomechanical measurements without sacrificing precision. Mechanical properties can be extracted quickly and reproducibly across thousands of single cells. This could support studies in areas such as cancer diagnostics, stem cell differentiation, tissue engineering, and drug response, where mechanical markers are increasingly used to assess cellular state and function. By eliminating the computational bottleneck, the method also makes high-throughput screening feasible for applications that were previously limited by analysis time.
The work demonstrates that physically informed machine learning can replace slow, error-prone analytical methods without compromising accuracy. The architecture reflects a careful balance between theoretical modeling and algorithmic design. It preserves interpretability, handles noisy data, and performs reliably across diverse biological contexts.
While the approach was developed for AFM nanoindentation, the underlying principles could be extended to other force-based microscopy techniques that rely on curve interpretation. For researchers aiming to understand cell mechanics at scale, the regressor offers a practical and validated solution.
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Ricardo Garcia (Instituto de Ciencia de Materiales de Madrid)
, 0000-0002-4766-2744 corresponding author
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