Deep learning based decoding of single local field potential events.

How is information processed in the cerebral cortex? In most cases, recorded brain activity is averaged over many (stimulus) repetitions, which erases the fine-structure of the neural signal. However, the brain is obviously a single-trial processor. Thus, we here demonstrate that an unsupervised machine learning approach can be used to extract meaningful information from electro-physiological recordings on a single-trial basis. We use an auto-encoder network to reduce the dimensions of single local field potential (LFP) events to create interpretable clusters of different neural activity patterns. Strikingly, certain LFP shapes correspond to latency differences in different recording channels. Hence, LFP shapes can be used to determine the direction of information flux in the cerebral cortex. Furthermore, after clustering, we decoded the cluster centroids to reverse-engineer the underlying prototypical LFP event shapes. To evaluate our approach, we applied it to both extra-cellular neural recordings in rodents, and intra-cranial EEG recordings in humans. Finally, we find that single channel LFP event shapes during spontaneous activity sample from the realm of possible stimulus evoked event shapes. A finding which so far has only been demonstrated for multi-channel population coding.

Predictive coding and stochastic resonance as fundamental principles of auditory phantom perception.

Mechanistic insight is achieved only when experiments are employed to test formal or computational models. Furthermore, in analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying healthy auditory perception. With a special focus on tinnitus-as the prime example of auditory phantom perception-we review recent work at the intersection of artificial intelligence, psychology and neuroscience. In particular, we discuss why everyone with tinnitus suffers from (at least hidden) hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that intrinsic neural noise is generated and amplified along the auditory pathway as a compensatory mechanism to restore normal hearing based on adaptive stochastic resonance. The neural noise increase can then be misinterpreted as auditory input and perceived as tinnitus. This mechanism can be formalized in the Bayesian brain framework, where the percept (posterior) assimilates a prior prediction (brain's expectations) and likelihood (bottom-up neural signal). A higher mean and lower variance (i.e. enhanced precision) of the likelihood shifts the posterior, evincing a misinterpretation of sensory evidence, which may be further confounded by plastic changes in the brain that underwrite prior predictions. Hence, two fundamental processing principles provide the most explanatory power for the emergence of auditory phantom perceptions: predictive coding as a top-down and adaptive stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles also play a crucial role in healthy auditory perception. Finally, in the context of neuroscience-inspired artificial intelligence, both processing principles may serve to improve contemporary machine learning techniques.

The desmin mutation R349P increases contractility and fragility of stem cell-generated muscle micro-tissues.

AIMS: Desminopathies comprise hereditary myopathies and cardiomyopathies caused by mutations in the intermediate filament protein desmin that lead to severe and often lethal degeneration of striated muscle tissue. Animal and single cell studies hinted that this degeneration process is associated with massive ultrastructural defects correlating with increased susceptibility of the muscle to acute mechanical stress. The underlying mechanism of mechanical susceptibility, and how muscle degeneration develops over time, however, has remained elusive. METHODS: Here, we investigated the effect of a desmin mutation on the formation, differentiation, and contractile function of in vitro-engineered three-dimensional micro-tissues grown from muscle stem cells (satellite cells) isolated from heterozygous R349P desmin knock-in mice. RESULTS: Micro-tissues grown from desmin-mutated cells exhibited spontaneous unsynchronised contractions, higher contractile forces in response to electrical stimulation, and faster force recovery compared with tissues grown from wild-type cells. Within 1 week of culture, the majority of R349P desmin-mutated tissues disintegrated, whereas wild-type tissues remained intact over at least three weeks. Moreover, under tetanic stimulation lasting less than 5 s, desmin-mutated tissues partially or completely ruptured, whereas wild-type tissues did not display signs of damage. CONCLUSIONS: Our results demonstrate that the progressive degeneration of desmin-mutated micro-tissues is closely linked to extracellular matrix fibre breakage associated with increased contractile forces and unevenly distributed tensile stress. This suggests that the age-related degeneration of skeletal and cardiac muscle in patients suffering from desminopathies may be similarly exacerbated by mechanical damage from high-intensity muscle contractions. We conclude that micro-tissues may provide a valuable tool for studying the organization of myocytes and the pathogenic mechanisms of myopathies.

Durotropic Growth of Pollen Tubes.

To reach the female gametophyte, growing pollen tubes must penetrate different tissues within the pistil, the female reproductive organ of a flower. Past research has identified various chemotropic cues that guide pollen tubes through the transmitting tract of the pistil, which represents the longest segment of its growth path. In addition, physical mechanisms also play a role in pollen tube guidance; however, these processes remain poorly understood. Here we show that pollen tubes from plants with solid transmitting tracts actively respond to the stiffness of the environment. We found that pollen tubes from Nicotiana tabacum and other plant species with a solid or semisolid transmitting tract increase their growth rate in response to an increasing matrix stiffness. By contrast, pollen tubes from Lilium longiflorum and other plant species with a hollow transmitting tract decrease their growth rate with increasing matrix stiffness, even though the forces needed to maintain a constant growth rate remain far below the maximum penetration force these pollen tubes are able to generate. Moreover, when confronted with a transition from a softer to a stiffer matrix, pollen tubes from N. tabacum display a greater ability to penetrate into a stiffer matrix compared with pollen tubes from L. longiflorum, even though the maximum force generated by pollen tubes from N. tabacum (11 µN) is smaller than the maximum force generated by pollen tubes from L. longiflorum (36 µN). These findings demonstrate a mechano-sensitive growth behavior, termed here durotropic growth, that is only expressed in pollen tubes from plants with a solid or semisolid transmitting tract and thus may contribute to an effective pollen tube guidance within the pistil.

Integration of Leaky-Integrate-and-Fire Neurons in Standard Machine Learning Architectures to Generate Hybrid Networks: A Surrogate Gradient Approach.

Up to now, modern machine learning (ML) has been based on approximating big data sets with high-dimensional functions, taking advantage of huge computational resources. We show that biologically inspired neuron models such as the leaky-integrate-and-fire (LIF) neuron provide novel and efficient ways of information processing. They can be integrated in machine learning models and are a potential target to improve ML performance. Thus, we have derived simple update rules for LIF units to numerically integrate the differential equations. We apply a surrogate gradient approach to train the LIF units via backpropagation. We demonstrate that tuning the leak term of the LIF neurons can be used to run the neurons in different operating modes, such as simple signal integrators or coincidence detectors. Furthermore, we show that the constant surrogate gradient, in combination with tuning the leak term of the LIF units, can be used to achieve the learning dynamics of more complex surrogate gradients. To prove the validity of our method, we applied it to established image data sets (the Oxford 102 flower data set, MNIST), implemented various network architectures, used several input data encodings and demonstrated that the method is suitable to achieve state-of-the-art classification performance. We provide our method as well as further surrogate gradient methods to train spiking neural networks via backpropagation as an open-source KERAS package to make it available to the neuroscience and machine learning community. To increase the interpretability of the underlying effects and thus make a small step toward opening the black box of machine learning, we provide interactive illustrations, with the possibility of systematically monitoring the effects of parameter changes on the learning characteristics.

High-Force Magnetic Tweezers with Hysteresis-Free Force Feedback.

Magnetic tweezers based on a solenoid with an iron alloy core are widely used to apply large forces (∼100 nN) onto micron-sized (∼5 µm) superparamagnetic particles for mechanical manipulation or microrheological measurements at the cellular and molecular level. The precision of magnetic tweezers, however, is limited by the magnetic hysteresis of the core material, especially for time-varying force protocols. Here, we eliminate magnetic hysteresis by a feedback control of the magnetic induction, which we measure with a Hall sensor mounted to the distal end of the solenoid core. We find that the generated force depends on the induction according to a power-law relationship and on the bead-tip distance according to a stretched exponential relationship. Combined, they describe with only three parameters the induction-force-distance relationship, enabling accurate force calibration and force feedback. We apply our method to measure the force dependence of the viscoelastic and plastic properties of fibroblasts using a protocol with stepwise increasing and decreasing forces. We group the measured cells in a soft and a stiff cohort and find that softer cells show an increasing stiffness but decreasing plasticity with higher forces, indicating a pronounced stress stiffening of the cytoskeleton. By contrast, stiffer cells show no stress stiffening but an increasing plasticity with higher forces. These findings indicate profound differences between soft and stiff cells regarding their protection mechanisms against external mechanical stress. In summary, our method increases the precision, simplifies the handling, and extends the applicability of magnetic tweezers.

Breast Cancer Cells Adapt Contractile Forces to Overcome Steric Hindrance.

Cell migration through the extracellular matrix is governed by the interplay between cell-generated propulsion forces, adhesion forces, and resisting forces arising from the steric hindrance of the matrix. Steric hindrance in turn depends on matrix porosity, matrix deformability, cell size, and cell deformability. In this study, we investigate how cells respond to changes in steric hindrance that arise from altered cell mechanical properties. Specifically, we measure traction forces, cell morphology, and invasiveness of MDA-MB 231 breast cancer cells in three-dimensional collagen gels. To modulate cell mechanical properties, we either decrease nuclear deformability by twofold overexpression of the nuclear protein lamin A or we introduce into the cells stiff polystyrene beads with a diameter larger than the average matrix pore size. Despite this increase of steric hindrance, we find that cell invasion is only marginally inhibited, as measured by the fraction of motile cells and the mean invasion depth. To compensate for increased steric hindrance, cells employ two alternative strategies. Cells with higher nuclear stiffness increase their force polarity, whereas cells with large beads increase their net contractility. Under both conditions, the collagen matrix surrounding the cells stiffens dramatically and carries increased strain energy, suggesting that increased force polarity and increased net contractility are functionally equivalent strategies for overcoming an increased steric hindrance.

Photoinducible DRONPA-s: a new tool for investigating cell-cell connectivity.

The development of multicellular plants relies on the ability of their cells to exchange solutes, proteins and signalling compounds through plasmodesmata, symplasmic pores in the plant cell wall. The aperture of plasmodesmata is regulated in response to developmental cues or external factors such as pathogen attack. This regulation enables tight control of symplasmic cell-to-cell transport. Here we report on an elegant non-invasive method to quantify the passive movement of protein between selected cells even in deeper tissue layers. The system is based on the fluorescent protein DRONPA-s, which can be switched on and off repeatedly by illumination with different light qualities. Using transgenic 35S::DRONPA-s Arabidopsis thaliana and a confocal microscope it was possible to activate DRONPA-s fluorescence in selected cells of the root meristem. This enabled us to compare movement of DRONPA-s from the activated cells into the respective neighbouring cells. Our analyses showed that pericycle cells display the highest efflux capacity with a good lateral connectivity. In contrast, root cap cells showed the lowest efflux of DRONPA-s. Plasmodesmata of quiescent centre cells mediated a stronger efflux into columella cells than into stele initials. To simplify measurements of fluorescence intensity in a complex tissue we developed software that allows simultaneous analyses of fluorescence intensities of several neighbouring cells. Our DRONPA-s system generates reproducible data and is a valuable tool for studying symplasmic connectivity.

Structural organisation and dynamics in king penguin colonies.

During breeding, king penguins do not build nests, however they show strong territorial behaviour and keep a pecking distance to neighbouring penguins. Penguin positions in breeding colonies are highly stable over weeks and appear regularly spaced, but thus far no quantitative analysis of the structural order inside a colony has been performed. In this study, we use the radial distribution function to analyse the spatial coordinates of penguin positions. Coordinates are obtained from aerial images of two colonies that were observed for several years. Our data demonstrate that the structural order in king penguin colonies resembles a 2-dimensional liquid of particles with a Lennard-Jones-type interaction potential. We verify this using a molecular dynamics simulation with thermally driven particles, whereby temperature corresponds to penguin movements, the energy well depth e of the attractive potential corresponds to the strength of the colony-forming behaviour, and the repulsive zone corresponds to the pecking radius. We can recapitulate the liquid disorder of the colony, as measured by the radial distribution function, when the particles have a temperature of several (1.4-10) ε/k B and a normally distributed repulsive radius. To account for the observation that penguin positions are stable over the entire breeding period, we hypothesize that the liquid disorder is quenched during the colony formation process. Quenching requires the temperature to fall considerably below 1 ε/k B, which corresponds to a glass transition, or the repulsion radius to exceed the distance between neighbouring penguins, which corresponds to a jamming transition. Video recordings of a breeding colony together with simulations suggest that quenching is achieved by a behavioural motility arrest akin to a glass transition. We suggest that a liquid disordered colony structure provides an ideal compromise between high density and high flexibility to respond to external disturbances that require a repositioning of penguins.

Mechanical plasticity of cells.

Under mechanical loading, most living cells show a viscoelastic deformation that follows a power law in time. After removal of the mechanical load, the cell shape recovers only incompletely to its original undeformed configuration. Here, we show that incomplete shape recovery is due to an additive plastic deformation that displays the same power-law dynamics as the fully reversible viscoelastic deformation response. Moreover, the plastic deformation is a constant fraction of the total cell deformation and originates from bond ruptures within the cytoskeleton. A simple extension of the prevailing viscoelastic power-law response theory with a plastic element correctly predicts the cell behaviour under cyclic loading. Our findings show that plastic energy dissipation during cell deformation is tightly linked to elastic cytoskeletal stresses, which suggests the existence of an adaptive mechanism that protects the cell against mechanical damage.

Measuring mechanical properties in cells: three easy methods for biologists.

The mechanism by which cells sense stresses and transmit them throughout the cytoplasm and the cytoskeleton (CSK) and by which these mechanical signals are converted into biochemical signaling responses is not clear. Specifically, there is little direct experimental evidence on how intracellular CSK structural elements in living cells deform and transmit stresses in response to external mechanical forces. Existing theories have invoked various biophysical and biochemical mechanisms to explain how cells spread, deform, divide, move, and change shape in response to mechanical inputs, but rigorous tests in cells are lacking. The lack of data and understanding is preventing the identification of mechanisms and sites of mechano-regulation in cells. Here, we introduce and describe three unique and easy methods for biologists to determine mechanical properties and signaling events in cells.

Coincidence detection and integration behavior in spiking neural networks.

Recently, the interest in spiking neural networks (SNNs) remarkably increased, as up to now some key advances of biological neural networks are still out of reach. Thus, the energy efficiency and the ability to dynamically react and adapt to input stimuli as observed in biological neurons is still difficult to achieve. One neuron model commonly used in SNNs is the leaky-integrate-and-fire (LIF) neuron. LIF neurons already show interesting dynamics and can be run in two operation modes: coincidence detectors for low and integrators for high membrane decay times, respectively. However, the emergence of these modes in SNNs and the consequence on network performance and information processing ability is still elusive. In this study, we examine the effect of different decay times in SNNs trained with a surrogate-gradient-based approach. We propose two measures that allow to determine the operation mode of LIF neurons: the number of contributing input spikes and the effective integration interval. We show that coincidence detection is characterized by a low number of input spikes as well as short integration intervals, whereas integration behavior is related to many input spikes over long integration intervals. We find the two measures to linearly correlate via a correlation factor that depends on the decay time. Thus, the correlation factor as function of the decay time shows a powerlaw behavior, which could be an intrinsic property of LIF networks. We argue that our work could be a starting point to further explore the operation modes in SNNs to boost efficiency and biological plausibility. Supplementary Information: The online version of this article (10.1007/s11571-023-10038-0) contains supplementary material, which is available to authorized users.

Noncanonical WNT5A controls the activation of latent TGF-ß to drive fibroblast activation and tissue fibrosis.

Transforming growth factor ß (TGF-ß) signaling is a core pathway of fibrosis, but the molecular regulation of the activation of latent TGF-ß remains incompletely understood. Here, we demonstrate a crucial role of WNT5A/JNK/ROCK signaling that rapidly coordinates the activation of latent TGF-ß in fibrotic diseases. WNT5A was identified as a predominant noncanonical WNT ligand in fibrotic diseases such as systemic sclerosis, sclerodermatous chronic graft-versus-host disease, and idiopathic pulmonary fibrosis, stimulating fibroblast-to-myofibroblast transition and tissue fibrosis by activation of latent TGF-ß. The activation of latent TGF-ß requires rapid JNK- and ROCK-dependent cytoskeletal rearrangements and integrin αV (ITGAV). Conditional ablation of WNT5A or its downstream targets prevented activation of latent TGF-ß, rebalanced TGF-ß signaling, and ameliorated experimental fibrosis. We thus uncovered what we believe to be a novel mechanism for the aberrant activation of latent TGF-ß in fibrotic diseases and provided evidence for targeting WNT5A/JNK/ROCK signaling in fibrotic diseases as a new therapeutic approach.

Fiber alignment in 3D collagen networks as a biophysical marker for cell contractility.

Cells cultured in 3D fibrous biopolymer matrices exert traction forces on their environment that induce deformations and remodeling of the fiber network. By measuring these deformations, the traction forces can be reconstructed if the mechanical properties of the matrix and the force-free matrix configuration are known. These requirements limit the applicability of traction force reconstruction in practice. In this study, we test whether force-induced matrix remodeling can instead be used as a proxy for cellular traction forces. We measure the traction forces of hepatic stellate cells and different glioblastoma cell lines and quantify matrix remodeling by measuring the fiber orientation and fiber density around these cells. In agreement with simulated fiber networks, we demonstrate that changes in local fiber orientation and density are directly related to cell forces. By resolving Rho-kinase (ROCK) inhibitor-induced changes of traction forces, fiber alignment, and fiber density in hepatic stellate cells, we show that the method is suitable for drug screening assays. We conclude that differences in local fiber orientation and density, which are easily measurable, can be used as a qualitative proxy for changes in traction forces. The method is available as an open-source Python package with a graphical user interface.

Intrinsic Noise Improves Speech Recognition in a Computational Model of the Auditory Pathway.

Noise is generally considered to harm information processing performance. However, in the context of stochastic resonance, noise has been shown to improve signal detection of weak sub- threshold signals, and it has been proposed that the brain might actively exploit this phenomenon. Especially within the auditory system, recent studies suggest that intrinsic noise plays a key role in signal processing and might even correspond to increased spontaneous neuronal firing rates observed in early processing stages of the auditory brain stem and cortex after hearing loss. Here we present a computational model of the auditory pathway based on a deep neural network, trained on speech recognition. We simulate different levels of hearing loss and investigate the effect of intrinsic noise. Remarkably, speech recognition after hearing loss actually improves with additional intrinsic noise. This surprising result indicates that intrinsic noise might not only play a crucial role in human auditory processing, but might even be beneficial for contemporary machine learning approaches.

Calcium supplementation of bioinks reduces shear stress-induced cell damage during bioprinting.

During bioprinting, cells are suspended in a viscous bioink and extruded under pressure through small diameter printing needles. The combination of high pressure and small needle diameter exposes cells to considerable shear stress, which can lead to cell damage and death. Approaches to monitor and control shear stress-induced cell damage are currently not well established. To visualize the effects of printing-induced shear stress on plasma membrane integrity, we add FM 1-43 to the bioink, a styryl dye that becomes fluorescent when bound to lipid membranes, such as the cellular plasma membrane. Upon plasma membrane disruption, the dye enters the cell and also stains intracellular membranes. Extrusion of alginate-suspended NIH/3T3 cells through a 200µm printing needle led to an increased FM 1-43 incorporation at high pressure, demonstrating that typical shear stresses during bioprinting can transiently damage the plasma membrane. Cell imaging in a microfluidic channel confirmed that FM 1-43 incorporation is caused by cell strain. Notably, high printing pressure also impaired cell survival in bioprinting experiments. Using cell types of different stiffnesses, we find that shear stress-induced cell strain, FM 1-43 incorporation and cell death were reduced in stiffer compared to softer cell types and demonstrate that cell damage and death correlate with shear stress-induced cell deformation. Importantly, supplementation of the suspension medium with physiological concentrations of CaCl2greatly reduced shear stress-induced cell damage and death but not cell deformation. As the sudden influx of calcium ions is known to induce rapid cellular vesicle exocytosis and subsequent actin polymerization in the cell cortex, we hypothesize that calcium supplementation facilitates the rapid resealing of plasma membrane damage sites. We recommend that bioinks should be routinely supplemented with physiological concentrations of calcium ions to reduce shear stress-induced cell damage and death during extrusion bioprinting.

Viscoelastic properties of suspended cells measured with shear flow deformation cytometry.

Numerous cell functions are accompanied by phenotypic changes in viscoelastic properties, and measuring them can help elucidate higher level cellular functions in health and disease. We present a high-throughput, simple and low-cost microfluidic method for quantitatively measuring the elastic (storage) and viscous (loss) modulus of individual cells. Cells are suspended in a high-viscosity fluid and are pumped with high pressure through a 5.8 cm long and 200 µm wide microfluidic channel. The fluid shear stress induces large, ear ellipsoidal cell deformations. In addition, the flow profile in the channel causes the cells to rotate in a tank-treading manner. From the cell deformation and tank treading frequency, we extract the frequency-dependent viscoelastic cell properties based on a theoretical framework developed by R. Roscoe [1] that describes the deformation of a viscoelastic sphere in a viscous fluid under steady laminar flow. We confirm the accuracy of the method using atomic force microscopy-calibrated polyacrylamide beads and cells. Our measurements demonstrate that suspended cells exhibit power-law, soft glassy rheological behavior that is cell-cycle-dependent and mediated by the physical interplay between the actin filament and intermediate filament networks.

Cells in the human body are viscoelastic: they have some of the properties of an elastic solid, like rubber, as well as properties of a viscous fluid, like oil. To carry out mechanical tasks ­ such as, migrating through tissues to heal a wound or to fight inflammation ­ cells need the right balance of viscosity and elasticity. Measuring these two properties can therefore help researchers to understand important cell tasks and how they are impacted by disease. However, quantifying these viscous and elastic properties is tricky, as both depend on the time-scale they are measured: when pressed slowly, cells appear soft and liquid, but they turn hard and thick when rapidly pressed. Here, Gerum et al. have developed a new system for measuring the viscosity and elasticity of individual cells that is fast, simple, and inexpensive. In this new method, cells are suspended in a specialized solution with a consistency similar to machine oil which is then pushed with high pressure through channels less than half a millimeter wide. The resulting flow of fluid shears the cells, causing them to elongate and rotate, which is captured using a fast camera that takes 500 images per second. Gerum et al. then used artificial intelligence to extract each cell's shape and rotation speed from these images, and calculated their viscosity and elasticity based on existing theories of how viscoelastic objects behave in fluids. Gerum et al. also investigated how the elasticity and viscosity of cells changed with higher rotation frequencies, which corresponds to shorter time-scales. This revealed that while higher frequencies made the cells appear more viscous and elastic, the ratio between these two properties remained the same. This means that researchers can compare results obtained from different experimental techniques, even if the measurements were carried out at completely different frequencies or time-scales. The method developed by Gerum et al. provides a fast an inexpensive way for analyzing the viscosity and elasticity of cells. It could also be a useful tool for screening the effects of drugs, or as a diagnostic tool to detect diseases that affect the mechanical properties of cells.

Quantifying the separability of data classes in neural networks.

We introduce the Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given layer of an artificial neural network. It turns out that, at the end of the training period, the GDV in each given layer L attains a highly reproducible value, irrespective of the initialization of the network's connection weights. In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal reduction of class separability, marked by a characteristic 'energy barrier' in the initial part of the GDV(L) curve. Even more surprisingly, for a given data set, the GDV(L) is running through a fixed 'master curve', independently from the total number of network layers. Finally, due to its invariance with respect to dimensionality, the GDV may serve as a useful tool to compare the internal representational dynamics of artificial neural networks with different architectures for neural architecture search or network compression; or even with brain activity in order to decide between different candidate models of brain function.

Sparsity through evolutionary pruning prevents neuronal networks from overfitting.

Modern Machine learning techniques take advantage of the exponentially rising calculation power in new generation processor units. Thus, the number of parameters which are trained to solve complex tasks was highly increased over the last decades. However, still the networks fail - in contrast to our brain - to develop general intelligence in the sense of being able to solve several complex tasks with only one network architecture. This could be the case because the brain is not a randomly initialized neural network, which has to be trained from scratch by simply investing a lot of calculation power, but has from birth some fixed hierarchical structure. To make progress in decoding the structural basis of biological neural networks we here chose a bottom-up approach, where we evolutionarily trained small neural networks in performing a maze task. This simple maze task requires dynamic decision making with delayed rewards. We were able to show that during the evolutionary optimization random severance of connections leads to better generalization performance of the networks compared to fully connected networks. We conclude that sparsity is a central property of neural networks and should be considered for modern Machine learning approaches.

Collective forces of tumor spheroids in three-dimensional biopolymer networks.

We describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that our method is accurate up to strains of 50% and remains valid even for irregularly shaped tissue samples when considering only the deformations in the far field. Finally, we demonstrate that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1 hr after seeding, while collective forces on longer timescales are guided by mechanical feedback from the extracellular matrix.