The Manning group is interested in non-equilibrium collective behavior in both biological and non-biological systems. The uniting principle is that physics-based statistical mechanics models can provide insight into the emergent behavior of large groups of strongly interacting objects (granular particles, biological cells, atoms, droplets) at high densities. The systems we study can be though of as disordered (as opposed to crystalline) "materials" with many metastable mechanical states, and we explore the dynamics and thermodynamics of these "materials". Our work can be divided into two categories:
Groups of cells at high densities interact strongly with one another and generate emergent collective behavior that is more than just the sum of the parts. The mechanical properties of embryonic tissues likely play an important role in cell movements and pattern formation during embryogenesis. Our group collaborates with the Amack lab at SUNY Upstate medical school, the Henderson group at the Syracuse Biomaterials Institute, the Schoetz group at UCSD, and others.
- Motion and migration of cells in dense tissues (Max Dapeng Bi)
- Cell Shapes in Kupffer's Vescicle (Craig Fox)
- Cells on 2D substrates (Giuseppe Passucci)
- Surface tension in tissues
- Model for glassy dynamics of cells in 3D
- Mitotic waves in Drosophila
Energy barriers govern glassy dynamics in tissues: Recent observations demonstrate that confluent tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. We develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which help govern cell migration in cell monolayers. In contrast to work on sheared foams, we find that energy barrier heights are exponentially distributed and depend systematically on the cell's number of neighbors. Based on these results, we predict glassy two-time correlation functions for cell motion, with a timescale that increases rapidly as cell activity decreases. These correlation functions are used to construct simple random walks that reproduce the caging behavior observed for cell trajectories in experiments.
Migration of Tumorous Cells in Confluent Tissues: Effect of Cortical Tension and Elasticity We develop numerical and theoretical models to calculate migration rates for cells with abnormal cortical tension and cortical elasticity embedded in a confluent tissue composed of stiffer ‘normal’ cells. Also we study the general shape morphology of soft cells embedded in a stiffer matrix under confluent conditions. This work provides a theoretical framework for predicting collective motion of cells during cancer tumorigenesis and metastasis.
Dynamical simulation of collective cell migration in tissues We simulate the dynamics of cell motion in confluent tissue with a minimal model. This model takes into account the shape of each cell rather using point-like particles. The model also includes the mechanical properties of the active cortex of cells, as well as the interaction between cell polarization. In addition we also capture the active rearrangements of a cell and its neighbors by implementing T1 moves induced by active traction forces. The results of the model will be compared to experiments of tissue spreading and embryogenisis.
During embryonic development individual cells must actively change their shapes in a coordinated way to generate large-scale patterns that are critical for the formation of tissues and organs. An open question is how these programmed cell shape changes are regulated via a combination of mechanical forces and biochemical signaling pathways. In order to make progress in understanding and treating developmental diseases, we must account for both types of interactions and use predictive models to identify feedbacks between them.
The zebrafish embryo is an excellent vertebrate system for investigating tissue patterning and organogenesis. To study cell shape changes during organogenesis, we are using the zebrafish organ of asymmetry—called Kupffer’s vesicle (KV)—as a model organ. KV is a simple organ with a fluid-filled lumen surrounded by a single layer of monociliated epithelial cells. Motile cilia projecting into the lumen create an asymmetric fluid flow that is necessary for specifying the left-right body axis. We have identified cell shape changes during KV morphogenesis that are essential for KV organ formation and function. This morphogenetic process, which we refer to as ‘KV remodeling,’ provides an opportunity to characterize biophysical mechanisms that drive organogenesis.
Currently, Craig Fox is working in collaboration with Amack lab to image and analyze fluid flows inside the KV. He is also working to understand how the mechanical properties of tissues like the notochord that are near the KV influence cell shapes and left-right patterning.
Understanding single and collective cell motility in model environments is foundational to many current research efforts in biology and bioengineering. To elucidate subtle differences in cell behavior despite cell-to-cell variability, we introduce an algorithm for tracking large numbers of cells for long time periods and present a set of physics-based metrics that quantify differences in cell trajectories. Our algorithm, termed Automated Contour-based Tracking for In Vitro Environments (ACTIVE), is distinct from existing tracking software because it accommodates both variability in image intensity and multi-cell interactions, such as division and occlusion. When applied to low-contrast images from live-cell experiments, ACTIVE reduced error in analyzing cell occlusion events by half compared to a benchmark tracking program, while simultaneously tracking cell divisions and resulting mother-daughter cell relationships with accuracy greater than 70 %. The large dataset generated by ACTIVE allowed us to develop metrics that capture subtle differences between cell trajectories on different substrates. We present cell motility data for thousands of cells studied at varying densities on varying shape-memory-polymer-based nanotopographies, and identify several quantitative differences, including an unanticipated difference between two “control” substrates. We expect that ACTIVE will be immediately useful to researchers who require accurate, long-timescale motility data for many cells.
Manuscript is submitted.
Giuseppe Passucci has been working with the Turner lab at Upstate Medical on image analysis, contributing a method to analyze movies of Golgi bodies quantitatively using a clustering algorithm. In addition, we are interested in creating a self propelled particle model to recapitulate cells moving on shape memory polymers with topological asymmetries, namely oriented channels. By analyzing the state of a Golgi body, which is strongly correlated with cell polarization, we hope to incorporate additional internal degrees of freedom into existing SPP models to capture the physics of collective cell behavior. Understanding collective cell behavior would contribute to physical models and also have significant biological implications.
Biological tissues share many properties with liquids, including a reproducible surface tension. Different types of tissues have different surface tensions, which can be used to predict cell sorting behavior in aggregates and morphogenetic movements during development. We have developed a minimal mechanical model for individual cells in an aggregate based on observations from confocal slices of cell aggregates. The model accounts for adhesion and cortical tension, and makes novel predictions about surface cell shapes that we verify experimentally. We show that there is an analytic solution for the surface tension which arises from the collective interactions of cells in ordered and disordered 2D and 3D aggregates, and show that the surface tension crosses over from a region with a strong dependence on adhesion to region where cortical tension dominates. This has important implications for drugs designed to alter macroscopic tissue properties. Furthermore, our analytic method also makes novel predctions for the surface energy of dry foams.
|Electron microscope images of LP1 cell aggregates(left) and locally minimal energy cellular structures generated by our surface tension model(right). The upper panel has a higher surface tension than the lower panel.|
It is clear that biological tissues are not simple liquids. In fact, the structure and rheology of cell packings share striking similarities with foams and emulsions, although active processes generate significant differences. Together with member of the Schoetz lab, we have shown that cells in 3D embryonic explants exhibit glassy or "supercooled" dynamics — suggesting that while these tissues are fluid-like on long timescales, they display "caging" behaviors that indicate the system is close to a jamming or glass transition. We have developed a minimal three-parameter active matter model (with some interesting noise correlations) that makes predictions about the viscous relaxation in tissue compression and fusion experiments, which we have verified experimentally. This illustrates that a very simple model can can qualitatively and quantitatively explain the bulk behavior of the system. It also suggsts that, in agreement with our work on surface tension described above, the surface properties do in fact require more information about cell shapes and intracellular feedbacks.
In collaboration with Timon Idema, Louis Kang, Tom Lubensky, Andrea Liu and Phil Nelson at UPenn, and Julien Dubuis and Thomas Gregor at Princeton University, we are studying and modeling the waves of mitotic divisiont that occur in the fruit fly embryo during early development.
Preprint available at the arXiv: The syncytial Drosophila embryo as a mechanically excitable medium.
Amorphous, glassy materials often comprise or lubricate sheared material interfaces and require more complicated constitutive equations than simple fluids or crystalline solids. They flow like a fluid under large stresses, creep or remain stationary under smaller stresses, and have complex, history-dependent behavior. Bulk metallic glasses, granular materials, and bubble rafts are just some of the disordered materials that exhibit a yield stress. These materials exhibit lots of interesting behaviors, which we study using theoretical and computational techniques.
- New definition for the boson peak in terms of eigenvector statistics
- Identifying flow defects or "soft spots"
- Accurate, efficient method for characterizing soft spots
- Shear bands
- Glassy dynamics and STZ theory
- Friction and earthquakes
Both solids and fluids can flow under applied stress. In crystalline solids, flow occurs via particle rearrangements controlled by a population of dislocations, while in fluids, particle rearrangements occur everywhere throughout the material. In disordered solids, flow generally occurs via localized rearrangements, but no one has been able to identify a population of flow defects, analogous to dislocations, that are structurally different from the rest of the system and more susceptible to flow. It has therefore remained unclear whether a solid-like or fluid-like description is more appropriate for describing flow in such systems. By analyzing the low-energy vibrational modes in a model glass, we have identified a population of structurally distinct, long-lived “soft spots'', and we show that particle rearrangements are initiated at these spots. These results support a solid-like description of flow controlled by a population of localized flow defects in glassy materials, and provide new insight into related problems, such as the origin of localization at low frequencies and the development of predictive continuum models for solids. With Ke Chen and members of the Yodh group at UPenn, we have also verified that these soft spots control rearrangements in a thermal, experimental colloidal system.
Granular materials and other disordered can range from highly disordered to ordered, depending on the material preparation. By developing simulations and new analytic techniques, we can find and characterize soft spots in disordered materials, and thus predict where they will deform when subjected to strain. Our new technique, which adds "spring-like" interactions between coarse-grained gridpoints, provide a great deal more information about "soft spots" than previous efforts, including the ability to detect the energy needed to cause a spot to deform (i.e. "energy barriers"), and an approximate vibrational energy for each localized soft spot. These are important ingrdients in continuum models for granular and disordered solids. In addition, we can clearly separate phonon-like modes from boson peak modes and localized excitiations. We are also interested in how the properties of granular materials evolve as we go from a completely ordered system (a crystal) to a highly disordered system.
Strain localization, or shear banding, is the spontaneous development of coexisting flowing and stationary regions in a sheared material. Strain localization has been identified and studied experimentally in granular materials, bubble rafts, complex fluids, and bulk metallic glasses. Shear banding may play an important role in the failure modes of structural materials and earthquake faults. Localization is a precursor to fracture in bulk metallic glasses and has been cited as a mechanism for material weakening in granular fault gouge on faults.
We model amorphous solids with a set of partial differential equations that describe Shear Transformation Zones (STZs) (Falk and Langer, 1998) with an effective temperature. We find small perturbations in the effective temperature can lead to localized regions of higher strain, or shear bands, in our numerically integrated solution, and show that the system is linearly unstable with repect to perturbations to a time-varying trajectory.
We have also shown that an STZ model with a rate-dependent effective temperature predicts differet types of localization behavior as a function of two important parameters: applied strain rate and quench rate for initializing the sample. For quickly strained or slowly quenched systems, thin diffusion limited shear bands are predicted. In contrast, slowly sheared or quickly quneched samples undergo homogeneous deformation, and in between there is a regime of thick shear bands where the length scale is determined by the steady state density of STZs.
Thomas Haxton and Andrea Liu have shown that an "effective temperature" measured using a fluctuation-dissipation relation correlates with flow and stress in a simulated glass [Phys. Rev. Lett. 99, 195701 (2007)]. The extensive Haxton and Liu (HL) data sharply test the basic assumptions of STZ theory, especially the central role played by the effective disorder temperature as a dynamical state variable. We find that the theory survives these tests, and that the HL data provide important and interesting constraints on some of its specific ingredients. Our most surprising conclusion is that, when driven at various constant shear rates in the low-temperature glassy state, the HL system exhibits a classic glass transition, including super-Arrhenius behavior, as a function of the effective temperature.
As explained in the reference above, the effective temperature STZ theory provides a mechanism for aging in glassy materials: in thermal systems the effective temperature is weakly coupled to the thermal bath and in the absence of applied strain the effective temperature approaches the bath temperature. Joerg Rottler has shown that two variations of STZ theory, one which includes an effective temperature and another which includes an aging timescale qualitatively explain simulation data for aging. In collaboration with Joerg, I am exploring whether the effective temperature STZ model quantitatively matches aging dynamics.
We use STZ equations that exhibit localized shear regions to generate constitutive relations for interfaces between sheared materials (such as fault planes in earthquakes). We have shown that shear bands are a strong strain-rate weakening mechanism, and when they form they greatly reduce the shear stress supported by the fault. This new friction law, which permits spontaneous shear bands, changes the rupture dynamics on simulated earthquake faults. This is a novel mechanism for fault weakening at high velocities.
We have also incorporated the idea that the steady state configurational disorder changes with strain rate (see shear bands above) into the friction law for earthquake faults. Incorporating the rate dependence shows that the degree of localization depends on the slip speed, and the model therefore predicts that there will be a strong feedback between slip speed and the friction coefficient. This has important implications for earthquake rupture propagation.
- Jeff Amack, SUNY Upstate Medical University
- James Henderson and lab, Syracuse Biomaterials Institute SU
- Chris Turner lab, SUNY Upstate Medical University
- Eva-Maria Schoetz Collins and lab, UCSD
- Andrea Liu, U. Penn.
- Timon Idema, TU Delft
- Julien Dubuis and Gregor lab, Princeton
- Ke Chen and Yodh lab, U. Penn
- Eric Daub, Los Alamos
- Mikko Haataja, Princeton
- Jean Carlson, Jim Langer, UC Santa Barbara