Realizations of highly heterogeneous collagen networks via stochastic reconstruction for micromechanical analysis of tumor cell invasion

Polychromatic Polarization Microscopy Differentiates Collagen Fiber Signatures in Benign Pancreatic Tissue and Pancreatic Ductal Adenocarcinoma

The orientation of collagen fibers in relation to malignant epithelium is known to carry prognostic information in a variety of tissues. The data are strongest for breast and pancreatic ductal adenocarcinoma (PDAC). However, the information inherent in collagen fiber topology in malignant tissues remains untapped in daily surgical pathology practice, largely because collagen fibers within areas of desmoplasia cannot be resolved with standard diagnostic microscopy. The methodologies used to visualize collagen fiber orientation are either of insufficient resolution to consistently capture collagen fiber topology or require resources in time and money that do not fit into the daily surgical pathology workflow. Polychromatic polarization microscopy (PPM) has the potential to bring collagen topology to the attention of pathologists during their routine work. It has been demonstrated to be equivalent to the gold standard methodology used to research collagen, second harmonic generation (SHG). We use PPM to visualize and describe the differences in collagen topology in normal pancreas, chronic pancreatitis, and PDAC with a standard microscope, using H&E-stained sections. In the process, we propose a lexicon with which to describe the morphologic characteristics of collagen in benign and malignant pancreatic tissue.

Subcellular mechano-regulation of cell migration in confined extracellular microenvironment

Cell migration is a highly coordinated cellular event that determines diverse physiological and pathological processes in which the continuous interaction of a migrating cell with neighboring cells or the extracellular matrix is regulated by the physical setting of the extracellular microenvironment. In confined spaces, cell migration occurs differently compared to unconfined open spaces owing to the additional forces that limit cell motility, which create a driving bias for cells to invade the confined space, resulting in a distinct cell motility process compared to what is expected in open spaces. Moreover, cells in confined environments can be subjected to elevated mechanical compression, which causes physical stimuli and activates the damage repair cycle in the cell, including the DNA in the nucleus. Although cells have a self-restoring system to repair damage from the cell membrane to the genetic components of the nucleus, this process may result in genetic and/or epigenetic alterations that can increase the risk of the progression of diverse diseases, such as cancer and immune disorders. Furthermore, there has been a shift in the paradigm of bioengineering from the development of new biomaterials to controlling biophysical cues and fine-tuning cell behaviors to cure damaged/diseased tissues. The external physical cues perceived by cells are transduced along the mechanosensitive machinery, which is further channeled into the nucleus through subcellular molecular linkages of the nucleoskeleton and cytoskeleton or the biochemical translocation of transcription factors. Thus, external cues can directly or indirectly regulate genetic transcriptional processes and nuclear mechanics, ultimately determining cell fate. In this review, we discuss the importance of the biophysical cues, response mechanisms, and mechanical models of cell migration in confined environments. We also discuss the effect of force-dependent deformation of subcellular components, specifically focusing on subnuclear organelles, such as nuclear membranes and chromosomal organization. This review will provide a biophysical perspective on cancer progression and metastasis as well as abnormal cellular proliferation.

Micromechanical remodeling of the extracellular matrix by invading tumors: anisotropy and heterogeneity

Altered tissue mechanics is an important signature of invasive solid tumors. While the phenomena have been extensively studied by measuring the bulk rheology of the extracellular matrix (ECM) surrounding tumors, micromechanical remodeling at the cellular scale remains poorly understood. By combining holographic optical tweezers and confocal microscopy on in vitro tumor models, we show that the micromechanics of collagen ECM surrounding an invading tumor demonstrate directional anisotropy, spatial heterogeneity and significant variations in time as tumors invade. To test the cellular mechanisms of ECM micromechanical remodeling, we construct a simple computational model and verify its predictions with experiments. We find that collective force generation of a tumor stiffens the ECM and leads to anisotropic local mechanics such that the extension direction is more rigid than the compression direction. ECM degradation by cell-secreted matrix metalloproteinase softens the ECM, and active traction forces from individual disseminated cells re-stiffen the matrix. Together, these results identify plausible biophysical mechanisms responsible for the remodeled ECM micromechanics surrounding an invading tumor.

Collagen Remodeling along Cancer Progression Providing a Novel Opportunity for Cancer Diagnosis and Treatment

The extracellular matrix (ECM) is a significant factor in cancer progression. Collagens, as the main component of the ECM, are greatly remodeled alongside cancer development. More and more studies have confirmed that collagens changed from a barrier to providing assistance in cancer development. In this course, collagens cause remodeling alongside cancer progression, which in turn, promotes cancer development. The interaction between collagens and tumor cells is complex with biochemical and mechanical signals intervention through activating diverse signal pathways. As the mechanism gradually clears, it becomes a new target to find opportunities to diagnose and treat cancer. In this review, we investigated the process of collagen remodeling in cancer progression and discussed the interaction between collagens and cancer cells. Several typical effects associated with collagens were highlighted in the review, such as fibrillation in precancerous lesions, enhancing ECM stiffness, promoting angiogenesis, and guiding invasion. Then, the values of cancer diagnosis and prognosis were focused on. It is worth noting that several generated fragments in serum were reported to be able to be biomarkers for cancer diagnosis and prognosis, which is beneficial for clinic detection. At a glance, a variety of reported biomarkers were summarized. Many collagen-associated targets and drugs have been reported for cancer treatment in recent years. The new targets and related drugs were discussed in the review. The mass data were collected and classified by mechanism. Overall, the interaction of collagens and tumor cells is complicated, in which the mechanisms are not completely clear. A lot of collagen-associated biomarkers are excavated for cancer diagnosis. However, new therapeutic targets and related drugs are almost in clinical trials, with merely a few in clinical applications. So, more efforts are needed in collagens-associated studies and drug development for cancer research and treatment.

Physically-based structural modeling of a typical regenerative tissue analog bridges material macroscale continuum and cellular microscale discreteness and elucidates the hierarchical characteristics of cell-matrix interaction

This paper presents a comprehensive physically-based structural modelling for the passive and active biomechanical processes in a typical engineered tissue - namely, cell-compacted collagen gel. First, it introduces a sinusoidal curve analog for quantifying the mechanical response of the collagen fibrils and a probability distribution function of the characteristic crimp ratio for taking into account the fibrillar geometric entropic effect. The constitutive framework based on these structural characteristics precisely reproduces the nonlinearity, the viscoelasticity, and fairly captures the Poisson effect exhibiting in the macroscale tensile tests; which, therefore, substantially validates the structural modelling for the analysis of the cell-gel interaction during collagen gel compaction. Second, a deterministic molecular clutch model specific to the interaction between the cell pseudopodium and the collagen network is developed, which emphasizes the dependence of traction force on clutch number altering with the retrograde flow velocity, actin polymeric velocity, and the deformation of the stretched fibril. The modelling reveals the hierarchical features of cellular substrate sensing, i.e. a biphasic traction force response to substrate elasticity begins at the level of individual fibrils and develops into the second biphasic sensing by means of the fibrillar number integration at the whole-cell level. Singular in crossing the realms of continuum and discrete mechanics, the methodologies developed in this study for modelling the filamentous materials and cell-fibril interaction deliver deep insight into the temporospatially dynamic 3D cell-matrix interaction, and are able to bridge the cellular microscale and material macroscale in the exploration of related topics in mechanobiology.

A computational framework for modeling cell-matrix interactions in soft biological tissues

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Deriving time-varying cellular motility parameters via wavelet analysis

Cell migration, which is regulated by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays an indispensable role in many physiological and pathological process such as normal tissue development and cancer metastasis. However, there is a lack of rigorous and quantitative tools for analyzing the time-varying characteristics of cell migration in heterogeneous microenvironment, resulted from, e.g. the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop a wavelet-analysis approach to derive the time-dependent motility parameters from cell migration trajectories, based on the time-varying persistent random walk model. In particular, the wavelet denoising and wavelet transform are employed to analyze migration velocities and obtain the wavelet power spectrum. Subsequently, the time-dependent motility parameters are derived via Lorentzian power spectrum. Our results based on synthetic data indicate the superiority of the method for estimating the intrinsic transient motility parameters, robust against a variety of stochastic noises. We also carry out a systematic parameter study and elaborate the effects of parameter selection on the performance of the method. Moreover, we demonstrate the utility of our approach via analyzing experimental data ofin vitrocell migration in distinct microenvironments, including the migration of MDA-MB-231 cells in confined micro-channel arrays and correlated migration of MCF-10A cells due to ECM-mediated mechanical coupling. Our analysis shows that our approach can be as a powerful tool to accurately derive the time-dependent motility parameters, and further analyze the time-dependent characteristics of cell migration regulated by complex microenvironment.

Shannon entropy for time-varying persistence of cell migration

Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and pathological processes. Cell migration is typically modeled as a persistent random walk, which depends on two critical motility parameters, i.e., migration speed and persistence time. It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data. Here, we introduce the normalized Shannon entropy (SE) based on the FPS of cellular velocity autocovariance function to quantify migration dynamics. The SE introduced here possesses a similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration, attaining the maximal value of unity for purely diffusive migration (i.e., SE = 1 for the most "random" dynamics) and the minimal value of 0 for purely ballistic dynamics (i.e., SE = 0 for the most "ordered" dynamics). We also find that SE is strongly correlated with the migration persistence but is less sensitive to the migration speed. Moreover, we introduce the time-varying SE based on the WPS of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which typically results from complex and time-varying intra- or extracellular mechanisms. We employ our approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the SE and wavelet transform (i.e., SE-based approach) offers a simple and efficient tool to quantify cell migration dynamics in complex microenvironment.

Dynamically Re-Organized Collagen Fiber Bundles Transmit Mechanical Signals and Induce Strongly Correlated Cell Migration and Self-Organization

Correlated cell migration in fibrous extracellular matrix (ECM) is important in many biological processes. During migration, cells can remodel the ECM, leading to the formation of mesoscale structures such as fiber bundles. However, how such mesoscale structures regulate correlated single-cells migration remains to be elucidated. Here, using a quasi-3D in vitro model, we investigate how collagen fiber bundles are dynamically re-organized and guide cell migration. By combining laser ablation technique with 3D tracking and active-particle simulations, we definitively show that only the re-organized fiber bundles that carry significant tensile forces can guide strongly correlated cell migration, providing for the first time a direct experimental evidence supporting that matrix-transmitted long-range forces can regulate cell migration and self-organization. This force regulation mechanism can provide new insights for studies on cellular dynamics, fabrication or selection of biomedical materials in tissue repairing, and many other biomedical applications.

Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction

Collective cell migration is crucial to many physiological and pathological processes such as embryo development, wound healing, and cancer invasion. Recent experimental studies have indicated that the active traction forces generated by migrating cells in a fibrous extracellular matrix (ECM) can mechanically remodel the ECM, giving rise to bundlelike mesostructures bridging individual cells. Such fiber bundles also enable long-range propagation of cellular forces, leading to correlated migration dynamics regulated by the mechanical communication among the cells. Motivated by these experimental discoveries, we develop an active-particle model with polarized effective attractions (APPA) to investigate emergent multicellular migration dynamics resulting from ECM-mediated mechanical communications. In particular, the APPA model generalizes the classic active-Brownian-particle (ABP) model by imposing a pairwise polarized attractive force between the particles, which depends on the instantaneous dynamic states of the particles and mimics the effective mutual pulling between the cells via the fiber bundle bridge. The APPA system exhibits enhanced aggregation behaviors compared to the classic ABP system, and the contrast is more apparent at lower particle densities and higher rotational diffusivities. Importantly, in contrast to the classic ABP system where the particle velocities are not correlated for all particle densities, the high-density phase of the APPA system exhibits strong dynamic correlations, which are characterized by the slowly decaying velocity correlation functions with a correlation length comparable to the linear size of the high-density phase domain (i.e., the cluster of particles). The strongly correlated multicellular dynamics predicted by the APPA model is subsequently verified in in vitro experiments using MCF-10A cells. Our studies indicate the importance of incorporating ECM-mediated mechanical coupling among the migrating cells for appropriately modeling emergent multicellular dynamics in complex microenvironments.

Probing information content of hierarchical n-point polytope functions for quantifying and reconstructing disordered systems

Disordered systems are ubiquitous in physical, biological, and material sciences. Examples include liquid and glassy states of condensed matter, colloids, granular materials, porous media, composites, alloys, packings of cells in avian retina, and tumor spheroids, to name but a few. A comprehensive understanding of such disordered systems requires, as the first step, systematic quantification, modeling, and representation of the underlying complex configurations and microstructure, which is generally very challenging to achieve. Recently, we introduced a set of hierarchical statistical microstructural descriptors, i.e., the "n-point polytope functions" P_{n}, which are derived from the standard n-point correlation functions S_{n}, and successively included higher-order n-point statistics of the morphological features of interest in a concise, explainable, and expressive manner. Here we investigate the information content of the P_{n} functions via optimization-based realization rendering. This is achieved by successively incorporating higher-order P_{n} functions up to n=8 and quantitatively assessing the accuracy of the reconstructed systems via unconstrained statistical morphological descriptors (e.g., the lineal-path function). We examine a wide spectrum of representative random systems with distinct geometrical and topological features. We find that, generally, successively incorporating higher-order P_{n} functions and, thus, the higher-order morphological information encoded in these descriptors leads to superior accuracy of the reconstructions. However, incorporating more P_{n} functions into the reconstruction also significantly increases the complexity and roughness of the associated energy landscape for the underlying stochastic optimization, making it difficult to convergence numerically.

Tumor-associated collagen signatures: pushing tumor boundaries

In 2006, a new model of invasive breast tumor emerged and, since 2011, is gaining recognition and research momentum. "Tumor-associated collagen signatures" describe 3 distinct layers of collagen which radiate outward in shells from the main body of the tumor. The outermost layer (TACS3) features branches of collagen radiating away from the tumor, 90° perpendicular to the tumor surface. TACS3 increases tumor span and correlates directly with metastasis, though presently difficult to detect in breast tissue. TACS is an emerging model but has been validated by multiple labs in vitro and in vivo, specifically for breast cancer prognostics. Newly recognized and accepted tumor borders will impact both R0 resections and downstream surgical reconstruction. This review aims to comprehensively introduce and connect the ranging literature on linearized collagen of invasive tumor borders. Using PubMed keyword searches containing "aligned," "linear," "oriented," and "organized," we have gathered the studies on TACS, integrated the concept into the clinic, and projected future platforms.

Three-dimensional pore network characterization of reconstructed extracellular matrix

The extracellular matrix (ECM) has a fiber network that provides physical scaffolds to cells and plays important roles by regulating cellular functions. Some previous works characterized the mechanical and geometrical properties of the ECM fiber network using reconstituted collagen-I. However, the characterization of the porous structure of reconstituted collagen-I has been limited to the pore diameter measurement, and pore network extraction has not been applied to reconstituted collagen-I despite the importance of pore interconnectivity. Here, we aim to show the importance of characterizing the pore network of reconstituted collagen-I by comparing the pore networks of structures that have different fiber alignments. We show that the fiber alignment significantly changes the pore throat area but not the pore diameter. Also, we demonstrate that larger pore throats are directed in the direction of the fiber alignment, which may help in understanding the enhanced cell migration when fibers are aligned.

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

Geometric Dependence of 3D Collective Cancer Invasion

Metastasis of mesenchymal tumor cells is traditionally considered as a single-cell process. Here, we report an emergent collective phenomenon in which the dissemination rate of mesenchymal breast cancer cells from three-dimensional tumors depends on the tumor geometry. Combining experimental measurements and computational modeling, we demonstrate that the collective dynamics is coordinated by the mechanical feedback between individual cells and their surrounding extracellular matrix (ECM). We find the tissue-like fibrous ECM supports long-range physical interactions between cells, which turn geometric cues into regulated cell dissemination dynamics. Our results suggest that migrating cells in three-dimensional ECM represent a distinct class of an active particle system in which the collective dynamics is governed by the remodeling of the environment rather than direct particle-particle interactions.

Force chains in cell-cell mechanical communication

Force chains (FCs) are a key determinant of the micromechanical properties and behaviour of heterogeneous materials, such as granular systems. However, less is known about FCs in fibrous materials, such as the networks composing the extracellular matrix (ECM) of biological systems. Using a finite-element computational model, we simulated the contraction of a single cell and two nearby cells embedded in two-dimensional fibrous elastic networks and analysed the tensile FCs that developed in the ECM. The role of ECM nonlinear elasticity on FC formation was evaluated by considering linear and nonlinear, i.e. exhibiting 'buckling' and/or 'strain-stiffening', stress-strain curves. The effect of the degree of cell contraction and network coordination value was assessed. We found that nonlinear elasticity of the ECM fibres influenced the structure of the FCs, facilitating the transition towards more distinct chains that were less branched and more radially oriented than the chains formed in linear elastic networks. When two neighbouring cells contract, a larger number of FCs bridged between the cells in nonlinear networks, and these chains had a larger effective rigidity than the chains that did not reach a neighbouring cell. These results suggest that FCs function as a route for mechanical communication between distant cells and highlight the contribution of ECM fibre nonlinear elasticity to the formation of FCs.

Absorbing-active transition in a multi-cellular system regulated by a dynamic force network

Collective cell migration in 3D extracellular matrix (ECM) is crucial to many physiological and pathological processes. Migrating cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers and lead to a dynamically evolving force network in the system. Here, we elucidate the role of this force network in regulating collective cell behaviors using a minimal active-particle-on-network (APN) model, in which active particles can pull the fibers and hop between neighboring nodes of the network following local durotaxis. Our model reveals a dynamic transition as the particle number density approaches a critical value, from an "absorbing" state containing isolated stationary small particle clusters, to an "active" state containing a single large cluster undergoing constant dynamic reorganization. This reorganization is dominated by a subset of highly dynamic "radical" particles in the cluster, whose number also exhibits a transition at the same critical density. The transition is underlaid by the percolation of "influence spheres" due to the particle pulling forces. Our results suggest a robust mechanism based on ECM-mediated mechanical coupling for collective cell behaviors in 3D ECM.

Biomechanics of Collective Cell Migration in Cancer Progression: Experimental and Computational Methods

Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities such as restructuring of extracellular matrix (ECM), stress and force distribution profiles, and reorganization of the cytoskeleton. Therefore, the phenomenon could be understood by an in-depth study of cells' behavior determinants, including but not limited to mechanical cues from the environment and from fellow "travelers". This review article aims to cover the recent development of experimental and computational methods for studying the biomechanics of collective cell migration during cancer progression and invasion. We also summarized the tested hypotheses regarding the mechanism underlying collective cell migration enabled by these methods. Together, the paper enables a broad overview on the methods and tools currently available to unravel the biophysical mechanisms pertinent to cell collective migration as well as providing perspectives on future development toward eventually deciphering the key mechanisms behind the most lethal feature of cancer.

Hierarchical Optimization: Fast and Robust Multiscale Stochastic Reconstructions with Rescaled Correlation Functions

Stochastic reconstructions based on universal correlation functions allow obtaining spatial structures based on limited input data or to fuse multiscale images from different sources. Current application of such techniques is severely hampered by the computational cost of the annealing optimization procedure. In this study we propose a novel hierarchical annealing method based on rescaled correlation functions, which improves both accuracy and computational efficiency of reconstructions while not suffering from disadvantages of existing speeding-up techniques. A significant order of magnitude gains in computational efficiency now allows us to add more correlation functions into consideration and, thus, to further improve the accuracy of the method. In addition, the method provides a robust multiscale framework to solve the universal upscaling or downscaling problem. The novel algorithm is extensively tested on binary (two-phase) microstructures of different genesis. In spite of significant improvements already in place, the current implementation of the hierarchical annealing method leaves significant room for additional accuracy and computational performance tweaks. As described here, (multiscale) stochastic reconstructions will find numerous applications in material and Earth sciences. Moreover, the proposed hierarchical approach can be readily applied to a wide spectrum of constrained optimization problems.