Matrix Dimensionality Research Articles

Erlotinib Promotes Ligand-Induced EGFR Degradation in 3D but Not 2D Cultures of Pancreatic Ductal Adenocarcinoma Cells.

Simple SummaryThe EGFR is a tyrosine kinase receptor that responds to different stresses such as UV irradiation, hypoxia and drug treatment by internalizing into endosomal compartments. Receptor trafficking and degradation due to tyrosine kinase inhibitors has been widely studied in two- dimensional (2D) cell culture systems, but little is known about how cells respond to these types of drugs in more physiologically relevant models such as three-dimensional (3D) cultures, whose nanostructured properties allow cells to grow, proliferate, migrate and extend cellular processes in their 3D space. In this study, we show that EGFR suffers degradation in response to erlotinib treatment in 3D-cultured cancer cells but not in classic 2D culture systems, demonstrating that dimensionality strongly affects cell drug response. This 3D model may pave the way for the development of more physiological culture platforms to obtain mechanistic insights into how cells respond to chemotherapy.The epithelial growth factor receptor (EGFR) is a tyrosine kinase receptor that participates in many biological processes such as cell proliferation. In addition, EGFR is overexpressed in many epithelial cancers and therefore is a target for cancer therapy. Moreover, EGFR responds to lots of stimuli by internalizing into endosomes from where it can be recycled to the membrane or further sorted into lysosomes where it undergoes degradation. Two-dimensional cell cultures have been classically used to study EGFR trafficking mechanisms in cancer cells. However, it has been widely demonstrated that in 2D cultures cells are exposed to a non-physiological environment as compared to 3D cultures that provide the normal cellular conformation, matrix dimensionality and stiffness, as well as molecular gradients. Therefore, the microenvironment of solid tumors is better recreated in 3D culture models, and this is why they are becoming a more physiological alternative to study cancer physiology. Here, we develop a new model of EGFR internalization and degradation upon erlotinib treatment in pancreatic ductal adenocarcinoma (PDAC) cells cultured in a 3D self-assembling peptide scaffold. In this work, we show that treatment with the tyrosine kinase inhibitor erlotinib promotes EGFR degradation in 3D cultures of PDAC cell lines but not in 2D cultures. We also show that this receptor degradation does not occur in normal fibroblast cells, regardless of culture dimensionality. In conclusion, we demonstrate not only that erlotinib has a distinct effect on tumor and normal cells but also that pancreatic ductal adenocarcinoma cells respond differently to drug treatment when cultured in a 3D microenvironment. This study highlights the importance of culture systems that can more accurately mimic the in vivo tumor physiology.

The methodology for communication problem in telecom sector using fuzzy sub-monoid and group theory

In order to address the ‘channel’ problem for telecommunications operators, this study is a pioneer in the application of Fuzzy Sub monoid and Group Theory to the communication channel system. The channel entity community model was developed for the transmission of information in the channel system to analyses the operation of channel entities. The channel system network traffic equations were developed in accordance with the theory of stream conservation and the channel network matrix. The matrix dimensionality was reduced on the basis of the channel entity Fuzzy Sub monoid and group model. A solution to the flow-state transfer relationship of the channel system is obtained, which will be very useful for telecommunications operators to create a high-level mobile e-commerce application model and architecture.

基于法化矩阵降维的多相机快速光束法平差算法

基于法化矩阵降维的多相机快速光束法平差算法

基于法化矩阵降维的多相机快速光束法平差算法

基于法化矩阵降维的多相机快速光束法平差算法

Enhanced Matrix CFAR Detection With Dimensionality Reduction of Riemannian Manifold

This letter proposes an enhanced matrix constant false alarm rate (CFAR) detection method that works on the lower-dimensional Riemannian manifold. Motivated by general matrix CFAR detection method and dimensionality reduction scheme of the Riemannian manifold, this method obtains a mapping by maximizing the geometric test statistic. Dimensionality reduction is formulated as an orthonormal constraint optimization problem on the Grassmann manifold. Moreover, an explicit mapping is obtained by solving the optimization problem via conjugate gradient approach. Performances of the proposed method are evaluated on the lower-dimensional Riemannian manifold. Experiments on simulated data and real sea clutter data demonstrate that our method leads to the robustness to outliers and the improvement of detection performance over classical methods.

Abstract 1028: Extracellular matrix dimensionality reduces cellular cortical tension to stimulate pro-survival signaling in mammary epithelial cells

Abstract Tumor dormancy is a clinical phenomenon in which disseminated tumor cells remain asymptomatic and undetectable over a long period of time. Dormant cells are able to maintain quiescence in hostile microenvironments, escape frontline cancer therapies and evade the immune system, as well as their propensity to reactivate from latency and cause metastatic relapse. Although tumor dormancy is an important problem in the treatment of cancer, the molecular mechanisms underlying this complex process remain unclear. Because dormant cells are frequently found surrounded by a laminin-rich ECM, we hypothesized that ECM dimensionality intrinsically affects cell behaviors that predispose to dormancy. Accordingly, we assessed the biophysical and biochemical response of mammary epithelial cells (MECs) to compliant polyacrylamide (PA) gels and micropatterned surfaces in which ligand presentation and ECM dimensionality were modulated to recapitulate different ECM landscapes. Using traction force microscopy, atomic force microscopy indentation, and laser ablation studies, we found that a 3D ECM led to a drop in cortical tension of MECs. Computational modeling predicted that reduced cortical tension should lead to an increase in the number and/or residence time of actin protrusions as well as a net increase in negative membrane curvature. To test the prediction, we ectopically expressed F-actin and plasma membrane markers in MECs to examine the plasma membrane topography and actin protrusion dynamics. Indeed, MECs in 3D ECM had longer and more stable actin protrusions and more negative membrane curvature inducing proteins, including Exo70, at the plasma membrane. The enrichment of Exo70 at the plasma membrane accompanied the activation of Arf6, which led to an increase in Rac/p38 pro-survival signaling pathway. Consistently, we found that the non-spread cells were able to survive in 3D ECM but the non-spread MECs plated on either a soft 2D PA gels or rigid micropatterned adhesive islands died. We next examined if reduced cortical tension is sufficient to activate pro-survival pathways in cells in 2D. Importantly, pharmacological inhibition of myosin in non-spread MECs on a 2D ECM, which causes loss of cortical tension, increased negative membrane curvature and cell viability. Conversely, genetic knockdown of the negative curvature-inducing protein Exo70 compromised MEC survival in a 3D ECM. Our results provide the first evidence demonstrating that ECM dimensionality alters the biophysical properties of cells to modulate plasma membrane curvature and activate pro-survival signaling pathways. Our findings also offer a unique perspective for why Arf6 and Rac GTPases have been implicated in cancer aggression and suggest that targeting the tissue ECM or cellular cortical tension may provide a novel therapeutic approach to target dormant cells. Citation Format: FuiBoon Kai, Guanqing Ou, Alexandra Long, Wei Guo, Richard Tourdot, Ravi Radhakrishnan, Christopher Chen, Sophie Dumont, Valerie M. Weaver. Extracellular matrix dimensionality reduces cellular cortical tension to stimulate pro-survival signaling in mammary epithelial cells [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 1028.

Spot image ablated by femtosecond laser segmentation and feature clustering after dimension reduction reconstruction

When monocrystalline silicon material is ablated by femtosecond laser, plasma derived luminescence also occurs. By collecting plasma spot image and analyzing the feature of spot image, which can be used for the classification of laser ablation power and the parameters optimization of ablation process. Considering that the contrast between edge and background area of plasma spot is not obvious and the signal to noise ratio is lower, we analyzes the segmentation efficiency for dim spot target by comparing the traditional Otsu (maximum class square error method) and PCA(Principal Component Analysis). The experimental study shows that the extracted multiple geometric features of spot image segmented by PCA method are more consistent; however, the ablation transition zone and part halo are segmented into target by traditional Otsu, which leads to the larger dispersion among extracted geometric features of spot, and it is also not beneficial for feature analysis and recognition of ablation process parameters. Further, the brightness of spot image under different ablation power was extracted, combining with pixel area, perimeter, long and short axis and long and short axis ratio of spot image, a six-dimensional feature matrix is built to classify the laser ablation power. Because of the large amount of data collected plasma spot sequence image, the manifold learning algorithm is used to reduce the dimension of feature matrix. Each spot image with 10mW, 20mW and 50mW ablation power is selected respectively 100 frames to build the six-dimensional feature matrix, three manifold learning algorithms are used in contrast to realize matrix dimensionality reduction and scatter plot reconstruction, then the feature distributions of spot image ablated by three kinds of ablation power are observed in three-dimensional space and two-dimensional plane, we find that the clustering effect for decreased dimension feature points using LPP(Locality preserving projections) algorithm and LLTSA(Linear Local Tangent Space Alignment) are better, they can be used to classify the spot image under different ablation power.

Finite-range Coulomb gas models of banded random matrices and quantum kicked rotors

Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality. As d increases, there is a transition from Poisson to classical random matrix statistics.

Controlling of magnetocaloric effect in Gd2O3@SiO2 nanocomposites by substrate dimensionality and particles’ concentration

The magnetocaloric effect (MCE) of hybrid nanostructures consisting of fine gadolinium oxide (Gd2O3) nanoparticles with diameter 7 nm and 12 nm loaded into the pores of the periodically ordered mesoporous silica with hexagonal (SBA-15) or cubic (SBA-16) symmetry were investigated. The concentration effect of the added nanoparticles (NPs) and the effect of the silica matrix dimensionality on the structural properties, magnetization M(H), magnetic entropy change ΔSM, and parameters A(T) and B(T) derived from Arrott plots were studied in four samples. Examined nanocomposites exhibited reasonable high values of magnetic entropy change ΔSM varying from 29 J/kgK established for Gd2O3@SBA-15 up to 64 J/kgK observed in Gd2O3@SBA-16 at maximal field change 5 T at low temperatures. This suggests that studied nanocomposites, where diamagnetic silica matrices serve as nanoreactors for growth of Gd2O3 nanoparticles and their symmetry strongly affect magnetic properties of whole composites, could be feasible for cryomagnetic refrigeration applications.

Invariant manifolds and Lax pairs for integrable nonlinear chains

We continue the previously started study of the development of a direct method for constructing the Lax pair for a given integrable equation. This approach does not require any addition assumptions about the properties of the equation. As one equation of the Lax pair, we take the linearization of the considered nonlinear equation, and the second equation of the pair is related to its generalized invariant manifold. The problem of seeking the second equation reduces to simple but rather cumbersome calculations and, as examples show, is effectively solvable. It is remarkable that the second equation of this pair allows easily finding a recursion operator describing the hierarchy of higher symmetries of the equation. At first glance, the Lax pairs thus obtained differ from usual ones in having a higher order or a higher matrix dimensionality. We show with examples that they reduce to the usual pairs by reducing their order. As an example, we consider an integrable double discrete system of exponential type and its higher symmetry for which we give the Lax pair and construct the conservation laws.

Automatic Human Facial Expression Recognition Based on Integrated Classifier From Monocular Video with Uncalibrated Camera

An automatic recognition framework for human facial expressions from a monocular video with an uncalibrated camera is proposed. The expression characteristics are first acquired from a kind of deformable template, similar to a facial muscle distribution. After associated regularization, the time sequences from the trait changes in space-time under complete expressional production are then arranged line by line in a matrix. Next, the matrix dimensionality is reduced by a method of manifold learning of neighborhood-preserving embedding. Finally, the refined matrix containing the expression trait information is recognized by a classifier that integrates the hidden conditional random field (HCRF) and support vector machine (SVM). In an experiment using the Cohn–Kanade database, the proposed method showed a comparatively higher recognition rate than the individual HCRF or SVM methods in direct recognition from two-dimensional human face traits. Moreover, the proposed method was shown to be more robust than the typical Kotsia method because the former contains more structural characteristics of the data to be classified in space-time

Actomyosin stress fiber mechanosensing in 2D and 3D.

Mechanotransduction is the process through which cells survey the mechanical properties of their environment, convert these mechanical inputs into biochemical signals, and modulate their phenotype in response. These mechanical inputs, which may be encoded in the form of extracellular matrix stiffness, dimensionality, and adhesion, all strongly influence cell morphology, migration, and fate decisions. One mechanism through which cells on planar or pseudo-planar matrices exert tensile forces and interrogate microenvironmental mechanics is through stress fibers, which are bundles composed of actin filaments and, in most cases, non-muscle myosin II filaments. Stress fibers form a continuous structural network that is mechanically coupled to the extracellular matrix through focal adhesions. Furthermore, myosin-driven contractility plays a central role in the ability of stress fibers to sense matrix mechanics and generate tension. Here, we review the distinct roles that non-muscle myosin II plays in driving mechanosensing and focus specifically on motility. In a closely related discussion, we also describe stress fiber classification schemes and the differing roles of various myosin isoforms in each category. Finally, we briefly highlight recent studies exploring mechanosensing in three-dimensional environments, in which matrix content, structure, and mechanics are often tightly interrelated. Stress fibers and the myosin motors therein represent an intriguing and functionally important biological system in which mechanics, biochemistry, and architecture all converge.

Computer aided detection and classification of acute lymphoblastic leukemia cell subtypes based on microscopic image analysis.

Acute lymphoblastic leukemia (ALL) is a cancer that starts from the early version of white blood cells called lymphocytes in the bone marrow. It can spread to different parts of the body rapidly and if not treated, would probably be deadly within a couple of months. Leukemia cells are categorized into three types of L1, L2, and L3. The cancer is detected through screening of blood and bone marrow smears by pathologists. But manual examination of blood samples is a time-consuming and boring procedure as well as limited by human error risks. So to overcome these limitations a computer-aided detection system, capable of discriminating cancer from noncancer cases and identifying the cancerous cell subtypes, seems to be necessary. In this article an automatic detection method is proposed; first cell nucleus is segmented by fuzzy c-means clustering algorithm. Then a rich set of features including geometric, first- and second-order statistical features are obtained from the nucleus. A principal component analysis is used to reduce feature matrix dimensionality. Finally, an ensemble of SVM classifiers with different kernels and parameters is applied to classify cells into four groups, that is noncancerous, L1, L2, and L3. Results show that the proposed method can be used as an assistive diagnostic tool in laboratories.

Direct influence of culture dimensionality on human mesenchymal stem cell differentiation at various matrix stiffnesses using a fibrous self-assembling peptide hydrogel.

Much is unknown about the effects of culture dimensionality on cell behavior due to the lack of biomimetic substrates that are suitable for directly comparing cells grown on two-dimensional (2D) and encapsulated within three-dimensional (3D) matrices of the same stiffness and biochemistry. To overcome this limitation, we used a self-assembling peptide hydrogel system that has tunable stiffness and cell-binding site density as well as a fibrous microarchitecture resembling the structure of collagen. We investigated the effect of culture dimensionality on human mesenchymal stem cell differentiation at different values of matrix stiffness (G'=0.25, 1.25, 5, and 10 kPa) and a constant RGD (Arg-Gly-Asp) binding site concentration. In the presence of the same soluble induction factors, culture on top of stiff gels facilitated the most efficient osteogenesis, while encapsulation within the same stiff gels resulted in a switch to predominantly terminal chondrogenesis. Adipogenesis dominated at soft conditions, and 3D culture induced better adipogenic differentiation than 2D culture at a given stiffness. Interestingly, initial matrix-induced cell morphology was predictive of these end phenotypes. Furthermore, optimal culture conditions corresponded to each cell type's natural niche within the body, highlighting the importance of incorporating native matrix dimensionality and stiffness into tissue engineering strategies. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 2356-2368, 2016.

Minimum Entropy as a Measure of Effective Dimensionality

We demonstrate that eigenvalues minimize information entropy of the main diagonal elements of a symmetric matrix over all possible orthogonal transforms. This legitimizes the use of the exponential entropy of standardized eigenvalues as a measure of effective covariance matrix dimensionality. In particular, this provides rigorous justification for the choice of the PCA basis in the construction of Effective Number of Trading Dimensions (ENTD) introduced in Gnedenko and Yelnik (2016).

Assessing the impact of grass invasion on the population dynamics of a threatened Caribbean dry forest cactus

The negative impact of invasive plants on native species has been well documented, but little is known about the specific role that invaders play on the population decline of native species. Here we used demographic models to evaluate how the alien grass Megathyrsus maximus affects the population dynamics of the native cactus Harrisia portoricensis. Demographic data gathered for H. portoricensis in grass-invaded and non-invaded areas were used to construct matrix projection models. Our demographic analysis includes numerical simulations, life table response experiments, life-cycle parameters and a systematic evaluation of the effects of matrix dimensionality. Results revealed that, while positive λ values can be achieved in grass-free areas dominated by native vegetation, population growth rates of H. portoricensis are reduced in grass-invaded areas (λ=0.88–0.91). Models predicted that H. portoricensis populations in grass-invaded areas might become extinct in the next 14–59years, suggesting that the long-term persistence of this cactus may be linked to the fate of the grass invasion. Overall, our data show that the conversion of native forests into grass-dominated areas is having detrimental impacts on the population dynamics of native species, creating novel regeneration barriers that native species cannot surpass. Under this scenario, management strategies designed for the conservation of H. portoricensis should consider grass-eradication and control policies and long-term monitoring of populations. The information derived from this work may help us understand the mechanisms by which invasive species are gaining dominance over native species, which is crucial for managing and predicting biological invasions.

Role of Topographic Cues on Cancer Cell Proliferation

Metastasis from a primary epithelial tumor is one of the main causes of cancer related deaths. While the roles of biochemical cues on the metastatic cascade are well known, mounting evidences suggest that physical cues such as extracellular matrix (ECM) stiffness, dimensionality, and topography also direct cancer cell behavior. Although the role of stiffness on proliferative response of cancer cells has been well studied, little is known about the effect of topographic cues in guiding cancer cell proliferation. Here, we examined the effect of topographic cues on cancer cell proliferation by fabricating micron scale topographic features. We observed that the proliferation response of non-cancer breast epithelial cells (MCF-10A) but not of metastatic (MDA-MB-231) and non-metastatic (MCF-7) breast cancer cells; decreases on the microgratings (gratings widths of 2, 3 and 4 μm) across all the ECM proteins, namely, fibronectin, collagen and laminin. However, isotropic features such as micropillars (pillars diameters of 2, 3 and 4 μm) do not reduce the proliferation of MCF-10A, indicating that the anisotropic environmental cues are essential for this process. Interestingly, micrograting mediated proliferation reduction is prevented in presence of acto-myosin contraction inhibitory drugs, namely, Y-27632 and blebbistatin, thereby confirming the activation of Rho-ROCK-Myosin in this phenomenon. In conclusion, we observe the existence of Mechanically Induced Dormancy (MID) where topographical cues induces proliferation inhibitory response to the normal epithelial cells but the malignant cells could successfully overcome this inhibitory barrier and continue uncontrolled proliferation.

Simulation of molecular Auger spectra using a two-electron Dyson propagator

In order to simulate Auger electron spectra (AES), we propose the use of the two-electron Dyson propagator with the shifted denominator approximation (SD2). The double ionization potentials (DIPs) of molecules calculated using the SD2 method have shown good agreement with experimental data. This method can be used to calculate each DIP separately, and reducing the matrix dimensionality into that of only a two-hole configurations. We carried out AES simulations of water (H2O), ethylene (C2H4), and formaldehyde (H2CO) molecules and compared with the observed spectra. Furthermore Auger line shapes of glycine and hydrated glycine molecules were simulated, it found out that the peaks of nitrogen K-LL Auger were broadened due to hydration. From these results, we conclude that the SD2 method is very useful for the calculation of DIPs to investigate the properties of a double ionized molecule.

Matrix dimensionality and stiffness cooperatively regulate osteogenesis of mesenchymal stromal cells

Osteogenic potential of mesenchymal stromal cells (MSCs) is mechanosensitive. It’s affected by the mechanical properties of the cellular microenvironment, particularly its mechanical modulus. To explore the effect of mechanical modulus on osteogenesis in the third dimension (3D), this study used a novel polyacrylamide (PA) scaffold whose pores are monodisperse and spherical, the mechanical moduli of which can be tuned across a wide range. It was found that MSCs have similar proliferation rates in PA scaffolds independent of the matrix stiffness. The contractile force exerted by MSCs inside PA scaffolds was strong enough to deform the pores of scaffolds made of more compliant PAs (whose shear modulus, Gscaffold′<4kPa). Only scaffolds of the highest stiffness (Gscaffold′=12kPa) can withhold the contraction from MSCs. After osteogenic induction for 21days, the expression profiles of marker genes showed that PA scaffolds of Gscaffold′=12kPa promoted osteogenesis of MSCs. Confocal image analysis demonstrated that there are more F-actin cytoskeletons and bundled stress fibers at higher matrix moduli in 2D and 3D. Moreover, the 3D porous structure promotes osteogenesis of MSCs more than 2D flat substrates. Together, the differences of cellular behaviors when cultured in 2D and 3D systems are evident. The PA scaffolds developed in the present study can be used for further investigation into the mechanism of MSC mechanosensing in the 3D context. Statement of SignificanceMechanical properties of the microenvironment affect cellular behaviors, such as matrix stiffness. Traditionally, cell biological investigations have mostly employed cells growing on 2D substrates. The 3D porous PA scaffolds with the same topological conformation and pore sizes but different stiffness generated in this study showed that the differences of cellular behaviors in 2D and 3D systems are evident. Our 3D scaffolds provide insights into tissue engineering when stem cells incorporated with 3D scaffolds and support the future studies of cellular mechanobiology as well as the elucidation the role mechanical factor plays on the physiology and fate determination of MSCs in the 3D context.

Application of physics in the study of cell polarity during tumor cell migration

Investigation of tumors from a physics perspective has attracted more and more attention since the initiation, development, and metastasis of tumors are strongly influenced by the physical interactions between the tumor cells and their microenvironments. Since tumor metastasis accounts for more than 90% of cancer-associated death, one of the focuses is to understand its underlying mechanism, especially how tumor cells polarize during their migration. Cell polarization directs tumor-cell migration in response to a spatial stimulus, e.g., the gradient of chemokine or oxygen molecules. It forms the front and back edges of cells by estiblishing asymmetric distributions of cell polarity proteins such as the Rho family GTPases and organelles such as Golgi. This paper reviews how the experimental and theoretical studies combining physics with biology reveal the underlying mechanisms of cell migration and cell polarity. Experimental results demonstrate that the physics clues including extracellular matrix's mechanical properties, dimensionality, and topography are strongly coupled with the biochemical reactions to establish and maintain the cell polarity and direct cell migration. The cell migration mode in a more physiological three-dimensional (3D) matrix is different from that in a two-dimensional(2D) system. Moreover, the membrane tension is suggested to maitain cell polarity by inhibiting polarization processes outside the front edge. On the other hand, a series of reaction diffusion models have been developed to characterize cell polarity. Representative examples inculding Turing-type model, local-excitation and global-inhibition (LEGI) model, and wave-pinning model can capture certain features of cell polarization, however none of them takes the physical factors, such as the membrane tension, into account hence fails to explain previous published experimental results about the membrane tension with cell polarization. To further improve our understanding of the mechanism of cell polarity, in the future study it is experimentally important to estiblish 3D tumor systems and study the gene regulation network that can control cell polariztion by advanced microscope; theroetically it is of importance to build mathematical models for the chemical reaction diffusion systems coupled with the mechanical factors such as membarne tension. These studies will reveal the molecular mechanism of cell polarization and cell migration under a more physiological relevant condition. They may also help us understand how the higher deformation ability of cancer stem cells provides the higher migration capability compared with the normal cancer cells. Ultimately, they will facilitate developing new therapeutic strategy against tumor metastasis by targeting the signaling of tumor cells in response of physical stimuli.