Modeling the topological organization of cellular processes

The cell as a dynamical system presents the characteristics of having a dynamical structure. That is, the exact phase space of the system cannot be fixed before the evolution and integrative cell models must state the evolution of the structure jointly with the evolution of the cell state. This kind of dynamical systems is very challenging to model and simulate. New programming concepts must be developed to ease their modeling and simulation. In this context, the goal of the MGS project is to develop an experimental programming language dedicated to the simulation of this kind of systems. MGS proposes a unified view on several computational mechanisms (CHAM, Lindenmayer systems, Paun systems, cellular automata) enabling the specification of spatially localized computations on heterogeneous entities. The evolution of a dynamical structure is handled through the concept of transformation which relies on the topological organization of the system components. An example based on the modeling of spatially distributed biochemical networks is used to illustrate how these notions can be used to model the spatial and temporal organization of intracellular processes.     

Modeling cell migration in 3D

Cell migration is a multi-scale process that integrates signaling, mechanics and biochemical reaction kinetics. Various mathematical models accurately predict cell migration on 2-D surfaces, but are unable to capture the complexities of 3D migration. Additionally, quantitative 3D cell migration models have been few and far between. In this review we look and characterize various mathematical models available in literature to predict cell migration in 3-D matrices and analyze their strengths and possible changes to these models that could improve their predictive capabilities.     

Localised interventions in cellular processes

The once linear view of cell regulatory processes is now changing as we begin to overlay spatial and temporal characteristics onto signalling pathways and dynamic membranous events. To better understand the properties of these spatially restricted processes we must refine our targeting of these events with acute localised manipulations. We review here the diverse application of a dimerisation system, which exploits immunosuppressor/immunophilin biology to provide a route to drug-inducible subdomain interventions. This article is part of a Special Issue entitled: Inhibitors of Protein Kinases (2012).     

Modeling tissue morphogenesis and cancer in 3D

Three-dimensional (3D) in vitro models span the gap between two-dimensional cell cultures and whole-animal systems. By mimicking features of the in vivo environment and taking advantage of the same tools used to study cells in traditional cell culture, 3D models provide unique perspectives on the behavior of stem cells, developing tissues and organs, and tumors. These models may help to accelerate translational research in cancer biology and tissue engineering.     

Stochastic Modeling of Calcium in 3D Geometry

Release of inflammatory mediators by mast cells in type 1 immediate-hypersensitivity allergic reactions relies on antigen-dependent increases in cytosolic calcium. Here, we used a series of electron microscopy images to build a 3D reconstruction representing a slice through a rat tumor mast cell, which then served as a basis for stochastic modeling of inositol-trisphosphate-mediated calcium responses. The stochastic approach was verified by reaction-diffusion modeling within the same geometry. Local proximity of the endoplasmic reticulum to either the plasma membrane or mitochondria is predicted to differentially impact local inositol trisphosphate receptor transport. The explicit consideration of organelle spatial relationships represents an important step toward building a comprehensive, realistic model of cellular calcium dynamics.     

Modeling 3D Facial Shape from DNA

Human facial diversity is substantial, complex, and largely scientifically unexplained. We used spatially dense quasi-landmarks to measure face shape in population samples with mixed West African and European ancestry from three locations (United States, Brazil, and Cape Verde). Using bootstrapped response-based imputation modeling (BRIM), we uncover the relationships between facial variation and the effects of sex, genomic ancestry, and a subset of craniofacial candidate genes. The facial effects of these variables are summarized as response-based imputed predictor (RIP) variables, which are validated using self-reported sex, genomic ancestry, and observer-based facial ratings (femininity and proportional ancestry) and judgments (sex and population group). By jointly modeling sex, genomic ancestry, and genotype, the independent effects of particular alleles on facial features can be uncovered. Results on a set of 20 genes showing significant effects on facial features provide support for this approach as a novel means to identify genes affecting normal-range facial features and for approximating the appearance of a face from genetic markers.     

Ubiquitin crosstalk connecting cellular processes

Cullin 4 (Cul4), a member of the evolutionally conserved cullin protein family, serves as a scaffold to assemble multisubunit ubiquitin E3 ligase complexes. Cul4 interacts with the Ring finger-containing protein ROC1 through its C-terminal cullin domain and with substrate recruiting subunit(s) through its N-terminus. Previous studies have demonstrated that Cul4 E3 ligase ubiquitylates key regulators in cell cycle control and mediates their degradation through the proteasomal pathway, thus contributing to genome stability. Recent studies from several groups have revealed that Cul4 E3 ligase can target histones for ubiquitylation, and importantly, ubiquitylation of histones may facilitate the cellular response to DNA damage. Therefore, histone ubiquitylation by Cul4 E3 ligase constitutes a novel mechanism through which Cul4 regulates chromatin function and maintains genomic integrity. We outline these studies and suggest that histone ubiquitylation might play important roles in Cul4-regualted chromatin function including the cellular response to DNA damage and heterochromatin gene silencing.     

Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering

Novel tissue‐culture bioreactors employ flow‐induced shear stress as a means of mechanical stimulation of cells. We developed a computational fluid dynamics model of the complex three‐dimensional (3D) microstructure of a porous scaffold incubated in a direct perfusion bioreactor. Our model was designed to predict high shear‐stress values within the physiological range of those naturally sensed by vascular cells (1–10 dyne/cm²), and will thereby provide suitable conditions for vascular tissue‐engineering experiments. The model also accounts for cellular growth, which was designed as an added cell layer grown on all scaffold walls. Five model variants were designed, with geometric differences corresponding to cell‐layer thicknesses of 0, 50, 75, 100, and 125 µm. Four inlet velocities (0.5, 1, 1.5, and 2 cm/s) were applied to each model. Wall shear‐stress distribution and overall pressure drop calculations were then used to characterize the relation between flow rate, shear stress, cell‐layer thickness, and pressure drop. The simulations showed that cellular growth within 3D scaffolds exposes cells to elevated shear stress, with considerably increasing average values in correlation to cell growth and inflow velocity. Our results provide in‐depth analysis of the microdynamic environment of cells cultured within 3D environments, and thus provide advanced control over tissue development in vitro. Biotechnol. Bioeng. 2010; 105: 645–654. © 2009 Wiley Periodicals, Inc.     

Modeling cell migration in 3D: Status and challenges

Cell migration is a multi-scale process that integrates signaling, mechanics and biochemical reaction kinetics. Various mathematical models accurately predict cell migration on 2D surfaces, but are unable to capture the complexities of 3D migration. Additionally, quantitative 3D cell migration models have been few and far between. In this review we look and characterize various mathematical models available in literature to predict cell migration in 3D matrices and analyze their strengths and possible changes to these models that could improve their predictive capabilities.Key words: cell migration, 3D motility, mathematical models, cancer, multi-scale     

The role of the cytoskeleton in cellular force generation in 2D and 3D environments

To adhere and migrate, cells generate forces through the cytoskeleton that are transmitted to the surrounding matrix. While cellular force generation has been studied on 2D substrates, less is known about cytoskeletal-mediated traction forces of cells embedded in more in vivo-like 3D matrices. Recent studies have revealed important differences between the cytoskeletal structure, adhesion, and migration of cells in 2D and 3D. Because the cytoskeleton mediates force, we sought to directly compare the role of the cytoskeleton in modulating cell force in 2D and 3D. MDA-MB-231 cells were treated with agents that perturbed actin, microtubules, or myosin, and analyzed for changes in cytoskeletal organization and force generation in both 2D and 3D. To quantify traction stresses in 2D, traction force microscopy was used; in 3D, force was assessed based on single cell-mediated collagen fibril reorganization imaged using confocal reflectance microscopy. Interestingly, even though previous studies have observed differences in cell behaviors like migration in 2D and 3D, our data indicate that forces generated on 2D substrates correlate with forces within 3D matrices. Disruption of actin, myosin or microtubules in either 2D or 3D microenvironments disrupts cell-generated force. These data suggest that despite differences in cytoskeletal organization in 2D and 3D, actin, microtubules and myosin contribute to contractility and matrix reorganization similarly in both microenvironments.     

Translational control in cellular and developmental processes

Growing evidence indicates that translational control of specific mRNAs contributes importantly to genetic regulation across the breadth of cellular and developmental processes. Synthesis of protein from a specific mRNA can be controlled by RNA-binding proteins at the level of translational initiation and elongation, and translational control is also sometimes coupled to mRNA localization mechanisms. Recent discoveries from invertebrate and vertebrate systems have uncovered novel modes of translational regulation, have provided new insights into how specific regulators target the general translational machinery and have identified several new links between translational control and human disease.     

Phospholipase D in cellular senescence

Cellular senescence appears to be an important part of organismal aging. Cellular senescence is characterized by flattened enlarged morphology, inhibition of DNA replication in response to growth factors, inability to phosphorylate the pRb tumor suppressor protein, inability to produce c-fos or AP-1 and overexpression of a variety of genes, notably p21 (CIP-1/WAF-1) and p16^INK. It is now clear that certain early mitotic signals become defective with the onset of senescence. Among these is the PLD/PKC pathway. Evidence suggests that activation of PLD and PKC is critical for mitogenesis. Recent data suggest that the defect in PLD/PKC in cellular senescence is a result of elevated cellular ceramide levels which inhibit PLD activation. It appears that the elevated ceramide is a result of neutral sphingomyelinase activation. Ceramide acts to inhibit the activation of PLD by possibly three mechanisms, inhibiting activation by Rho, translocation to the membrane and gene expression. Addition of ceramide to young cells not only inhibits PLD but also recapitulates all the standard measures of cellular senescence as described above.     

Modeling of transport processes in stellarators

A relatively simple model of transport processes in stellarators is constructed that is based on neoclassical theory and accounts for anomalous heat losses. The model is used to perform calculations for the L-2M, ATF, CHS, and LHD stellarators over a wide range of plasma densities and absorbed powers. The plasma energy lifetimes calculated for these devices coincide to within factors on the order of unity with those obtained from the ISS95 and LHD empirical scalings.