Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools.

Biophysical cues influence many aspects of cell behavior. Stiffness of the extracellular matrix is probed by cells and transduced into biochemical signals through mechanotransduction protein networks, strongly influencing stem cell behavior. Cellular stemness is intimately related with mechanical properties of the cell, like intracellular contractility and stiffness, which in turn are influenced by the microenvironment. Pluripotency is associated with soft and low-contractility cells. Hence, we postulated that soft cell culture substrates, presumably inducing low cellular contractility and stiffness, increase the reprogramming efficiency of mesenchymal stem/stromal cells (MSCs) into induced pluripotent stem cells (iPSCs). We demonstrate that soft substrates (1.5 or 15 kPa polydimethylsiloxane – PDMS) caused modulation of several cellular features of MSCs into a phenotype closer to pluripotent stem cells (PSCs). MSCs cultured on soft substrates presented more relaxed nuclei, lower maturation of focal adhesions and F-actin assembling, more euchromatic and less heterochromatic nuclear DNA regions, and increased expression of pluripotency-related genes. These changes correlate with the reprogramming of MSCs, with a positive impact on the kinetics, robustness of colony formation and reprogramming efficiency. Additionally, substrate stiffness influences several phenotypic features of iPS cells and colonies, and data indicates that soft substrates favor full iPSC reprogramming.

Hydrogen peroxide (H2O2) is a key signaling agent. Its best characterized signaling actions in mammalian cells involve the early oxidation of thiols in cytoplasmic phosphatases, kinases and transcription factors. However, these redox targets are orders of magnitude less H2O2-reactive and abundant than cytoplasmic peroxiredoxins. How can they be oxidized in a signaling time frame? Here we investigate this question using computational reaction-diffusion models of H2O2 signaling. The results show that at H2O2 supply rates commensurate with mitogenic signaling a H2O2 concentration gradient with a length scale of a few tenths of μm is established. Even near the supply sites H2O2 concentrations are far too low to oxidize typical targets in an early mitogenic signaling time frame. Furthermore, any inhibition of the peroxiredoxin or increase in H2O2 supply able to drastically increase the local H2O2 concentration would collapse the concentration gradient and/or cause an extensive oxidation of the peroxiredoxins I and II, inconsistent with experimental observations. In turn, the local concentrations of peroxiredoxin sulfenate and disulfide forms exceed those of H2O2 by several orders of magnitude. Redox targets reacting with these forms at rate constants much lower than that for, say, thioredoxin could be oxidized within seconds. Moreover, the spatial distribution of the concentrations of these peroxiredoxin forms allows them to reach targets within 1 μm from the H2O2 sites while maintaining signaling localized. The recruitment of peroxiredoxins to specific sites such as caveolae can dramatically increase the local concentrations of the sulfenic and disulfide forms, thus further helping these species to outcompete H2O2 for the oxidation of redox targets. Altogether, these results suggest that H2O2 signaling is mediated by localized redox relays whereby peroxiredoxins are oxidized to sulfenate and disulfide forms at H2O2 supply sites and these forms in turn oxidize the redox targets near these sites.

Sprouting angiogenesis, where new blood vessels grow from pre-existing ones, is a complex process where biochemical and mechanical signals regulate endothelial cell proliferation and movement. Therefore, a mathematical description of sprouting angiogenesis has to take into consideration biological signals as well as relevant physical processes, in particular the mechanical interplay between adjacent endothelial cells and the extracellular microenvironment. In this work, we introduce the first phase-field continuous model of sprouting angiogenesis capable of predicting sprout morphology as a function of the elastic properties of the tissues and the traction forces exerted by the cells. The model is very compact, only consisting of three coupled partial differential equations, and has the clear advantage of a reduced number of parameters. This model allows us to describe sprout growth as a function of the cell-cell adhesion forces and the traction force exerted by the sprout tip cell. In the absence of proliferation, we observe that the sprout either achieves a maximum length or, when the traction and adhesion are very large, it breaks. Endothelial cell proliferation alters significantly sprout morphology, and we explore how different types of endothelial cell proliferation regulation are able to determine the shape of the growing sprout. The largest region in parameter space with well formed long and straight sprouts is obtained always when the proliferation is triggered by endothelial cell strain and its rate grows with angiogenic factor concentration. We conclude that in this scenario the tip cell has the role of creating a tension in the cells that follow its lead. On those first stalk cells, this tension produces strain and/or empty spaces, inevitably triggering cell proliferation. The new cells occupy the space behind the tip, the tension decreases, and the process restarts. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of forces in sprouting, hence underlining the necessary collaboration between modelling and molecular biology techniques to improve the current state-of-the-art. Sprouting angiogenesis—a process by which new blood vessels grow from existing ones—is an ubiquitous phenomenon in health and disease of higher organisms, playing a crucial role in organogenesis, wound healing, inflammation, as well as on the onset and progression of over 50 different diseases such as cancer, rheumatoid arthritis and diabetes. Mathematical models have the ability to suggest relevant hypotheses with respect to the mechanisms of cell movement and rearrangement within growing vessel sprouts. The inclusion of both biochemical and mechanical processes in a mathematical model of sprouting angiogenesis permits to describe sprout extension as a function of the forces exerted by the cells in the tissue. It also allows to question the regulation of biochemical processes by mechanical forces and vice-versa. In this work we present a compact model of sprouting angiogenesis that includes the mechanical characteristics of the vessel and the tissue. We use this model to suggest the mechanism for the regulation of proliferation within sprout formation. We conclude that the tip cell has the role of creating a tension in the cells that follow its lead. On those first cells of the stalk, this tension produces strain and/or empty spaces, inevitably triggering cell proliferation. The new cells occupy the space behind the tip, the tension decreases, and the process restarts. The modelling strategy used, deemed phase-field, permits to describe the evolution of the shape of different domains in complex systems. It is focused on the movement of the interfaces between the domains, and not on an exhaustive description of the transport properties within each domain. For this reason, it requires a reduced number of parameters, and has been used extensively in modelling other biological phenomena such as tumor growth. The coupling of mechanical and biochemical processes in a compact mathematical model of angiogenesis will enable the study of lumen formation and aneurisms in the near future. Also, this framework will allow the study of the action of flow in vessel remodelling, since local forces can readily be coupled with cell movement to obtain the final vessel morphology.

We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order parameter advected by a fluid whose velocity field satisfies the Navier-Stokes equation. In each case the equation of motion for the interface height reduces to an anisotropic Burgers equation. The scaling exponents that describe the growth and coarsening of the interface are calculated exactly in any dimension in the case of conserved and nonconserved dynamics. For a fluid-advected conserved order parameter we determine the exponents, but we are unable to build a consistent perturbative expansion to support their validity.

We carry out systematic Monte Carlo simulations of Gō lattice proteins to investigate and compare the folding processes of two model proteins whose native structures differ from each other due to the presence of a trefoil knot located near the terminus of one of the protein chains. We show that the folding time of the knotted fold is larger than that of the unknotted protein and that this difference in folding time is particularly striking in the temperature region below the optimal folding temperature. Both proteins display similar folding transition temperatures, which is indicative of similar thermal stabilities. By using the folding probability reaction coordinate as an estimator of folding progression we have found out that the formation of the knot is mainly a late folding event in our shallow knot system.