In embryogenesis, immature mesenchymal cells aggregate and organize into patterned tissues. Later in life, a pathological recapitulation of this process takes place in atherosclerotic lesions, when vascular mesenchymal cells organize into trabecular bone tissue within the artery wall. Here we show that multipotential adult vascular mesenchymal cells self-organize in vitro into patterns that are predicted by a mathematical model based on molecular morphogens interacting in a reaction-diffusion process. We identify activator and inhibitor morphogens for stripe, spot, and labyrinthine patterns and confirm the model predictions in vitro. Thus, reaction-diffusion principles may play a significant role in morphogenetic processes in adult mesenchymal cells. In embryonic development, mesenchymal stem cells organize into condensations of varying sizes and shapes to form patterned tissues, such as ribs, vertebrae, and honeycombed trabeculae in long bones. In adult disease, such as atherosclerosis and aortic valvular stenosis, these embryonic events recur, as multipotential vascular mesenchymal cells (VMCs) differentiate into osteoblasts and other cell types (1). Fully formed bone arises in the artery wall and in cardiac valves, under the control of developmental genes (2, 3). This ectopic tissue forms focal and nodular patterns in a patchy distribution throughout the vasculature. We investigated the pattern formation mechanisms in these cells.When cultures of VMCs are enzymatically dissociated and plated homogeneously in tissue culture, they first form uniform monolayers, with no apparent pattern. But over Ϸ20 days, the cells proliferate and organize into a sequence of distinct patterns. At day 1, the VMCs show no preferred alignment (Fig. 1a). By day 4, cells begin to align with their neighbors (Fig. 1b, ''swirls''). By day 10, the cells aggregate into regularly spaced, stripe-like ridges of high cell density, Ϸ40 m in width (Fig. 1c). Over the next several days, these high-density ridges gradually interconnect into labyrinthine patterns, with a preferred spacing, Ϸ100 m (Fig. 1d). Cells in the center of the ridge then calcify, forming the bone mineral hydroxylapatite (2). At higher magnification, individual monolayer cells can be seen to orient perpendicular to the edges of the multicellular ridge (Fig. 1e), suggesting chemotactic migration.As first proposed by Turing (4), pattern formation in biology can often be modeled mathematically by postulating ''morphogens'' that react chemically and diffuse. He showed that a highly simplified reaction-diffusion partial differential equation could indeed exhibit pattern formation emerging from a homogeneous state (4). Reaction-diffusion equations, modeling the interactions of activators and their inhibitors, have since been used to analyze pattern formation in many chemical and biological systems (5-9). Pattern formation modeling in biology began with mathematical models of the chemotaxis of single-celled organisms (10); more sophisticated models for chemotaxis have since been d...

The reductionist approach has dominated the fields of biology and medicine for nearly a century. Here, we present a systems science approach to the analysis of physiological waveforms in the context of a specific case, cardiovascular physiology. Our goal in this study is to introduce a methodology that allows for novel insight into cardiovascular physiology and to show proof of concept for a new index for the evaluation of the cardiovascular system through pressure wave analysis. This methodology uses a modified version of sparse time-frequency representation (STFR) to extract two dominant frequencies we refer to as intrinsic frequencies (IFs; v 1 and v 2 ). The IFs are the dominant frequencies of the instantaneous frequency of the coupled heart þ aorta system before the closure of the aortic valve and the decoupled aorta after valve closure. In this study, we extract the IFs from a series of aortic pressure waves obtained from both clinical data and a computational model. Our results demonstrate that at the heart rate at which the left ventricular pulsatile workload is minimized the two IFs are equal (v 1 ¼ v 2 ). Extracted IFs from clinical data indicate that at young ages the total frequency variation (Dv ¼ v 1 2 v 2 ) is close to zero and that Dv increases with age or disease (e.g. heart failure and hypertension). While the focus of this paper is the cardiovascular system, this approach can easily be extended to other physiological systems or any biological signal.

The electrogenic Na(+)-HCO(3)(-) cotransporters play an essential role in regulating intracellular pH and extracellular acid-base homeostasis. Of the known members of the bicarbonate transporter superfamily (BTS), NBC1 and NBC4 proteins have been shown to be electrogenic. The electrogenic nature of these transporters results from the unequal coupling of anionic and cationic fluxes during each transport cycle. This unique property distinguishes NBC1 and NBC4 proteins from other sodium bicarbonate cotransporters and members of the bicarbonate transporter superfamily that are known to be electroneutral. Structure-function studies have played an essential role in revealing the basis for the modulation of the coupling ratio of NBC1 proteins. In addition, the recent transmembrane topographic analysis of pNBC1 has shed light on the potential structural determinants that are responsible for ion permeation through the cotransporter. The experimentally difficult problem of determining the nature of anionic species being transported by these proteins (HCO(3)(-) versus CO(3)(2-)) is analyzed using a theoretical equilibrium thermodynamics approach. Finally, our current understanding of the molecular mechanisms responsible for the regulation of ion coupling and flux through electrogenic sodium bicarbonate cotransporters is reviewed in detail.

Because Raman spectroscopy has high discrimination for glucose, a data set of practical dimensions appears to be sufficient for universal calibration. Improvements based on reducing the variance of blood perfusion are expected to reduce the prediction errors substantially, and the inclusion of supplementary calibration points for the wearable device under development will be permissible and beneficial.