Universality in Few-Body Systems

Low-energy universality in atomic few-body systems as a result of a large two-body scattering length has gained a lot of attention recently. Here, I discuss recent progress in describing the three-body recombination of cold atoms in terms of a finite set of universal scaling functions and review results for the recombination length of cesium-133 atoms obtained with these functions. Furthermore, I will consider the inclusion of effective range corrections and the relevance for further calculations in atomic and nuclear physics.Comment: Plenary talk at 20th European Conference on Few-Body Problems in Physics (EFB 20), Pisa, Italy, 10-14 Sep 2007, FBS style, 2 figue

A mathematical model for electrical stimulation of a monolayer of cardiac cells

BACKGROUND: The goal of our study is to examine the effect of stimulating a two-dimensional sheet of myocardial cells. We assume that the stimulating electrode is located in a bath perfusing the tissue. METHODS: An equation governing the transmembrane potential, based on the continuity equation and Ohm's law, is solved numerically using a finite difference technique. RESULTS: The sheet is depolarized under the stimulating electrode and is hyperpolarized on each side of the electrode along the fiber axis. CONCLUSIONS: The results are similar to those obtained previously by Sepulveda et al. (Biophys J, 55: 987–999, 1989) for stimulation of a two-dimensional sheet of tissue with no perfusing bath present

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.Comment: 26 pages, 13 figures, appendix and 2 movies, as accepted to PLoS ONE 2011/08/0

A reconfigurable real-time compressive-sampling camera for biological applications

Many applications in biology, such as long-term functional imaging of neural and cardiac systems, require continuous high-speed imaging. This is typically not possible, however, using commercially available systems. The frame rate and the recording time of high-speed cameras are limited by the digitization rate and the capacity of on-camera memory. Further restrictions are often imposed by the limited bandwidth of the data link to the host computer. Even if the system bandwidth is not a limiting factor, continuous high-speed acquisition results in very large volumes of data that are difficult to handle, particularly when real-time analysis is required. In response to this issue many cameras allow a predetermined, rectangular region of interest (ROI) to be sampled, however this approach lacks flexibility and is blind to the image region outside of the ROI. We have addressed this problem by building a camera system using a randomly-addressable CMOS sensor. The camera has a low bandwidth, but is able to capture continuous high-speed images of an arbitrarily defined ROI, using most of the available bandwidth, while simultaneously acquiring low-speed, full frame images using the remaining bandwidth. In addition, the camera is able to use the full-frame information to recalculate the positions of targets and update the high-speed ROIs without interrupting acquisition. In this way the camera is capable of imaging moving targets at high-speed while simultaneously imaging the whole frame at a lower speed. We have used this camera system to monitor the heartbeat and blood cell flow of a water flea (Daphnia) at frame rates in excess of 1500 fps

Multi-omics integration identifies key upstream regulators of pathomechanisms in hypertrophic cardiomyopathy due to truncating MYBPC3 mutations

BACKGROUND: Hypertrophic cardiomyopathy (HCM) is the most common genetic disease of the cardiac muscle, frequently caused by mutations in MYBPC3. However, little is known about the upstream pathways and key regulators causing the disease. Therefore, we employed a multi-omics approach to study the pathomechanisms underlying HCM comparing patient hearts harboring MYBPC3 mutations to control hearts. RESULTS: Using H3K27ac ChIP-seq and RNA-seq we obtained 9310 differentially acetylated regions and 2033 differentially expressed genes, respectively, between 13 HCM and 10 control hearts. We obtained 441 differentially expressed proteins between 11 HCM and 8 control hearts using proteomics. By integrating multi-omics datasets, we identified a set of DNA regions and genes that differentiate HCM from control hearts and 53 protein-coding genes as the major contributors. This comprehensive analysis consistently points toward altered extracellular matrix formation, muscle contraction, and metabolism. Therefore, we studied enriched transcription factor (TF) binding motifs and identified 9 motif-encoded TFs, including KLF15, ETV4, AR, CLOCK, ETS2, GATA5, MEIS1, RXRA, and ZFX. Selected candidates were examined in stem cell-derived cardiomyocytes with and without mutated MYBPC3. Furthermore, we observed an abundance of acetylation signals and transcripts derived from cardiomyocytes compared to non-myocyte populations. CONCLUSIONS: By integrating histone acetylome, transcriptome, and proteome profiles, we identified major effector genes and protein networks that drive the pathological changes in HCM with mutated MYBPC3. Our work identifies 38 highly affected protein-coding genes as potential plasma HCM biomarkers and 9 TFs as potential upstream regulators of these pathomechanisms that may serve as possible therapeutic targets

Adenoma Formation following Limited Ablation of p120-Catenin in the Mouse Intestine

p120 loss destabilizes E-cadherin and could therefore result in tumor and/or metastasis-promoting activities similar to those caused by E-cadherin downregulation. Previously, we reported that p120 is essential in the intestine for barrier function, epithelial homeostasis and survival. Conditional p120 ablation in the mouse intestine induced severe inflammatory bowel disease, but long-term cancer-related studies were impossible because none of the animals survived longer than 21 days. Here, we used a tamoxifen-inducible mouse model (Vil-Cre-ERT2;p120fl/fl) to limit the extent of p120 ablation and thereby enable long-term studies. Reducing p120 KO to ∼10% of the intestinal epithelium produced long-lived animals outwardly indistinguishable from controls. Effects of prolonged p120 absence were then evaluated at intervals spanning 2 to 18 months. At all time points, immunostaining revealed microdomains of p120-null epithelium interspersed with normal epithelium. Thus, stochastic p120 ablation is compatible with crypt progenitor cell function and permitted lifelong renewal of the p120-null cells. Consistent with previous observations, a barrier defect and frequent infiltration of neutrophils was observed, suggesting that focal p120 loss generates a microenvironment disposed to chronic inflammation. We report that 45% of these animals developed tumors within 18 months of tamoxifen induction. Interestingly, β-catenin was upregulated in the majority, but none of the tumors were p120 null. Although further work is required to directly establish mechanism, we conclude that limited p120 ablation can promote tumorigenesis by an indirect non-cell autonomous mechanism. Given that byproducts of inflammation are known to be highly mutagenic, we suggest that tumorigenesis in this model is ultimately driven by the lifelong inability to heal chronic wounds and the substantially increased rates of stochastic gene mutation in tissue microenvironments subjected to chronic inflammation. Indeed, although technical issues precluded direct identification of mutations, β-catenin upregulation in human colon cancer almost invariably reflects mutations in APC and/or β-catenin

Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study

Mathematical Modeling and Simulation of Ventricular Activation Sequences: Implications for Cardiac Resynchronization Therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy