Low-dimensional models of single neurons: A review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as sub-threshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type

Deletion or inhibition of NOD1 favors plaque stability and attenuates atherothrombosis in advanced atherogenesis

Atherothrombosis, the main cause of acute coronary syndromes (ACS), is characterized by the rupture of the atherosclerotic plaque followed by the formation of thrombi. Fatal plaque rupture sites show large necrotic cores combined with high levels of inflammation and thin layers of collagen. Plaque necrosis due to the death of macrophages and smooth muscle cells (SMCs) remains critical in the process. To determine the contribution of the innate immunity receptor NOD1 to the stability of atherosclerotic plaque, Apoe-/- and Apoe-/- Nod1-/- atherosclerosis prone mice were placed on a high-fat diet for 16 weeks to assess post-mortem advanced atherosclerosis in the aortic sinus. The proliferation and apoptosis activity were analyzed, as well as the foam cell formation capacity in these lesions and in primary cultures of macrophages and vascular SMCs obtained from both groups of mice. Our results reinforce the preeminent role for NOD1 in human atherosclerosis. Advanced plaque analysis in the Apoe-/- atherosclerosis model suggests that NOD1 deficiency may decrease the risk of atherothrombosis by decreasing leukocyte infiltration and reducing macrophage apoptosis. Furthermore, Nod1-/- SMCs exhibit higher proliferation rates and decreased apoptotic activity, contributing to thicker fibrous caps with reduced content of pro-thrombotic collagen. These findings demonstrate a direct link between NOD1 and plaque vulnerability through effects on both macrophages and SMCs, suggesting promising insights for early detection of biomarkers for treating patients before ACS occurs.This work was supported by the Ministerio Economía, Industria y Competitividad/Agencia Estatal de Investigación (SAF2016-79490-R, RTI2018-094727-B-100, SAF2015-64767-R, SAF2016-75004-R, SAF2017-82436-R/RTC2017-6283-1, PID2019-108977RB-100), Centro de Investigación Biomédica en Red en Enfermedades Cardiovasculares (CB16/11/00405, CB16/11/00257, CB16/11/00222), Fundación Ramón Areces (CIUP18A3864), Consorcio de Investigación en Red de la Comunidad de Madrid, S2017/BMD-3686 and Fondo Europeo de Desarrollo Regional

Endothelial NOD1 directs myeloid cell recruitment in atherosclerosis through VCAM-1

Atherosclerosis is a chronic disease characterized by vascular lipid retention and inflammation, and pattern recognition receptors (PRRs) are important contributors in early stages of the disease. Given the implication of the intracellular PRR nucleotide-binding oligomerization domain 1 (NOD1) in cardiovascular diseases, we investigated its contribution to early atherosclerosis. We evidenced NOD1 induction in atherosclerotic human and mouse tissues, predominantly in vascular endothelial cells. Accordingly, NOD1 genetic inactivation in Apoe-/- mice reduced not only atherosclerosis burden, but also monocyte and neutrophil accumulation in atheromata. Of note, in the presence of either peptidoglycan or oxidized LDLs, endothelial NOD1 triggered VCAM-1 up-regulation through the RIP2-NF-¿B axis in an autocrine manner, enhancing firm adhesion of both sets of myeloid cells to the inflamed micro- and macrovasculature in vivo. Our data define a major proatherogenic role for endothelial NOD1 in early leukocyte recruitment to the athero-prone vasculature, thus introducing NOD1 as an innovative therapeutic target and potential prognostic moleculeThis work was supported bythe the Ministry of Science, Innovation and Universities(Grants SAF2015-64767-R, SAF2016-79490-R, SAF2015-70747-R, SAF2016-75004-R, SAF2017-82436-R/RTC2017-6283-1), the Center for Biomedical Research Network Consortium in Cardiovascular Diseases (Grants CB16/11/00257, CB16/11/00405, CB/11/00222), Community of Madrid Grant BMD/3686, the German Research Foundation (Grants SFB914 TPA02/B08/B09/Z03, SFB1123 TP A06/B05/B08/Z01), and the Netherlands Organization for Scientific Research (VIDI proj-ect 91712303). This project was also financed, in part, by theEuropean Regional Development Fund. O.S. and L.B. con-tributed equally as senior authors