A condition for setting off ectopic waves in computational models of excitable cells

The purpose of this paper is to study the stability of steady state solutions of the Monodomain model equipped with Luo-Rudy I kinetics. It is well established that re-entrant arrhythmias can be created in computational models of excitable cells. Such arrhythmias can be initiated by applying an external stimulus that interacts with a partially refractory region, and spawn breaking waves that can eventually generate extremely complex wave patterns commonly referred to as fibrillation. An ectopic wave is one possible stimulus that may initiate fibrillation. Physiologically, it is well known that ectopic waves exist, but the mechanism for initiating ectopic waves in a large collection of cells is poorly understood. In the present paper we consider computational models of collections of excitable cells in one and two spatial dimensions. The cells are modeled by Luo-Rudy I kinetics, and we assume that the spatial dynamics is governed by the Monodomain model. The mathematical analysis is carried out for a reduced model that is known to provide good approximations of the initial phase of solutions of the Luo-Rudy I model. A further simplification is also introduced to motivate and explain the results for the more complicated models. In the analysis the cells are divided into two regions; one region (N) consists of normal cells as model by the standard Luo-Rudy I model, and another region (A) where the cells are automatic in the sense that they would act as pacemaker cells if they where isolated from their surroundings. We let delta denote the spatial diffusion and a denote a characteristic length of the automatic region. It has previously been shown that reducing diffusion or increasing the automatic region enhances ectopic activity. Here we derive a condition for the transition from stable resting state to ectopic wave spread. Under suitable assumptions on the model we provide mathematical and computational arguments indicating that there is a constant eta such that a steady state solution of this system is stable whenever delta approximately > etaa(2), and unstable whenever delta approximately < etaa(2).     

Marfan syndrome: exclusion of genetic linkage to five genes coding for connective tissue components in the long arm of chromosome 2

Summary Marfan syndrome represents a heterogeneous connective tissue disease, the symptoms arising in several tissues and organs. The defective gene(s) behind this autosomal dominant condition has not been found despite considerable research. The main targets of the research have been the genes coding for connective tissue components. Several of the candidate genes suspected to be defective in Marfan syndrome are located on the long arm of chromosome 2. These genes include a cluster of two genes coding for fibrillar collagens COL3A1 and COL5A2, and a third member of the collagen gene family: COL6A3. Furthermore, genes for elastin (ELN) and fibronectin (FN) are also located in this area of chromosome 2. We studied this chromosomal area using restriction fragment length polymorphism (RFLP) linkage analysis in five Finnish Marfan families with affected members in three generations. In two point linkage analyses, Lod scores of –3.192 ( = 0.1) to COL3A1, –1.683 ( = 0) to COL6A3 and –2.664 ( = 0.01) to FN were obtained, whereas the linkage analysis between elastin and the disease was non-informative (Lod score 0.444, = 0). With the multipoint linkage analysis that permits simultaneous examination of several loci and more efficient use of family data, we obtained an exclusion of all these loci as the site of the mutation leading to Marfan syndrome in these families.     

First record of cysts in the tidal tardigrade Echiniscoides sigismundi

Tardigrades are microscopic metazoans that withstand environmental extremes by entering dormant states, such as cryptobiosis (latent life). In addition, they may also form cysts. Here, we present the first report of cyst formation in a marine heterotardigrade, i.e., Echiniscoides sigismundi, which constitutes a cryptic species complex present worldwide in tidal zones. The cysts were initially discovered during experimental series constructed to investigate osmotic stress tolerance. The animals, which eventually formed cysts, showed signs of an imminent molt at the beginning of experimentation. We use the term “cyst” for stages, where a total of three or more cuticles have been synthesized. Our observations show that encystment in E. sigismundi involves synthesizing of at least two new cuticle layers. Legs with discharged claws are present in connection with the first outer cuticle, as well as the second cuticular layer. In the most developed cyst, a third cuticle lacking claws seems to surround the animal, which is delineated by a fourth cuticle. Many features are shared with the well-studied cysts of eutardigrades. The cysts of E. sigismundi, however, lack pigmentation and have an extra set of claws, and the animal inside retains buccopharyngeal sclerified parts, until discharging the third cuticle. The finding of cysts in a marine heterotardigrade is novel and confirms that encystment also occurs within this major evolutionary lineage.     

A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells

Regional hyperkalemia during acute ischemia may provoke cardiac arrhythmias such as ventricular fibrillation. Despite intense research efforts over the last decades, the problem of finding an efficient anti-arrhythmic drug without dangerous side effects is still open. One approach to analyze the effect of anti-arrhythmic drugs is to do simulations based on mathematical models of collections of cardiomyocytes. Such simulations have recently illuminated the pro-arrhythmic capability of well-established anti-arrhythmic drugs.The purpose of the present note is to introduce a method intended for computing advantageous properties of an anti-arrhythmic drug. For a given model of a normal and an ischemic cell, we introduce a drug as a vector of non-negative real numbers whose components are multiplied by individual terms representing specific ionic currents. The drug vector is computed such that the action potentials of the resulting drugged cells are as close as possible to the action potential of a normal (not drugged) cell. Numerical simulations based on the Luo-Rudy I model and the Hund-Rudy model show that the classical shortened action potential obtained due to hyperkalemia is prolonged by using the drug computed by this method. Furthermore, for both models a 2D collection of spatially coupled ischemic cells give arrhythmogenic solutions before the drug is applied, and stable solutions after the drug is applied. It is emphasized that we do not address the possibility of realizing a drug with the properties computed in this note.