THE RESEARCH INSTITUTE OF BIOLOGY OF SOUTHERN FEDERAL UNIVERSITY. ROSTOV-ON-DON. Simulation of Drosophila aging in silico

One of the main tasks of modern gerontology is isolation of a group of phenomena essential for aging from epiphenomenona accompanying them. The modern methods of simulation modeling may be the proper tool for correct isolation. The point of their application is reproduction of external aging manifestations in silico, and, in the first place, of standard survival curves with the help of the simplest internal mechanism. It seems that such a mechanism will be prime mover of aging. The aging model of one the most popular objects of experimental biology a fruit fly (Drosophila melanogaster) created by us (http://winmobile.biz/moton/en/moto.html) , is based on the assumption that the key mechanism of aging is cellularity loss, the speed of which is determined by the parameters of active oxygen forms generation in motoneurons. Aging is an amazing phenomenon and in the course of biology development scientists get more and more interested in studying it. The most intriguing question of this field of knowledge can be formulated as follows: what mechanism provides gradual decrease in viability of a multicellular organism? Development of experimental biology methods aroused a desire to answer it, studying the molecular changes which accompany the aging process. Researchers have revealed many such changes starting from lipofuscin accumulation to telomere shortening [1]. Moreover, the system of mechanisms of the somatic cells programmed death was discovered and its participation in "self-destruction" of the whole organism was proved by the number of observations [5, 14]. The success in the search of processes characteristics of which correlate with age also had a reverse side. A lot of aging theories exaggerating the value of some or another molecular change have sprung up. Redundancy of the existing aging hypotheses pool is evident to the majority of authors trying to analyze the state of things in gerontology [1]. A multicellular organism is a multilevel self-organizing system. Activity of its elements is coordinated by the most complicated network of feedbacks. Any action is accompanied by a loop of gene expression changes, synthesis of hormones, immune and electrophysiological reactions, etc. The majority of them influences fitness. Nevertheless, for understanding of the processes taking place, for example, at digestion of food it is enough to keep in mind not more than ten physiological and biochemical reactions. The dialectics of the cognitive process is such that abstraction from the majority of details allows creating conceptual models which become a basis of the further detailed elaboration, but already without any loss of understanding of the essence of the phenomenon studied. The theorist who is searching for the main laws of biological processes can achieve success only referring the majority of reactions accompanying them to epiphenomena. Distinguishing the group of phenomena essential for aging from epiphenomena accompanying them is one of the main tasks of modern gerontology. We believe that modern methods of mathematical modeling can be the tool for distinguishing them properly. The sense of their application is reproduction of the "external" aging manifestations in silico, first of all of the standard survivor curves , by means of the simplest «internal mechanism». This mechanism will apparently be the most essential aging mover. Naturally "the internal mechanism» modeling should be based on the biological facts without contradicting them. Creating the aging model of one of the most popular experimental biology objects – a fruit fly (Drosophila melanogaster) based on the simplest presuppositions possible was the task of this research. Drosophila melanogaster life expectancy is measured by several weeks. This organism is an insect with complete metamorphosis. All somatic cells of an imago are postmitotic. Nevertheless, drosophila «survivor curves» have the S-shape characteristic for the majority of animals [8, 12]. Aging modeling of the given object is essentially facilitated by the fact that cells responsible for this process are identified reliably enough and that the key role of the free-radical processes in aging [12] is clearly demonstrated. As it is known, the basic source of reactive oxygen species in eukaryotic cells is a respiratory chain of mitochondria. One of the main enzymesantioxidants is superoxide dismutase (SOD), catalyzing superoxide anion transformation into hydro peroxide and oxygen. It is known that the drosophilae, incapable of SOD synthesis are characterized by short life expectancy [16]. In the early nineties of the last century scientists succeeded in breeding drosophila, having appreciable quantities of human SOD, however, their life expectancy practically didn't differ from that of the wild type. Then the technique appeared that allowed to "switch on" SOD expression only in the necessary tissues by means of additional genetic construction. Specific expression of this gene in motoneurons turned out to make life expectancy longer. Moreover, human SOD introduction into motoneurons only returned life expectancy characteristic for the wild type to the flies defective in this enzyme. Motoneurons are convenient for modeling because of the fact that their quantity in one fly is defined precisely enough and is about 80 [11]. It is possible to assume that the natural death of a drosophila occurs due to the motoneurons number decrease to a critical level. The model of cellularity loss of a homogeneous population of postmitotic cells describedhttp://www.winmobile.biz/shou/en/demoApp.php, in our work [7] has served as the basis for creation of the drosophila aging model. Its logical bases are as follows: • Postmitotic cells are capable to generate a number of substances provoking programmed cellular death (PCD) for example, hydrogen peroxide. Let us call X the total concentration of such apoptosis signals. • At the increase of X quantity up to a certain limit produced during a time interval which can be named a «cycle»( in this particular case the length of one cycle is 24 hours), the mechanism of self-liquidation works • The average X quantity, produced in cells during a cycle is lower than «a threshold of self-liquidation». • As X quantities for various cells are weakly interdependent, they will be distributed according to the normal law (Gaussian law). The presence of an asymmetry and an excess at the X distribution does not change the analyzed laws essentially. The main thing is that the function of X distribution at convergence of argument to infinity asymptotically approaches zero. As this curve does not cross the X-axis, there can be arbitrary large deviations from average X size. • In a cellular population, at an average level of X production that is lower than the threshold, there will be cells producing the amount of X which will exceed «the threshold of self-liquidation». • The proportion of «self-liquidating» cells during one cycle, and, hence the speed of cellularity loss, depends on the average size and a standard X deviation and level of «a self-destruction threshold» The modification of the model created for the drosophila aging modeling allows to take into account the death of flies reaching some critical level of motoneurons loss. Materials and methods. For the quantitative analysis of the described concept the multiagent imitating model of flies population has been created. The model is realized on Java 2 platform. In the realization of the model the algorithms from the work [3] were used. During model creation organisms (flies) are formed as independent agents. In the simplest studied case such agents do not interact with the environment and with one another. Each fly bears the amount of motoneurons set by the experimenter. The behavior of motoneurons submits to the following logic: it is considered that each motoneuron produces X substance, and its production during the cycle is regulated by the normal distribution law with the parameters that can be set. Threshold value of the Х quantity is also set and exceeding it leads to motoneuron destruction. When the agreed percentage of motoneurons destruction in each separate organism is achieved the fly dies. Thus, observing of the set of the agents formed according to the stated rules, it is possible to draw a survivor curve for flies population. In the course of the experiment two populations of the flies are formed one of which is the control one and the second is exposed to the influence of the geroprotector, changing development of a substance X. The geroprotector introduction schedule is set by the experimenter. The size of control and experimental populations is limited by technical possibilities of a computing platform. Program realization of the model is supplied by user-friendly interface and demands from the potential experimenter the minimum skills of work with computer technics. There is a possibility to vary the parameters mentioned above, or to make computational experiment with parameters by default. It is possible to familiarize with work of the full-function version of this model on the following website:http://winmobile.biz/moton/en/moto.html Results. Survivor curves of wild type flies and of flies with additional superoxide dismutase activity in motoneurons from this work [12] are presented on fig. 1A. Fig. 1. A – experimental survivor curves of wild type flies (empty squares) and of flies with additional SOD expression (black squares); B – virtual survivor curves of wild type flies (black dots) and of flies with additional SOD expression (gray dots) As the figures show, in spite of short life expectancy, experimental drosophilas survivor curves show elements, characteristic for the universal survivor curve for multicellular organisms, including the human – Gompertz-Mejkham curve [10]. It includes the “youth” period (days 0-30) when the survival rate doesn't fall considerably with the years; “maturity-old age