Mathematical model to study the aging of the human follicle according to the telomerase activity

An in-silico approach to the dynamics of proliferation potential in stem cells and the study of different therapies in cases of ovarian dysfunction

A discrete mathematical model based on ordinary differential equations and the associated continuous model formed by a partial differential equation, which simulate the generational and temporal evolution of a stem cell population, are proposed. The model parameters are the maximum proliferation potential and the rates of mitosis, death events and telomerase activity. The mean proliferation potential at each point in time is suggested as an indicator of population aging. The model is applied on hematopoietic stem cells (HSCs), with different telomerase activity rates, in a range of variation of maximum proliferation potential in healthy individuals, to study the temporal evolution of aging. HSCs express telomerase, however not at levels that are sufficient for maintaining constant telomere length with aging [1,2]. Women with primary ovarian insufficiency (POI) are known to have low telomerase activity in granulosa cells and peripheral blood mononuclear cells [3]. Extrapolating this to hematopoietic stem cells, the mathematical model shows the differences in proliferation potential of the cell populations when telomerase expression is activated using sexual steroids, though the endogenous promoter or with gene therapy using exogenous, stronger promoters within the adeno-associated virus. In the first case, proliferation potential of cells from POI condition increases, but when adeno-associated viruses are used, the proliferation potential reaches the levels of healthy cell populations.

Human-mouse comparison of the multistage nature of radiation carcinogenesis in a mathematical model

Mouse models are vital for assessing risk from environmental carcinogens, including ionizing radiation, yet the interspecies difference in the dose response precludes direct application of experimental evidence to humans. Herein, we take a mathematical approach to delineate the mechanism underlying the human-mouse difference in radiation-related cancer risk. We used a multistage carcinogenesis model assuming a mutational action of radiation to analyze previous data on cancer mortality in the Japanese atomic bomb survivors and in lifespan mouse experiments. Theoretically, the model predicted that exposure will chronologically shift the age-related increase in cancer risk forward by a period corresponding to the time in which the spontaneous mutational process generates the same mutational burden as that the exposure generates. This model appropriately fitted both human and mouse data and suggested a linear dose response for the time shift. The effect per dose decreased with increasing age at exposure similarly between humans and mice on a per-lifespan basis (0.72- and 0.71-fold, respectively, for every tenth lifetime). The time shift per dose was larger by two orders of magnitude in humans (7.8 and 0.046 years per Gy for humans and mice, respectively, when exposed at ~35% of their lifetime). The difference was mostly explained by the two orders of magnitude difference in spontaneous somatic mutation rates between the species plus the species-independent radiation-induced mutation rate. Thus, the findings delineate the mechanism underlying the interspecies difference in radiation-associated cancer mortality and may lead to the use of experimental evidence for risk prediction in humans.

Influence of telomerase activity and initial distribution on human follicular aging: Moving from a discrete to a continuum model

A discrete model is proposed for the temporal evolution of a population of cells sorted according to their telomeric length. This model assumes that, during cell division, the distribution of the genetic material to daughter cells is asymmetric, i.e. chromosomes of one daughter cell have the same telomere length as the mother, while in the other daughter cell telomeres are shorter. Telomerase activity and cell death are also taken into account. The continuous model is derived from the discrete model by introducing the generational age as a continuous variable in [0,h], being h the Hayflick limit, i.e. the number of times that a cell can divide before reaching the senescent state. A partial differential equation with boundary conditions is obtained. The solution to this equation depends on the initial telomere length distribution. The initial and boundary value problem is solved exactly when the initial distribution is of exponential type. For other types of initial distributions, a numerical solution is proposed. The model is applied to the human follicular growth from preantral to preovulatory follicle as a case study and the aging rate is studied as a function of telomerase activity, the initial distribution and the Hayflick limit. Young, middle and old cell-aged initial normal distributions are considered. In all cases, when telomerase activity decreases, the population ages and the smaller the h value, the higher the aging rate becomes. However, the influence of these two parameters is different depending on the initial distribution. In conclusion, the worst-case scenario corresponds to an aged initial telomere distribution.

Ovarian Telomerase and Female Fertility

Women's fertility is characterized both quantitatively and qualitatively mainly by the pool of ovarian follicles. Monthly, gonadotropins cause an intense multiplication of granulosa cells surrounding the oocyte. This step of follicular development requires a high proliferation ability for these cells. Telomere length plays a crucial role in the mitotic index of human cells. Hence, disrupting telomere homeostasis could directly affect women's fertility. Strongly expressed in ovaries, telomerase is the most effective factor to limit telomeric attrition and preserve ovarian reserve. Considering these facts, two situations of infertility could be correlated with the length of telomeres and ovarian telomerase activity: PolyCystic Ovary Syndrome (PCOS), which is associated with a high density of small antral follicles, and Premature Ovarian Failure (POF), which is associated with a premature decrease in ovarian reserve. Several authors have studied this topic, expecting to find long telomeres and strong telomerase activity in PCOS and short telomeres and low telomerase activity in POF patients. Although the results of these studies are contradictory, telomere length and the ovarian telomerase impact in women's fertility disorders appear obvious. In this context, our research perspectives aimed to explore the stimulation of ovarian telomerase to limit the decrease in the follicular pool while avoiding an increase in cancer risk.

Mathematical modelling of ageing acceleration of the human follicle due to oxidative stress and other factors

There is a gradual telomere shortening due to the inability of the replication machinery to copy the very ends of chromosomes. Additionally, other factors such as high levels of oxidation (free radicals or reactive oxygen species (ROS)), e.g. due to cumulated stress, inflammation or tobacco smoke, accelerate telomere shortening. In humans, the average telomere length is about 10-15 kb at birth and telomeres shorten at a pace of 70 bp per year. However, when cells are exposed to ROS, telomere attrition happens at a faster pace, generating a wide variety of telomere size distribution in different length percentiles, which are different to what is expected just by age. In this work, the generational age of a cell is associated with its telomere length (TL), from certain maximum to the minimal TL that allows replication. In order to study the accumulation of aged granulosa cells in human follicles, from preantral to preovulatory size, a mathematical model is proposed, regarding different degrees of accelerated telomere shortening, which reflect the action of ROS in addition to the telomere shortening that happens after cell division. In cases of cells with TL shorter than cells with average TL, with low telomerase activity and accelerated telomere shortening, the mathematical model predicts an aged outcome in preovulatory follicles. The model provides a plausible explanation for what has been observed in oocytes from older women, which have been exposed to ROS for a longer period of time and have bad outcomes after in vitro fertilization.