Aging and immortality in a cell proliferation model

Redundancy principle and the role of extreme statistics in molecular and cellular biology

The paradigm of chemical activation rates in cellular biology has been shifted from the mean arrival time of a single particle to the mean of the first among many particles to arrive at a small activation site. The activation rate is set by extremely rare events, which have drastically different time scales from the mean times between activations, and depends on different structural parameters. This shift calls for reconsideration of physical processes used in deterministic and stochastic modeling of chemical reactions that are based on the traditional forward rate, especially for fast activation processes in living cells. Consequently, the biological activation time is not necessarily exponentially distributed. We review here the physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes. We provide examples in cellular transduction, gene activation, cell senescence activation or spermatozoa selection during fertilization, where the rate depends on numbers. We conclude that the statistics of the minimal time to activation set kinetic laws in biology, which can be very different from the ones associated to average times.

Reconstructing the in vivo dynamics of hematopoietic stem cells from telomere length distributions

We investigate the in vivo patterns of stem cell divisions in the human hematopoietic system throughout life. In particular, we analyze the shape of telomere length distributions underlying stem cell behavior within individuals. Our mathematical model shows that these distributions contain a fingerprint of the progressive telomere loss and the fraction of symmetric cell proliferations. Our predictions are tested against measured telomere length distributions in humans across all ages, collected from lymphocyte and granulocyte sorted telomere length data of 356 healthy individuals, including 47 cord blood and 28 bone marrow samples. We find an increasing stem cell pool during childhood and adolescence and an approximately maintained stem cell population in adults. Furthermore, our method is able to detect individual differences from a single tissue sample, i.e. a single snapshot. Prospectively, this allows us to compare cell proliferation between individuals and identify abnormal stem cell dynamics, which affects the risk of stem cell related diseases.

Stochastic simulations of normal aging and Werner's syndrome

Human cells typically consist of 23 pairs of chromosomes. Telomeres are repetitive sequences of DNA located at the ends of chromosomes. During cell replication, a number of basepairs are lost from the end of the chromosome and this shortening restricts the number of divisions that a cell can complete before it becomes senescent, or non-replicative. In this paper, we use Monte Carlo simulations to form a stochastic model of telomere shortening to investigate how telomere shortening affects normal aging. Using this model, we study various hypotheses for the way in which shortening occurs by comparing their impact on aging at the chromosome and cell levels. We consider different types of length-dependent loss and replication probabilities to describe these processes. After analyzing a simple model for a population of independent chromosomes, we simulate a population of cells in which each cell has 46 chromosomes and the shortest telomere governs the replicative potential of the cell. We generalize these simulations to Werner's syndrome, a condition in which large sections of DNA are removed during cell division and, amongst other conditions, results in rapid aging. Since the mechanisms governing the loss of additional basepairs are not known, we use our model to simulate a variety of possible forms for the rate at which additional telomeres are lost per replication and several expressions for how the probability of cell division depends on telomere length. As well as the evolution of the mean telomere length, we consider the standard deviation and the shape of the distribution. We compare our results with a variety of data from the literature, covering both experimental data and previous models. We find good agreement for the evolution of telomere length when plotted against population doubling.

Stress induced telomere shortening: longer life with less mutations?

Background

Mutations accumulate as a result of DNA damage and imperfect DNA repair machinery. In higher eukaryotes the accumulation and spread of mutations is limited in two primary ways: through p53-mediated programmed cell death and cellular senescence mediated by telomeres. Telomeres shorten at every cell division and cell stops dividing once the shortest telomere reaches a critical length. It has been shown that the rate of telomere attrition is accelerated when cells are exposed to DNA damaging agents. However the implications of this mechanism are not fully understood.

Results

With the help of in silico model we investigate the effect of genotoxic stress on telomere attrition and apoptosis in a population of non-identical replicating cells. When comparing the populations of cells with constant vs. stress-induced rate of telomere shortening we find that stress induced telomere shortening (SITS) increases longevity while reducing mutation rate. Interestingly, however, the effect takes place only when genotoxic stresses (e.g. reactive oxygen species due to metabolic activity) are distributed non-equally among cells.

Conclusions

Our results for the first time show how non-equal distribution of metabolic load (and associated genotoxic stresses) combined with stress induced telomere shortening can delay aging and minimize mutations.

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs

Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends of telomeres and thus prolongs the life span of cells, but also causes cellular immortalisation in human cancer. G-quadruplex (G4) stabilising drugs are a potential anticancer treatment which work by changing the molecular structure of telomeres to inhibit the activity of telomerase. We investigate the dynamics of telomere length in different conformational states, namely t-loops, G-quadruplex structures and those being elongated by telomerase. By formulating deterministic differential equation models we study the effects of various levels of both telomerase and concentrations of a G4-stabilising drug on the distribution of telomere lengths, and analyse how these effects evolve over large numbers of cell generations. As well as calculating numerical solutions, we use quasicontinuum methods to approximate the behaviour of the system over time, and predict the shape of the telomere length distribution. We find those telomerase and G4-concentrations where telomere length maintenance is successfully regulated. Excessively high levels of telomerase lead to continuous telomere lengthening, whereas large concentrations of the drug lead to progressive telomere erosion. Furthermore, our models predict a positively skewed distribution of telomere lengths, that is, telomeres accumulate over lengths shorter than the mean telomere length at equilibrium. Our model results for telomere length distributions of telomerase-positive cells in drug-free assays are in good agreement with the limited amount of experimental data available.

Telomere sister chromatid exchange and the process of aging

Telomeres are a hotspot for sister chromatid exchange (T-SCE). Any biological consequence of this form of instability remained obscure until quantitative modeling revealed a link between elevated T-SCE rates and accelerated cellular replicative senescence. This work strongly suggests that progressive telomere erosion is not the only determinant of replicative capacity; instead, T-SCE need to be considered as an independent factor controlling colony growth and senescence. Additionally high T-SCE rates have been observed in cells with deficiencies in WRN and BLM, the genes that are defective in Werner's and Bloom's syndromes, implying a connection to premature aging. In this Research Perspective we will explore some of the implications this recent work has for human health.

Hyper telomere recombination accelerates replicative senescence and may promote premature aging

Werner syndrome and Bloom syndrome result from defects in the RecQ helicases Werner (WRN) and Bloom (BLM), respectively, and display premature aging phenotypes. Similarly, XFE progeroid syndrome results from defects in the ERCC1-XPF DNA repair endonuclease. To gain insight into the origin of cellular senescence and human aging, we analyzed the dependence of sister chromatid exchange (SCE) frequencies on location [i.e., genomic (G-SCE) vs. telomeric (T-SCE) DNA] in primary human fibroblasts deficient in WRN, BLM, or ERCC1-XPF. Consistent with our other studies, we found evidence of elevated T-SCE in telomerase-negative but not telomerase-positive backgrounds. In telomerase-negative WRN-deficient cells, T-SCE-but not G-SCE-frequencies were significantly increased compared with controls. In contrast, SCE frequencies were significantly elevated in BLM-deficient cells irrespective of genome location. In ERCC1-XPF-deficient cells, neither T- nor G-SCE frequencies differed from controls. A theoretical model was developed that allowed an in silico investigation into the cellular consequences of increased T-SCE frequency. The model predicts that in cells with increased T-SCE, the onset of replicative senescence is dramatically accelerated even though the average rate of telomere loss has not changed. Premature cellular senescence may act as a powerful tumor-suppressor mechanism in telomerase-deficient cells with mutations that cause T-SCE levels to rise. Furthermore, T-SCE-driven premature cellular senescence may be a factor contributing to accelerated aging in Werner and Bloom syndromes, but not XFE progeroid syndrome.

Population mixture model for nonlinear telomere dynamics

Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.

Universal tree structures in directed polymers and models of evolving populations

By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few universality classes.

First-passage-time distribution for diffusion through a planar wedge

We obtain compact, exact, analytical expressions for the first-passage-time distribution for a particle diffusing on a planar wedge for special values of the wedge angle. Specifically, we calculate the first-passage-time distribution for the diffusing particle through a planar wedge of angle pi/n, where n is an integer. For the cases n=2 and n odd, we provide an exact closed-form expression to the first-passage-time distribution while for the remaining cases, we provide it in integral form and evaluate numerically using quadratures. We then show that our results are in good agreement with Markovian simulations in the continuum limit.

Multiple mutant clones in blood rarely coexist

Leukemias arise due to mutations in the genome of hematopoietic (blood) cells. Hematopoiesis has a multicompartment architecture, with cells exhibiting different rates of replication and differentiation. At the root of this process, one finds a small number of stem cells, and hence the description of the mutation-selection dynamics of blood cells calls for a stochastic approach. We use stochastic dynamics to investigate to which extent acquired hematopoietic disorders are associated with mutations of single or multiple genes within developing blood cells. Our analysis considers the appearance of mutations both in the stem cell compartment as well as in more committed compartments. We conclude that in the absence of genomic instability, acquired hematopoietic disorders due to mutations in multiple genes are most likely very rare events, as multiple mutations typically require much longer development times compared to those associated with a single mutation.