Radiation-Induced Processes of Adaptation: Research by statistical modelling

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If the signal spreads out via diffusion or other reasonably spatially uniform processes , then the signal concentration in the system evolves, in the absence of any new sources, according to.

Thus, in general, a given signal will tend to spatially equilibrate as it decays. Irradiated cells can then be represented as a series of point sources of signal. However, even for a single cell, equation 1 does not have a general analytic solution, due to the complex interplay between the rates of signal production, decay, and diffusion. By contrast, numerical solutions of equation 1 are straightforward — as outlined in the models and methods S1 — but often prohibitively time-consuming.

However, in most in vitro studies of these effects, little spatial variation is observed [25] , suggesting that the rate of diffusion is much greater than the rate of signal production. This simplified description largely reflects the kinetics of the full numerical modelling of the system as shown in figure S1. However, some quantitative discrepancies between this analytic solution and the numerical analysis exist.

Most significantly, while average concentrations are a useful description at long times, there is some heterogeneity at early times, particularly in the vicinity of signalling cells, which leads to lower rates of signal production. As a result, the rate at which the signal approaches equilibrium following irradiation is significantly slower than predicted above. This relationship retains the overall scaling of equation 3 , while also providing much better agreement at early times.

While this introduces a slight discrepancy at extremely high cell densities, it is minor in the data sets considered here. An illustration of the resulting kinetics can be seen in Figure 1. More generally, there are multiple populations of cells exposed to different doses. This can be extended, in a similar fashion, over any number of sub-populations exposed to different doses to describe the signal kinetics following an arbitrary radiation pattern in these in vitro radiation exposures.

It should be noted that while the assumption of spatial homogeneity has been made above to facilitate efficient fitting to the data sets, numerical modelling of intercellular signalling, as outlined in the supporting information, is also viable based on the same fundamental assumptions, and leads to similar results for these systems. These numerical models also allow for descriptions of signalling in systems where signal propagation is much slower, such as in the skin model described below.

The response of cells to these signals is a binary event — that is, cells either respond and see on average a fixed level of damage, or do not and see no effect [26] , [27]. The exact mechanism by which this DNA damage is induced is not yet fully elucidated, although it is believed that membrane-mediated signalling pathways and elevated levels of oxidative stress in recipient cells plays a role [27] , [28].

In this work, the probability of a response is predicted based on the signal kinetics outlined above. The exponential dependence is retained, giving. This period is illustrated in Figure 1. As noted above, cells which respond to these signals experience genotoxic stress, which can potentially lead to the induction of DNA damage, mutation and cell death [26] , [27] , [29] , [30].

This is modelled either as a simple probability of mutation induction or cell death or, where direct and intercellular signalling can potentially combine, a previously published model of radiation damage is used. This is briefly reviewed below for completeness.

This model was originally developed for a computational model of cellular response to ionising radiation [31] , and was extended to include effects of intercellular communication in a previous work [21]. Hits from ionising radiation are generated by sampling a Poisson distribution, with a mean proportional to the delivered dose. Indirect damage due to intercellular signalling is represented as additional hits, generated by sampling from a Poisson distribution with a mean of H B , which is a characteristic of the cell line.

More detail on the rationale and development of this model can be found in previous publications [21] , [31]. An example implementation of this model, applied to a half-field irradiation such as that of Butterworth et al is presented in example code S1.

A Kinetic-Based Model of Radiation-Induced Intercellular Signalling

The above models of signal production and response allow for predictions to be made of the probability of cells experiencing damage due to intercellular communication, as well as for the more general situations which also incorporate direct irradiation. In most data sets, there is insufficient experimental data to uniquely fit all of these parameters. A single fit was carried out over all media transfer and modulated field experiments, fitting the signal kinetic parameters plus cell- and experiment-specific response parameters e. Some of the first evidence for the effects of intercellular communication following irradiation were media transfer experiments [19].

In these experiments, a population of cells is uniformly irradiated and incubated for a time to allow for signal generation. The medium is then removed from these donor cells, filtered and added to a recipient cell population. These recipient cells see an increase in DNA damage, genomic instability and cell death, compared to cells grown in media taken from unirradiated cells. The resulting signalling kinetics are schematically illustrated in Figure 1.

Two media transfer experiments are considered in this work. Firstly, one of the earliest demonstrations of the effects of radiation-induced signalling, made by Mothersill et al [2].

Here, a population of 20, HaCat human keratinocyte cells were exposed to 5 Gy of radiation, and incubated for 1 hour. The treated media was added to a population of recipient cells for times varying from 6 minutes to hours. Following this exposure, the clonogenic survival of the recipient cells was measured.

These results are plotted in Figure 2a , showing an initial drop in survival with exposure time, which saturates after approximately two hours. In Mothersill et al a , the model solid line is able to reflect the onset of signalling-induced cell killing seen in a media-transfer experiment as a function of exposure time circle. Good agreement with the overall trends is found in all cases, with the exception of the small plateau in cell number dilution, which suggests some additional complexity in signal production at reduced cell densities. Secondly, the data set of Zhang et al [32] was investigated, as it offered a more robust of test the parameters in this model.

Here, the number of mutations induced by media-transfer mediated signalling was investigated in WTK1 lymphoblastoid cells. In the basic form of this experiment, 2. The cells were then incubated for 2 hours, after which the media was transferred to a recipient population for 24 hours. Following this, frequencies of mutations in the recipient cells were determined. Four parameters were then varied from this basic experimental condition to determine their effects on mutation frequencies induced by the intercellular signalling: Cell density, media dilution, the time for which the recipient cells were exposed to the media, and signal incubation time.

These results are plotted in Figure 2 b-e, respectively. Clear variations are seen with all these of these variables, with mutation frequency falling rapidly with signal dilution and reducing cell density, and showing a build-up time on the order of an hour for both incubation and exposure.

Associated Data

Once added to the recipient cells, the signal decays according to , so the maximum time the signal will remain above the response threshold is given by. This means that the amount of time the cells are exposed to a signal above the threshold is given by , where t exp is the amount of time recipient cells were exposed to the media from the irradiated cells.

Finally, the probability of a cell responding to the signal is given by. This response probability is common to both of the above data sets. However, different endpoints were used in each experiment. In Mothersill et al, cell killing was used as an endpoint. It is assumed that cells which respond to the intercellular signalling have a fixed probability of cell death, and the total survival probability can be expressed as where S is the fraction of surviving cells, and P 0 is the probability that a cell survives following response to these signals.

This predicted curve is plotted alongside the data in Figure 2a as a solid line. Zhang et al used mutation frequency as an endpoint. As above, a fixed mutation probability MF B , is associated with response to the signalling process. Thus, the total mutation probability can be expressed as , where MF 0 is the base mutation frequency.

Good agreement is seen with both experiments, across the majority of the parameters considered. Some disagreement is seen in the Zhang et al data at moderate cell dilutions, but this may be due to a breakdown in the assumptions of homogeneity and uniformity used to facilitate fitting this data. While media transfer experiments clearly demonstrate the effects of radiation-induced signalling, they are very different to in vivo situations, where cell populations necessarily remain in contact for extended periods.

This is partially addressed in modulated field exposures. In these experiments e. Following this, cell survival or DNA damage is measured in different areas of the flask, allowing for a quantification of direct and indirect effects. Because of the prolonged contact, out-of-field cells are exposed to signals from irradiated cells for a longer period than in media transfer experiments, as illustrated in Figure 1. Two sets of modulated field exposure experiments are studied here.

Firstly, a series of experiments from Butterworth et al [7] , which investigated the effects of modulated radiation fields on AGO and DU cells.

A Kinetic-Based Model of Radiation-Induced Intercellular Signalling

A clear contribution from intercellular communication was seen, with significantly lower survival in the low-dose region than would be predicted from the dose delivered to that region alone. Figure 3 presents the effects of varying of several experimental parameters on survival in this scenario, including the dose delivered in-field; the degree of attenuation in the out-of-field region; and the number of cells irradiated.

All points are cell survival in a region against the dose delivered to that region. Effect of varying delivered doses.

In addition, experiments were carried out where the in-field dose was constant and the out-of-field dose was varied by changing the level of shielding light blue diamonds, green squares. Effect of varying area in-field was investigated by holding the dose and attenuation constant, and varying the fraction of the flask under the shielding.

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The effect of out-of-field dose was tested by holding the in-field dose fixed and varying the degree of shielding, for transmissions varying from 1. Timofeeff-Ressovsky Book 1 edition published in in Russian and held by 4 WorldCat member libraries worldwide. I Korogodin Book 1 edition published in in Russian and held by 1 WorldCat member library worldwide. Information as the basis of life by V.

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I Korogodin Book 1 edition published in in English and held by 1 WorldCat member library worldwide. English 34 Russian 5 German 1. Project Page Feedback Known Problems. On its basis, we present statistical modeling of cellular distributions on the number of chromosomal abnormalities in root meristems of pea seeds that experienced low-dose-rate irradiation, high temperatures, and aging. From This Paper Figures, tables, and topics from this paper. Instability Search for additional papers on this topic. Topics Discussed in This Paper.

Adaptation and Radiation-Induced Chromosomal Instability Studied by Statistical Modeling

Congenital Abnormality Plant seeds Radioactivity. References Publications referenced by this paper. Showing of 51 references. Analysis of the distribution structure as exemplified by one cytogenetic problem.

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