**On the Dynamical Approach of Quantitative Radiation Biology**

Noriyuki B. Ouchi

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/60859

#### **Abstract**

A quantitative approach in radiation biology based on the clonogenic method and cell survival curves in various conditions are introduced. The cell survival curves seem to have universality with regard to its functional form; in other words, functional form of survival curve seems to be unchanged under various conditions including different species. Various factors affecting the radiosensitivity have been introduced to find macroscopic nature of living organisms. Mathematical models that describe cell sur‐ vival curves have been presented for discussing the derivation of the mathematical form based on biological mechanism. Finally, the possibility that the structural change of chromosome affects the repair process is discussed.

**Keywords:** Cell survival curves, Mathematical model, Target theory, Quantitative ra‐ diation biology, DNA repair

#### **1. Introduction**

Now, over ten years have passed since initial sequencing and analysis of the human genome [1]. The human genome is thought to contain approximately 20,000 protein-coding genes, which are supposed to drive a human being as a living system. The successful sequencing and analysis of the human genome made a major step forward in the understanding of life. The progress in decoding the human genome reveals aspects of the components of life; however, it is difficult to study dynamical principle of living organisms, which are supposed to emerge via many interactions between many proteins (30,000 or more) in a collective manner.

In fact, a major method in modern molecular biology is each event involved in the corre‐ sponding process will be examined by breaking the whole system into small pieces, and biological activity in each small part of the system is explained by the activation of corre‐

statistical physics [4].

basically the statistics.

sponding genes. This is the method so-called reductionism. This kind of reductionism has made great accomplishments in the physical sciences; however, only the knowledge of the breaking elements would not help to understand life, e.g. its origin, evolution, and persistence (Fig. 1). In other words, so-called emergent properties of the system would not be impossible to predict from knowledge of the breaking elements of the system [2]. Therefore, the under‐ standing of life itself requires research technique which handles the whole system. 2 On the Dynamical Approach of Quantitative Radiation Biology impossible to predict from knowledge of the breaking elements of the system [2]. Therefore,

the understanding of life itself requires research technique which handles the whole system.

Fig. 1. Karakuri ningyou (Japanese mechanized doll). This is a tea serving mechanized robot. The karakuri ningyou serves a cup of tea, and its sequence is roughly as follows: 1) When a cup of tea is placed on the hands, they start to move toward a guest by moving its feet like walking. 2) It moves, setting distance, and bows its head. 3) When a cup of tea is taken from the hands, it stops and waits for a next action. 4) It turns around and returns to the starting position (host's place) when an empty cup is placed on the hands. It works by springs. Only the examination of each mechanical gear would not help to understand the entire behavior of the doll. Picture is taken from Wikimedia Commons [3] and **Figure 1.** Karakuri ningyou (Japanese mechanized doll). This is a tea serving mechanized robot. The karakuri ningyou serves a cup of tea, and its sequence is roughly as follows: 1) When a cup of tea is placed on the hands, they start to move toward a guest by moving its feet like walking. 2) It moves, setting distance, and bows its head. 3) When a cup of tea is taken from the hands, it stops and waits for a next action. 4) It turns around and returns to the starting position (host's place) when an empty cup is placed on the hands. It works by springs. Only the examination of each mechani‐ cal gear would not help to understand the entire behavior of the doll. Picture is taken from Wikimedia Commons [3] and converted to gray scale

converted to gray scale There is a well-known logic of research methods that have been used to derive the theory or some formula without breaking the corresponding system. For example, linear response theory is based on the idea that the global behavior of the system is obtained by investigating the various responses of the system against the given perturbation/stimulation. Especially, this kind of research design, i.e., investigating the global response of the system to a spatiotemporally varying perturbation, e.g., electromagnetic field, temperature, etc., for analyzing dynamical properties of the system has been well adopted in nonequilibrium There is a well-known logic of research methods that have been used to derive the theory or some formula without breaking the corresponding system. For example, linear response theory is based on the idea that the global behavior of the system is obtained by investigat‐ ing the various responses of the system against the given perturbation/stimulation. Especial‐ ly, this kind of research design, i.e., investigating the global response of the system to a spatiotemporally varying perturbation, e.g., electromagnetic field, temperature, etc., for analyzing dynamical properties of the system has been well adopted in nonequilibrium statistical physics [4].

Turning now to the case of biological science, ionizing radiation seems to be a good example of such kind of "perturbation" to examine system's global behavior from the action to the living organisms. Generally, different types of scientific index of the biological responses to ionizing radiation are used to study the action of ionizing radiation, depending on the corresponding systems. For most cases, cancer incidence is used as the biological response if the corresponding system is a human being. This type of study, known as epidemiology, is Turning now to the case of biological science, ionizing radiation seems to be a good example of such kind of "perturbation" to examine system's global behavior from the action to the living organisms. Generally, different types of scientific index of the biological responses to ionizing radiation are used to study the action of ionizing radiation, depending on the corresponding systems. For most cases, cancer incidence is used as the biological response if the correspond‐ ing system is a human being. This type of study, known as epidemiology, is basically the statistics.

On the other hand, major advances have been made in the mechanism-based study of molecular radiation biology, and these advances shed light on the relationship between carcinogenesis and radiation-induced DNA damage. Biological studies on the various radiation responses are basically the cellular-scale investigation. By considering ionizing radiation as an example of external stimulus, many types of cellular responses, e.g., induction of chromosomal aberrations, gene mutations, cell apoptosis, cell transformation, and tumori‐ genesis, are known to occur. In many cases, quantification of these responses can help discuss these issues mathematically. In the next section, a very effective quantification experimental technique in radiation biology is discussed.

#### **2. Quantitative radiation biology**

sponding genes. This is the method so-called reductionism. This kind of reductionism has made great accomplishments in the physical sciences; however, only the knowledge of the breaking elements would not help to understand life, e.g. its origin, evolution, and persistence (Fig. 1). In other words, so-called emergent properties of the system would not be impossible to predict from knowledge of the breaking elements of the system [2]. Therefore, the under‐

2 On the Dynamical Approach of Quantitative Radiation Biology

impossible to predict from knowledge of the breaking elements of the system [2]. Therefore, the understanding of life itself requires research technique which handles the whole system.

Fig. 1. Karakuri ningyou (Japanese mechanized doll). This is a tea serving mechanized robot. The karakuri ningyou serves a cup of tea, and its sequence is roughly as follows: 1) When a cup of tea is placed on the hands, they start to move toward a guest by moving its feet like walking. 2) It moves, setting distance, and bows its head. 3) When a cup of tea is taken from the hands, it stops and waits for a next action. 4) It turns around and returns to the starting position (host's place) when an empty cup is placed on the hands. It works by springs. Only the examination of each mechanical gear would not help to understand the entire behavior of the doll. Picture is taken from Wikimedia Commons [3] and

**Figure 1.** Karakuri ningyou (Japanese mechanized doll). This is a tea serving mechanized robot. The karakuri ningyou serves a cup of tea, and its sequence is roughly as follows: 1) When a cup of tea is placed on the hands, they start to move toward a guest by moving its feet like walking. 2) It moves, setting distance, and bows its head. 3) When a cup of tea is taken from the hands, it stops and waits for a next action. 4) It turns around and returns to the starting position (host's place) when an empty cup is placed on the hands. It works by springs. Only the examination of each mechani‐ cal gear would not help to understand the entire behavior of the doll. Picture is taken from Wikimedia Commons [3]

There is a well-known logic of research methods that have been used to derive the theory or some formula without breaking the corresponding system. For example, linear response theory is based on the idea that the global behavior of the system is obtained by investigating the various responses of the system against the given perturbation/stimulation. Especially, this kind of research design, i.e., investigating the global response of the system to a spatiotemporally varying perturbation, e.g., electromagnetic field, temperature, etc., for analyzing dynamical properties of the system has been well adopted in nonequilibrium

There is a well-known logic of research methods that have been used to derive the theory or some formula without breaking the corresponding system. For example, linear response theory is based on the idea that the global behavior of the system is obtained by investigat‐ ing the various responses of the system against the given perturbation/stimulation. Especial‐ ly, this kind of research design, i.e., investigating the global response of the system to a spatiotemporally varying perturbation, e.g., electromagnetic field, temperature, etc., for analyzing dynamical properties of the system has been well adopted in nonequilibrium

Turning now to the case of biological science, ionizing radiation seems to be a good example of such kind of "perturbation" to examine system's global behavior from the action to the living organisms. Generally, different types of scientific index of the biological responses to ionizing radiation are used to study the action of ionizing radiation, depending on the corresponding systems. For most cases, cancer incidence is used as the biological response if the corresponding system is a human being. This type of study, known as epidemiology, is

converted to gray scale

and converted to gray scale

42 Evolution of Ionizing Radiation Research

statistical physics [4].

statistical physics [4].

basically the statistics.

standing of life itself requires research technique which handles the whole system.

Early in the twentieth century, it is known that the ionizing radiation may cause harmful effects on the biological organisms. Most of the experiments in the early radiation biology research are aimed to study the effects of X-ray irradiation on various types of living organisms: bacteria, virus, and unicellular organism. In short, unicellular organisms were mostly used to study the action of ionizing radiation on living organisms.

These early experiments have revealed the amount of radiation doses that needed to kill or inactivate the various species. For example, the mean lethal dose, D0 (dose required to reduce the population to the 37% level, i.e., fraction 1 /*e*) is over 150 Gy for *Chilomonas paramecium* and 400 Gy for virus (Table. 1). Here, Gy is a unit absorbed radiation dose, and 1 Gy=1 J kg-1, in SI unit. Therefore, the fact that there is a big difference in mean lethal dose between species, or, in other words, there is a big difference in radiosensitivity between species, has been recog‐ nized.

However, irradiation experiment of human cells was needed to study the radiosensitivity of humans. Therefore, experimental technique that possibly cultures the separated cells *in vitro* was needed. In 1907, a new technique, known as cell culture, was successfully introduced by Harrison [6] to study the argument of development process of the nervous system, whether the nervous system was composed of many cells (syncytial theory) or made up of a single seamless, continuous cell (reticular theory) [7]. Nowadays, this simple experiment, cell culture, is becoming a more and more important tool not only for radiation biology but also for other wide varieties of life sciences (Fig. 2). In this way, establishment of the cell culture technique has made possible to study the radiation effects using cultured human cells.

4 On the Dynamical Approach of Quantitative Radiation Biology

Fig. 2. Two examples of the cell culture system. Left: Flasks containing some growth medium for cell growth. Right: Petri dish containing growth medium, called agar plate. It contains cultured microorganisms. Taken from Wikimedia Commons [8, 9] and converted to gray scale **Figure 2.** Two examples of the cell culture system. Left: Flasks containing some growth medium for cell growth. Right: Petri dish containing growth medium, called agar plate. It contains cultured microorganisms. Taken from Wikimedia Commons [8, 9] and converted to gray scale

*paramecium*. Afterward, it was found not to be a true. Then, statistical scientific data taken


For a person who has a mass of 60 kg, the total absorbed energy from 4 Gy X-ray is calculated

4 Gy *×* 60 kg = 240 J, (1)

as follows: **Table 1.** Roughly estimated value of D0 for various biological species. After [5]

where 240 J = 57 cal. Energy of 1 J equals to the work done by a constant force of 1 N and moves a 1 m displacement. Therefore, 240 J equals to the work that lifts a 60 kg mass to a height of about 40 cm (Fig. 3). Thus, the energy level of lethal radiation dose seems sufficiently small compared to the other harmful sources. Naturally, this scientific fact suggests that there is a small target which controls cell life and death inside the living organisms and viruses, i.e., DNA. Now, return the discussion to the problem of the difference in radiosensitivity between human individuals (1–4 Gy) and its constituent cells (over 100 Gy). This problem has been clarified due to the successful development of new experimental technique. More precisely, for the sake According to the early human cell irradiation experiments, the D0 value for isolated human cells was found to have about 100 Gy; it is almost the same dose as that of *Chilomonas parame‐ cium*. Afterward, it was found not to be a true. Then, statistical scientific data taken from the investigation of A-bomb survivors of Hiroshima and Nagasaki and nuclear accident in the United States have revealed a scientific fact that the D0 of unicellular organisms (over 100 Gy) and human beings (1–4 Gy) is quite different. Furthermore, a big difference on lethal dose of human individuals (1–4 Gy) and its constituent cells (over 100 Gy!) was recognized. At that time, this big difference on lethal dose was one of the unresolved questions in radiation biology.

of clonogenic assay method developed by Puck and Marcus [5], quantitative study of cellular response of mammalian cells to an external stimulus is established. Thus, the first survival curve, which will be described later, for X-ray irradiated mammalian (HeLa) cells *in vitro* was obtained by the method. The cell culture technique made the observation of proliferation of Here, another important aspect of the radiation is discussed. It is important to emphasize that the total absorbed energy by a human body estimated from the lethal radiation dose for human (4 Gy) seems to be extremely small compared to the other harmful sources.

For a person who has a mass of 60 kg, the total absorbed energy from 4 Gy X-ray is calculated as follows:

4 On the Dynamical Approach of Quantitative Radiation Biology

Fig. 2. Two examples of the cell culture system. Left: Flasks containing some growth medium for cell growth. Right: Petri dish containing growth medium, called agar plate. It contains cultured

**Figure 2.** Two examples of the cell culture system. Left: Flasks containing some growth medium for cell growth. Right: Petri dish containing growth medium, called agar plate. It contains cultured microorganisms. Taken from Wikimedia

*paramecium*. Afterward, it was found not to be a true. Then, statistical scientific data taken from the investigation of A-bomb survivors of Hiroshima and Nagasaki and nuclear accident in the United States have revealed a scientific fact that the D0 of unicellular organisms (over 100 Gy) and human beings (1–4 Gy) is quite different. Furthermore, a big difference on lethal dose of human individuals (1–4 Gy) and its constituent cells (over 100 Gy!) was recognized. At that time, this big difference on lethal dose was one of the unresolved questions in radiation

Here, another important aspect of the radiation is discussed. It is important to emphasize that the total absorbed energy by a human body estimated from the lethal radiation dose for

For a person who has a mass of 60 kg, the total absorbed energy from 4 Gy X-ray is calculated

where 240 J = 57 cal. Energy of 1 J equals to the work done by a constant force of 1 N and moves a 1 m displacement. Therefore, 240 J equals to the work that lifts a 60 kg mass to a height of about 40 cm (Fig. 3). Thus, the energy level of lethal radiation dose seems sufficiently small compared to the other harmful sources. Naturally, this scientific fact suggests that there is a small target which controls cell life and death inside the living organisms and viruses, i.e.,

According to the early human cell irradiation experiments, the D0 value for isolated human cells was found to have about 100 Gy; it is almost the same dose as that of *Chilomonas parame‐ cium*. Afterward, it was found not to be a true. Then, statistical scientific data taken from the investigation of A-bomb survivors of Hiroshima and Nagasaki and nuclear accident in the United States have revealed a scientific fact that the D0 of unicellular organisms (over 100 Gy) and human beings (1–4 Gy) is quite different. Furthermore, a big difference on lethal dose of human individuals (1–4 Gy) and its constituent cells (over 100 Gy!) was recognized. At that time, this big difference on lethal dose was one of the unresolved questions in radiation biology.

Now, return the discussion to the problem of the difference in radiosensitivity between human individuals (1–4 Gy) and its constituent cells (over 100 Gy). This problem has been clarified due to the successful development of new experimental technique. More precisely, for the sake of clonogenic assay method developed by Puck and Marcus [5], quantitative study of cellular response of mammalian cells to an external stimulus is established. Thus, the first survival curve, which will be described later, for X-ray irradiated mammalian (HeLa) cells *in vitro* was obtained by the method. The cell culture technique made the observation of proliferation of

Here, another important aspect of the radiation is discussed. It is important to emphasize that the total absorbed energy by a human body estimated from the lethal radiation dose for human

(4 Gy) seems to be extremely small compared to the other harmful sources.

4 Gy *×* 60 kg = 240 J, (1)

human (4 Gy) seems to be extremely small compared to the other harmful sources.

microorganisms. Taken from Wikimedia Commons [8, 9] and converted to gray scale

biology.

Commons [8, 9] and converted to gray scale

44 Evolution of Ionizing Radiation Research

**Species D0 (Gy)** *E. coli* 40 T2 bacteriophage 400 Newcastle's disease virus 400 Yeast 50–180 *Chilomonas paramecium* 150 HeLa cell 1

**Table 1.** Roughly estimated value of D0 for various biological species. After [5]

as follows:

DNA.

$$4\text{Gy} \times 60\text{kg} = 240\text{J} \tag{1}$$

where 240J=57cal. Energy of 1 J equals to the work done by a constant force of 1 N and moves a 1 m displacement. Therefore, 240J equals to the work that lifts a 60 kg mass to a height of about 40 cm (Fig. 3). Thus, the energy level of lethal radiation dose seems sufficiently small compared to the other harmful sources. Naturally, this scientific fact suggests that there is a small target which controls cell life and death inside the living organisms and viruses, i.e., DNA.

Will-be-set-by-IN-TECH 5

Fig. 3. Lethal radiation dose explanation. Total energy imparted to the 60 kg mass by a 4 Gy radiation, which is the mean lethal dose D0 for human, is roughly equivalent to lifting 60 kg mass to a 40 cm height cells isolated from tissues easier; therefore, cell surviving fraction based on the ability of a **Figure 3.** Lethal radiation dose explanation. Total energy imparted to the 60 kg mass by a 4 Gy radiation, which is the mean lethal dose D0 for human, is roughly equivalent to lifting 60 kg mass to a 40 cm height

single cell to grow into a large colony was successfully conceived (Fig. 4).

100 400 1000 10000 **X-Ray** 0 4 2 8 Gy **1-2 weeks incubation** # of cells seeded xPE Now, return the discussion to the problem of the difference in radiosensitivity between human individuals (1–4 Gy) and its constituent cells (over 100 Gy). This problem has been clarified due to the successful development of new experimental technique. More precisely, for the sake of clonogenic assay method developed by Puck and Marcus [5], quantitative study of cellular response of mammalian cells to an external stimulus is established. Thus, the first survival curve, which will be described later, for X-ray irradiated mammalian (HeLa) cells *in vitro* was obtained by the method. The cell culture technique made the observation of proliferation of cells isolated from tissues easier; therefore, cell surviving fraction based on the ability of a single cell to grow into a large colony was successfully conceived (Fig. 4).

90 72 36 45 # of counted colonies plating efficiency (PE) 90% surviving fraction 1.0 0.2 0.04 0.005 Fig. 4. Illustration of the clonogenic assay method. Cell surviving fraction is finally calculated by dividing the counted number of colonies by the number of seeded cells which multiplied by plating efficiency (PE). PE is defined as the growing probability under the control condition (dose=0, in this case) The most important concept in the development of clonogenic assay is the definition of cell death. In other words, the cell survival is defined as whether the cell has a proliferation ability or not. In this situation, "dead cell" means the cell which loses its reproductive integrity, and this kind of cell death is called "reproductive cell death." The cells which cause reproductive cell death may still be present physically and morphologically intact, may even be able to make proteins or synthesize DNA, and may even be able to progress a few cell cycles and a few divisions may still occur. Generally, a dose of over 100 Gy is required to destroy basic cell function, in contrast to the 1–4 Gy for causing reproductive cell death. Quantifying the pure cell survival number by employing single-cell-based culturing technique has enabled to

> The most important concept in the development of clonogenic assay is the definition of cell death. In other words, the cell survival is defined as whether the cell has a proliferation ability or not. In this situation, "dead cell" means the cell which loses its reproductive integrity, and this kind of cell death is called "reproductive cell death." The cells which cause reproductive cell death may still be present physically and morphologically intact, may even be able to make proteins or synthesize DNA, and may even be able to progress a few cell cycles and a

**60**

Will-be-set-by-IN-TECH 5

**kg = 4Gy 60 kg**

which is the mean lethal dose D0 for human, is roughly equivalent to lifting 60 kg mass to a 40 cm height cells isolated from tissues easier; therefore, cell surviving fraction based on the ability of a

40cm

the counted number of colonies by the number of seeded cells which multiplied by plating efficiency (PE). PE is defined as the growing probability under the control condition (dose=0, in this case) The most important concept in the development of clonogenic assay is the definition of cell death. In other words, the cell survival is defined as whether the cell has a proliferation ability **Figure 4.** Illustration of the clonogenic assay method. Cell surviving fraction is finally calculated by dividing the count‐ ed number of colonies by the number of seeded cells which multiplied by plating efficiency (PE). PE is defined as the growing probability under the control condition (dose=0, in this case)

or not. In this situation, "dead cell" means the cell which loses its reproductive integrity, and

Fig. 4. Illustration of the clonogenic assay method. Cell surviving fraction is finally calculated by dividing

distinguish the reproductive cell death from the cell death in the narrow sense. Thus, clono‐ genic assay method may clarify the problem of the difference in radiosensitivity between human individuals and its constituent cells. Human individuals and its constituent cells may have almost the same value of mean lethal dose. Establishment of their work is often consid‐ ered to mark the beginning of quantitative cellular radiation biology [10]. this kind of cell death is called "reproductive cell death." The cells which cause reproductive cell death may still be present physically and morphologically intact, may even be able to make proteins or synthesize DNA, and may even be able to progress a few cell cycles and a

Generally, cell survival curves are used for the quantitative representation of biological cellular responses. Cell survival curves, or in short, survival curves, are defined by the proportion of surviving cells (*S*) as a function of radiation dose (*D*), as in Fig. 5, and known to be different, depending on corresponding biological systems (mammalian cells, virus, yeast, bacteria, etc.), both in terms of shape and absolute value of *S* at a given dose. In this sense, "slope" of each survival curve implies degree of radiation sensitivity of corresponding biological systems. Interestingly, its slope is known to vary with DNA content [11].

Until now, many experiments to measure radiation survival curves have been performed for various species, including human cells. As a consequence of these experiments, many new findings have been revealed. For example, radiosensitivities for the corresponding species A, mammalian cells; B, *E. coli*; C, *E.coli* B/r; D, yeast; E, phage staph E; F, *Bacillus megaterium*; G, potato virus; and H, *M. radiodurans*, are comparable in the slope of the cell survival curves, and they have the relation in radiosensitivity:

$$\mathbf{A} \rhd \mathbf{B} \rhd \mathbf{C} \rhd \mathbf{D} \rhd \mathbf{E} \rhd \mathbf{E} \rhd \mathbf{F} \rhd \mathbf{G} \rhd \mathbf{H} \tag{2}$$

Thus, the mammalian cells are most radiosensitive than other species. The differences of the radiosensitivity of various species are said to be correlated with its DNA content and efficiency of the DNA repair system [12].

6 On the Dynamical Approach of Quantitative Radiation Biology

few divisions may still occur. Generally, a dose of over 100 Gy is required to destroy basic cell function, in contrast to the 1–4 Gy for causing reproductive cell death. Quantifying the pure cell survival number by employing single-cell-based culturing technique has enabled

may have almost the same value of mean lethal dose. Establishment of their work is often

considered to mark the beginning of quantitative cellular radiation biology [10].

Fig. 5. Plot of cell survival curve for the surviving fraction data in Fig. 4. The survival curve is well fitted with *S* = *e−αD*, where *S* is cell survival and *D* is the radiation dose. *α* = 0.7 Generally, cell survival curves are used for the quantitative representation of biological cellular responses. Cell survival curves, or in short, survival curves, are defined by the **Figure 5.** Plot of cell survival curve for the surviving fraction data in Fig. 4. The survival curve is well fitted with *S* =*e* <sup>−</sup>*αD*, where *S* is cell survival and *D* is the radiation dose. *α* =0.7

proportion of surviving cells (*S*) as a function of radiation dose (*D*), as in Fig. 5, and known

Generally, differences on the biological or experimental conditions make the radiosensitivity change, even among the same type of cells. A lot of experiments have been performed to study various factors that affect the radiosensitivity until now; some of the major factors are described in the following. Here, various factors affecting the shape of survival curves (radiosensitivity) are summarized. to be different, depending on corresponding biological systems (mammalian cells, virus, yeast, bacteria, etc.), both in terms of shape and absolute value of *S* at a given dose. In this sense, "slope" of each survival curve implies degree of radiation sensitivity of corresponding biological systems. Interestingly, its slope is known to vary with DNA content [11]. Until now, many experiments to measure radiation survival curves have been performed for various species, including human cells. As a consequence of these experiments, many new findings have been revealed. For example, radiosensitivities for the corresponding species A,

A *>* B *>* C *>* D *>* E *>* F *>* G *>* H. (2)

The radiosensitivity is known to vary with various conditions, for example: mammalian cells; B, *E. coli*; C, *E.coli* B/r; D, yeast; E, phage staph E; F, *Bacillus megaterium*; G, potato virus; and H, *M. radiodurans*, are comparable in the slope of the cell survival curves,

**1.** species [11] and they have the relation in radiosensitivity:

distinguish the reproductive cell death from the cell death in the narrow sense. Thus, clono‐ genic assay method may clarify the problem of the difference in radiosensitivity between human individuals and its constituent cells. Human individuals and its constituent cells may have almost the same value of mean lethal dose. Establishment of their work is often consid‐

surviving fraction 1.0 0.2 0.04 0.005

Fig. 4. Illustration of the clonogenic assay method. Cell surviving fraction is finally calculated by dividing the counted number of colonies by the number of seeded cells which multiplied by plating efficiency (PE).

**Figure 4.** Illustration of the clonogenic assay method. Cell surviving fraction is finally calculated by dividing the count‐ ed number of colonies by the number of seeded cells which multiplied by plating efficiency (PE). PE is defined as the

The most important concept in the development of clonogenic assay is the definition of cell death. In other words, the cell survival is defined as whether the cell has a proliferation ability or not. In this situation, "dead cell" means the cell which loses its reproductive integrity, and this kind of cell death is called "reproductive cell death." The cells which cause reproductive cell death may still be present physically and morphologically intact, may even be able to make proteins or synthesize DNA, and may even be able to progress a few cell cycles and a

PE is defined as the growing probability under the control condition (dose=0, in this case)

Will-be-set-by-IN-TECH 5

**kg = 4Gy 60 kg**

Fig. 3. Lethal radiation dose explanation. Total energy imparted to the 60 kg mass by a 4 Gy radiation, which is the mean lethal dose D0 for human, is roughly equivalent to lifting 60 kg mass to a 40 cm height cells isolated from tissues easier; therefore, cell surviving fraction based on the ability of a

single cell to grow into a large colony was successfully conceived (Fig. 4).

40cm

100 400 1000 10000

**X-Ray** 0 4 2 8 Gy **1-2 weeks incubation**

90 72 36 45

**60**
