Estimating radiation-induced cancer risks at very low doses: rationale for using a linear no-threshold approach

The possible cancer risks caused by ionizing radiation doses of ~1 mSv or less are too small to be estimated directly from epidemiological data. The linear no-threshold (LNT) approach to estimating such risks involves using epidemiological data at higher (but still low) doses to establish an “anchor point”, and then extrapolating the excess cancer risk linearly down from this point to the low dose of interest. The study in this issue by Professor Tubiana and colleagues, summarizing a French Academy of Sciences report, argues that such LNT extrapolations systematically give substantial overestimates of the excess cancer risk at very low doses. We suggest that, to the contrary, even if there are significant deviations from linearity in the relevant dose range, potentially caused by the effects of inter-cellular interactions or immune surveillance, we know almost nothing quantitatively about these effects. Consequently, we do not know the magnitude, nor even the direction of any such deviations from linearity—the risks could indeed be lower than those predicted by a linear extrapolation, but they could well be higher.     

Explaining how and explaining why: developmental and evolutionary explanations of dominance

There have been two different schools of thought on the evolution of dominance. On the one hand, followers of Wright [Wright S. 1929. Am. Nat. 63: 274–279, Evolution: Selected Papers by Sewall Wright, University of Chicago Press, Chicago; 1934. Am. Nat. 68: 25–53, Evolution: Selected Papers by Sewall Wright, University of Chicago Press, Chicago; Haldane J.B.S. 1930. Am. Nat. 64: 87–90; 1939. J. Genet. 37: 365–374; Kacser H. and Burns J.A. 1981. Genetics 97: 639–666] have defended the view that dominance is a product of non-linearities in gene expression. On the other hand, followers of Fisher [Fisher R.A. 1928a. Am. Nat. 62: 15–126; 1928b. Am. Nat. 62: 571–574; Bürger R. 1983a. Math. Biosci. 67: 125–143; 1983b. J. Math. Biol. 16: 269–280; Wagner G. and Burger R. 1985. J. Theor. Biol. 113: 475–500; Mayo O. and Reinhard B. 1997. Biol. Rev. 72: 97–110] have argued that dominance evolved via selection on modifier genes. Some have called these “physiological” versus “selectionist,” or more recently [Falk R. 2001. Biol. Philos. 16: 285–323], “functional,” versus “structural” explanations of dominance. This paper argues, however, that one need not treat these explanations as exclusive. While one can disagree about the most likely evolutionary explanation of dominance, as Wright and Fisher did, offering a “physiological” or developmental explanation of dominance does not render dominance “epiphenomenal,” nor show that evolutionary considerations are irrelevant to the maintenance of dominance, as some [Kacser H. and Burns J.A. 1981. Genetics 97: 639–666] have argued. Recent work [Gilchrist M.A. and Nijhout H.F. 2001. Genetics 159: 423–432] illustrates how biological explanation is a multi-level task, requiring both a “top-down” approach to understanding how a pattern of inheritance or trait might be maintained in populations, as well as “bottom-up” modeling of the dynamics of gene expression.     

Cancer risk estimates from the combined Japanese A-bomb and Hodgkin cohorts for doses relevant to radiotherapy

Most information on the dose–response of radiation-induced cancer is derived from data on the A-bomb survivors who were exposed to γ-rays and neutrons. Since, for radiation protection purposes, the dose span of main interest is between 0 and 1 Gy, the analysis of the A-bomb survivors is usually focused on this range. However, estimates of cancer risk for doses above 1 Gy are becoming more important for radiotherapy patients and for long-term manned missions in space research. Therefore in this work, emphasis is placed on doses relevant for radiotherapy with respect to radiation-induced solid cancer. The analysis of the A-bomb survivor’s data was extended by including two extra high-dose categories (4–6 Sv and 6–13 Sv) and by an attempted combination with cancer data on patients receiving radiotherapy for Hodgkin’s disease. In addition, since there are some recent indications for a high neutron dose contribution, the data were fitted separately for three different values for the relative biological effectiveness (RBE) of the neutrons (10, 35 and 100) and a variable RBE as a function of dose. The data were fitted using a linear, a linear-exponential and a plateau-dose–response relationship. Best agreement was found for the plateau model with a dose-varying RBE. It can be concluded that for doses above 1 Gy there is a tendency for a nonlinear dose–response curve. In addition, there is evidence of a neutron RBE greater than 10 for the A-bomb survivor data. Many problems and uncertainties are involved in combing these two datasets. However, since very little is currently known about the shape of dose–response relationships for radiation-induced cancer in the radiotherapy dose range, this approach could be regarded as a first attempt to acquire more information on this area. The work presented here also provides the first direct evidence that the bending over of the solid cancer excess risk dose response curve for the A-bomb survivors, generally observed above 2 Gy, is due to cell killing effects.     

The probabilistic approach to the effects of radiations and variability of sensitivity

The calculation of the size of the “sensitive volume” or “control center” in biological effects of radiations is discussed from the viewpoint of the probabilistic theory of these phenomena based on the concept of random “effective events”. On the bases of that theory, the resistivity of a microorganism to radiation is defined as its “mean life” under a radiation of one roentgen per minute. This mean is calculated for processes with and without recovery. The case of variable sensitivity, as it occurs for instance during mitosis, is discussed in detail. Methods are given to calculate this variability from survival curves or similar experimental data. The theory is applied to experiments of A. Zuppinger on irradiation ofAscaris eggs with X-rays.     

Hematopoietic cell renewal systems: mechanisms of coping and failing after chronic exposure to ionizing radiation

On the occasion of the first international workshop on systems radiation biology we review the role of cell renewal systems in maintaining the integrity of the mammalian organism after irradiation. First, 11 radiation emergencies characterized by chronic or protracted exposure of the human beings to ionizing irradiation were “revisited”. The data provide evidence to suggest that at a daily exposure of about 10–100 mSv, humans are capable of coping with the excess cell loss for weeks or even many months without hematopoietic organ failure. Below 10 mSv/day, the organisms show some cellular or subcellular indicators of response. At dose rates above 100 mSv/day, a progressive shortening of the life span of the irradiated organism is observed. To elucidate the mechanisms relevant to tolerance or failure, the Megakaryocyte–thrombocyte cell renewal system was investigated. A biomathematical model of this system was developed to simulate the development of thrombocyte concentration as a function of time after onset of chronic radiation exposure. The hematological data were taken from experimental chronic irradiation studies with dogs at the Argonne National Laboratory, USA. The results of thrombocyte response patterns are compatible with the notion of an “excess cell loss” (compared to the steady-state) in all proliferative cell compartments, including the stem cell pool. The “excess cell loss” is a function of the daily irradiation dose rate. Once the stem cell pool is approaching an exhaustion level, a “turbulence region” is reached. Then it takes a very little additional stress for the system to fail. We conclude that in mammalian radiation biology (including radiation medicine), it is important to understand the physiology and pathophysiology of cell renewal systems in order to allow predicting the development of radiation induced lesions.     

The effect of the β-emitting yttrium-90 citrate on the dose–response of dicentric chromosomes in human lymphocytes: a basis for biological dosimetry after radiosynoviorthesis

The production of dicentric chromosomes in human lymphocytes by β-particles of yttrium-90 (Y-90) was studied in vitro to provide a basis of biological dosimetry after radiosynoviorthesis (RSO) of persistent synovitis by intra-articular administration of yttrium-90 citrate colloid. Since the injected colloid may leak into the lymphatic drainage exposing other parts of the body to radiation, the measurement of biological damage induced by β-particles of Y-90 is important for the assessment of radiation risk to the patients. A linear dose–response relationship (α = 0.0229 ± 0.0028 dicentric chromosomes per cell per gray) was found over the dose range of 0.2176–2.176 Gy. The absorbed doses were calculated for exposure of blood samples to Y-90 activities from 40 to 400 kBq using both Monte Carlo simulation and an analytical model. The maximum low-dose RBE, the RBE_M which is equivalent to the ratio of the α coefficients of the dose–response curves, is well in line with published results obtained earlier for irradiation of blood of the same donor with heavily filtered 220 kV X-rays (3.35 mm copper), but half of the RBE_M relative to weakly filtered 220 kV X-rays. Therefore, it can be concluded that for estimating an absorbed dose during RSO by the technique of biological dosimetry, in vitro and in vivo data for the same radiation quality are necessary.     

Causation in biology: stability,specificity, and the choice of levels of explanation

This paper attempts to elucidate three characteristics of causal relationships that are important in biological contexts. Stability has to do with whether a causal relationship continues to hold under changes in background conditions. Proportionality has to do with whether changes in the state of the cause “line up” in the right way with changes in the state of the effect and with whether the cause and effect are characterized in a way that contains irrelevant detail. Specificity is connected both to David Lewis’ notion of “influence” and also with the extent to which a causal relation approximates to the ideal of one cause–one effect. Interrelations among these notions and their possible biological significance are also discussed.     

Effects of Quaternary Climatic Change on Speciation in Mammals

An ongoing controversy in evolutionary biology is the extent to which climatic changes drive evolutionary processes. On the one hand are “Red Queen” hypotheses, which maintain that climatic change is less important than biotic interactions in causing evolutionary change. On the other hand are “Court Jester” models, which recognize climatic change as a very important stimulus to speciation. The Quaternary Period (the last 1.8 million years), characterized by multiple climatic changes in the form of glacial–interglacial transitions, offers a fertile testing ground for ascertaining whether cyclical climatic changes that operate at the 100,000-year time scale appreciably influence evolutionary patterns in mammals. Despite the increased potential for isolation of populations that should occur with multiple advances and retreats of glaciers and rearrangement of climatic zones, empirical data suggests that speciation rates were neither appreciably elevated for Quaternary mammals, nor strongly correlated with glacial–interglacial transitions. Abundant evidence attests to population-level changes within the Quaternary, but these did not usually lead to the origin of new species. This suggests that if climatic change does influence speciation rates in mammals, it does so over time scales longer than a typical glacial–interglacial cycle.     

Chain processes and their biophysical applications: Part I. General theory

A mathematical theory applicable to the biological effects of radiations as chain processes is developed. The theory may be interpreted substantially as a “hit theory” involving the concepts of “sensitive volume” or “target area”. The variability of the sensitivity of the organism to the radiation and its capacity of recovery between single hits is taken into account. It is shown that in a continuous irradiation of a biological aggregate in which the effect of each single hit cannot be observed, recovery and variation of sensitivity are formally equivalent to each other so that a discrimination between these two phenomena is possible only by discontinuous irradiation or by using different radiation intensities. Methods for the calculation of the “number of hits” and for the determination of the kinetics of the processes from “survival curves” or similar experimental data are given. The relation between the recovery and the Bunsen-Roscoe law is discussed. The case in which the injury of the organism is dependent on the destruction of more than one “sensitive volume” is also considered.     

Inventory, differentiation, and proportional diversity: a consistent terminology for quantifying species diversity

Almost half a century after Whittaker (Ecol Monogr 30:279–338, 1960) proposed his influential diversity concept, it is time for a critical reappraisal. Although the terms alpha, beta and gamma diversity introduced by Whittaker have become general textbook knowledge, the concept suffers from several drawbacks. First, alpha and gamma diversity share the same characteristics and are differentiated only by the scale at which they are applied. However, as scale is relative––depending on the organism(s) or ecosystems investigated––this is not a meaningful ecological criterion. Alpha and gamma diversity can instead be grouped together under the term “inventory diversity.” Out of the three levels proposed by Whittaker, beta diversity is the one which receives the most contradictory comments regarding its usefulness (“key concept” vs. “abstruse concept”). Obviously beta diversity means different things to different people. Apart from the large variety of methods used to investigate it, the main reason for this may be different underlying data characteristics. A literature review reveals that the multitude of measures used to assess beta diversity can be sorted into two conceptually different groups. The first group directly takes species distinction into account and compares the similarity of sites (similarity indices, slope of the distance decay relationship, length of the ordination axis, and sum of squares of a species matrix). The second group relates species richness (or other summary diversity measures) of two (or more) different scales to each other (additive and multiplicative partitioning). Due to that important distinction, we suggest that beta diversity should be split into two levels, “differentiation diversity” (first group) and “proportional diversity” (second group). Thus, we propose to use the terms “inventory diversity” for within-sample diversity, “differentiation diversity” for compositional similarity between samples, and “proportional diversity” for the comparison of inventory diversity across spatial and temporal scales. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The Ethical Basis for Sustainable Human Security: A Place for Anthropocentrism?

The deep and lasting changes to human behaviour that are required to address the global environmental crisis necessitate profound shifts in moral foundations. They amount to a change in what individuals and societies conceive of as progress. This imperative raises important questions about the justification, ends, and means of large-scale changes in people’s ethics. In this essay I will focus on the ends—the direction of moral change as prescribed by the goal of sustainable human flourishing. I shall present a meta-ethical critique of anthropocentrism and propose that only an ecocentric ethic can support the sustainable flourishing of humanity. This proposition does not necessarily contradict itself. My claim will be that the values subsumed under the broad concept of anthropocentrism are categorically counterproductive, informing an undesirable concept of “progress”. I support this claim with two lines of argument. On the one hand, the end values of anthropocentrism are shallow and the “flourishing of humanity” is ill-defined. The conceptual constraints of anthropocentrism itself preclude a more concise definition which would take into account the utter dependence of the flourishing of humanity on the health of ecological support structures. On the other hand, pursuing the values that inform the actions of anthropocentrists (which may be identical with the “flourishing of humanity”) leads to unintended and undesirable outcomes, even from the view of the anthropocentrist herself. Those problems are not encountered with an ecocentric ethic, and the conceptual steps necessary to adopt it are not insurmountable.     

Race: a social destruction of a biological concept

It is nowadays a dominant opinion in a number of disciplines (anthropology, genetics, psychology, philosophy of science) that the taxonomy of human races does not make much biological sense. My aim is to challenge the arguments that are usually thought to invalidate the biological concept of race. I will try to show that the way “race” was defined by biologists several decades ago (by Dobzhansky and others) is in no way discredited by conceptual criticisms that are now fashionable and widely regarded as cogent. These criticisms often arbitrarily burden the biological category of race with some implausible connotations, which then opens the path for a quick eliminative move. However, when properly understood, the biological notion of race proves remarkably resistant to these deconstructive attempts. Moreover, by analyzing statements of some leading contemporary scholars who support social constructivism about race, I hope to demonstrate that their eliminativist views are actually in conflict with what the best contemporary science tells us about human genetic variation.     

Dose–response relationship of dicentric chromosomes in human lymphocytes obtained for the fission neutron therapy facility MEDAPP at the research reactor FRM II

The biological effectiveness of neutrons from the neutron therapy facility MEDAPP (mean neutron energy 1.9 MeV) at the new research reactor FRM II at Garching, Germany, has been analyzed, at different depths in a polyethylene phantom. Whole blood samples were exposed to the MEDAPP beam in special irradiation chambers to total doses of 0.14–3.52 Gy at 2-cm depth, and 0.18–3.04 Gy at 6-cm depth of the phantom. The neutron and γ-ray absorbed dose rates were measured to be 0.55 Gy min⁻¹ and 0.27 Gy min⁻¹ at 2-cm depth, while they were 0.28 and 0.25 Gy min⁻¹ at 6-cm depth. Although the irradiation conditions at the MEDAPP beam and the RENT beam of the former FRM I research reactor were not identical, neutrons from both facilities gave a similar linear-quadratic dose–response relationship for dicentric chromosomes at a depth of 2 cm. Different dose–response curves for dicentrics were obtained for the MEDAPP beam at 2 and 6 cm depth, suggesting a significantly lower biological effectiveness of the radiation with increasing depth. No obvious differences in the dose–response curves for dicentric chromosomes estimated under interactive or additive prediction between neutrons or γ-rays and the experimentally obtained dose–response curves could be determined. Relative to ⁶⁰Co γ-rays, the values for the relative biological effectiveness at the MEDAPP beam decrease from 5.9 at 0.14 Gy to 1.6 at 3.52 Gy at 2-cm depth, and from 4.1 at 0.18 Gy to 1.5 at 3.04 Gy at 6-cm depth. Using the best possible conditions of consistency, i.e., using blood samples from the same donor and the same measurement techniques for about two decades, avoiding the inter-individual variations in sensitivity or the differences in methodology usually associated with inter-laboratory comparisons, a linear-quadratic dose–response relationship for the mixed neutron and γ-ray MEDAPP field as well as for its fission neutron part was obtained. Therefore, the debate on whether the fission-neutron induced yield of dicentric chromosomes increases linearly with dose remains open.     

The entropy of a continuous distribution

C. Shannon's definition (Bell System Technical Journal,27, 379–423, 1948) of the entropy of a continuous distribution is dimensionally incorrect and does not have the same significance as the corresponding definition in the discrete case. A new definition is proposed: this modified entropy is more like the entropy of a discrete distribution in one way, in another more like Shannon's “transmission rate.” The ideas are illustrated by reference to Wright's study of the hereditary influence on the coat pattern of the guinea pig.     

Question 2: Relation of Panspermia-Hypothesis to Astrobiology

In the answer to major questions of astrobiology and chirality, the panspermia-hypothesis is often discussed as the only proposal of transportation of life to the Earth. On the basis of the known presence of ionizing radiation in the space, assumed on the level calculated by Clark (Orig Life Evol Biosph 31:185–197, 2001), the hypothesis is rejected as the explanation of origins of life on Earth. In fact, comparatively low doses of radiation sterilize irreversibly all biological material. Sufficiently long sojourn in space of objects containing prebiotic chemical blocks also does not contribute to the origins of life on Earth, because of elimination of homochirality, if any, and of radiation induced reactions of dehydrogenation, decarboxylation and deamination of chemical compounds closing with complete decomposition of organics, leaving elementary nano-carbon and/or minerals like calcium carbonate. Presented at the International School of Complexity – 4th Course: Basic Questions on the Origins of Life; “Ettore Majorana” Foundation and Centre for Scientific Culture, Erice, Italy, 1–6 October 2006.     

A comparative investigation of certain difference equations and related differential equations: Implications for model-building

Many mathematical models for physical and biological problems have been and will be built in the form of differential equations or systems of such equations. With the advent of digital computers one has been able to find (approximate) solutions for equations that used to be intractable. Many of the mathematical techniques used in this area amount to replacing the given differential equations by appropriate difference equations, so that extensive research has been done into how to choose appropriate difference equations whose solutions are “good” approximations to the solutions of the given differential equations. The present paper investigates a different, although related problem. For many physical and biological phenomena the “continuum” type of thinking, that is at the basis of any differential equation, is not natural to the phenomenon, but rather constitutes an approximation to a basically discrete situation: in much work of this type the “infinitesimal step lengths” handled in the reasoning which leads up to the differential equation, are not really thought of as infinitesimally small, but as finite; yet, in the last stage of such reasoning, where the differential equation rises from the differentials, these “infinitesimal” step lengths are allowed to go to zero: that is where the above-mentioned approximation comes in. Under this kind of circumstances, it seems more natural tobuild themodel as adiscrete difference equation (recurrence relation) from the start, without going through the painful, doubly approximative process of first, during the modeling stage, finding a differential equation to approximate a basically discrete situation, and then, for numerical computing purposes, approximating that differential equation by a difference scheme. The paper pursues this idea for some simple examples, where the old differential equation, though approximative in principle, had been at least qualitatively successful in describing certain phenomena, and shows that this idea, though plausible and sound in itself, does encounter some difficulties. The reason is that each differential equation, as it is set up in the way familiar to theoretical physicists and biologists, does correspond to a plethora of discrete difference equations, all of which in the limit (as step length→0) yield the same differential equation, but whose solutions, for not too small step length, are often widely different, some of them being quite irregular. The disturbing thing is that all these difference equations seem to adequately represent the same (physical or biological) reasoning as the differential equation in question. So, in order to choose the “right” difference equation, one may need to draw upon more detailed (physical or) biological considerations. All this does not say that one should not prefer discrete models for phenomena that seem to call for them; but only that their pursuit may require additional (physical or) biological refinement and insight. The paper also investigates some mathematical problems related to the fact of many difference equations being associated with one differential equation.     

Physics,biology and sociology: II. Suggestion for a synthesis

In continuation of previous studies (Bull. Math. Biophysics,28, 283–308; 655–661, 1966;29, 139–152, 1967) it is shown that the difference between the “metric” aspects of physics and the “relational” aspects of biological and social sciences disappear by accepting the broader definition of “relation”, such as that given in mathematics and logic. A conceptual superstructure then becomes possible from which all three branches of knowledge may be derived, though none of them can be derived from the others.     

Radiation risk estimates after radiotherapy: application of the organ equivalent dose concept to plateau dose–response relationships

Estimates of secondary cancer risk after radiotherapy are becoming more important for comparative treatment planning. Modern treatment planning systems provide accurate three-dimensional (3D) dose distributions for each individual patient. The dose distributions can be converted into organ equivalent doses to describe radiation-induced cancer after radiotherapy (OED_rad-ther) in the irradiated organs. The OED_rad-ther concept assumes that any two dose distributions in an organ are equivalent if they cause the same radiation-induced cancer risk. In this work, this concept is applied to dose–response relationships, which are leveling off at high dose. The organ-dependent operational parameter of this dose–response relationship was estimated by analyzing secondary cancer incidence data of patients with Hodgkin’s disease. The dose distributions of a typical radiotherapy treatment plan for treating Hodgkin’s disease was reconstructed. Dose distributions were calculated in individual organs from which cancer incidence data were available. The model parameter was obtained by comparing dose and cancer incidence rates for the individual organs.     

Terahertz vibrational properties of water nanoclusters relevant to biology

Water nanoclusters are shown from first-principles calculations to possess unique terahertz-frequency vibrational modes in the 1–6 THz range, corresponding to O–O–O “bending,” “squashing,” and “twisting” “surface” distortions of the clusters. The cluster molecular-orbital LUMOs are huge Rydberg-like “S,” “P,” “D,” and “F” orbitals that accept an extra electron via optical excitation, ionization, or electron donation from interacting biomolecules. Dynamic Jahn–Teller coupling of these “hydrated-electron” orbitals to the THz vibrations promotes such water clusters as vibronically active “structured water” essential to biomolecular function such as protein folding. In biological microtubules, confined water-cluster THz vibrations may induce their “quantum coherence” communicated by Jahn–Teller phonons via coupling of the THz electromagnetic field to the water clusters’ large electric dipole moments.