Median, Puzzling Doses. Column in KomputerraOnline #93
High doses of damaging factors cause harm – that much is clear. Low doses very often produce a stimulating effect. But the most difficult thing to understand is how intermediate doses act. Much remains unclear on this point.
Dmytro Shabanov
Average, unclear doses
Work for an activist
I think one reason is the fanatical character of propaganda typical of many "green" agitators. The threat of ecological catastrophe is spoken of by people who seek merely to manipulate their listeners and readers—and you have all encountered propaganda of this kind. But could anyone have perceived my column in the same vein? Oddly, I tried to avoid categorical statements, indicating that the discussion concerns conclusions from models treating one or another future as probabilistic...
Column in KompyuterraOnline #93 Column in KompyuterraOnline #94
In this column, I want to talk about a problem of factorial ecology that is interesting to me. To start, I will quote a fragment of the discussion of the penultimate column. In the comments, I mentioned a well-known fact: the stimulating effect of low doses of radiation. It is obvious that the most active participant in the discussion of my columns could not miss this. He even read the article in \"Wikipedia\" dedicated to so-called hormesis - the stimulating effect of low doses of damaging factors. This insightful reader copies a piece of text from Wikipedia and concludes with his own categorical judgment.
"Currently, the theory of radiation hormesis in humans does not have sufficiently significant empirical evidence. In practice, a linear-quadratic model is usually used, which is based on the assumption that any, even the smallest, dose of radiation is harmful." So what heresy are you writing, Shabanov Dmitry. Rough heresy. IMHO".
The esteemed reader was so offended by my mention of the stimulating effect of low doses of radiation that he never tires of citing this example in other contexts as a rare piece of absurdity. This example of "network democracy" seems to me quite characteristic. A person who has read Wikipedia feels qualified to render verdicts on complex theoretical questions and to put anyone in their place (the "imho" at the end changes little). The issue here is not academic status but simply the amount of intellectual effort invested in understanding a problem. I should note, incidentally, that my foreign-language publication on the stimulating effect of low doses of radiation appeared back in Soviet times, when I was still a student. Nevertheless, I have no full certainty that I know the solution to so complex a problem... Thus, the first caveat I must make is that I am describing a hypothesis, not an established consensus. The second caveat is that I am not even the author of this hypothesis. It belongs to the supervisor of my diploma thesis, Artur Baranovsky. As a supervisor, I once chose a laboratory assistant who was five years my senior and had only just finished university — chosen, despite his singular character, for his capacity for non-trivial thinking. And the third important caveat is that I will present my own understanding of these ideas, which Artur may or may not agree with. Why, then, am I voicing my interpretation of someone else's ideas in a non-specialised, popular text? The normal path of a scientific hypothesis should be quite different: first (given sufficient empirical support) it should be published in a specialised journal, and only then communicated to the general public. Unfortunately, we did not carry the verification of our assumptions to completion, and I am about to describe an unfinished piece of work. It seems to me permissible to release this idea into the public domain: perhaps it will prove useful to someone. I will speak about the response of organisms to ecological factors, and I shall begin by noting that these factors are divided into two fundamentally different categories: resources and conditions. Resources are consumed by the organism and become depleted; conditions do not possess this property. As early as 1840, the German agricultural chemist Justus Liebig formulated the so-called law of the minimum. In modern terms it can be stated as follows: the greatest influence on growth and development is exerted by whichever resource is most limiting. Unfortunately, the elementary fact that Liebig's law of the minimum applies only to resources is mentioned in only a handful of ecology textbooks. The typical response of an organism to resource availability is quite simple: a saturation curve. [IMG_1] How, then, do conditions act? They are governed by the generalisation put forward in 1913 by the American ecologist Victor Shelford: the rule of tolerance. According to Shelford's rule (or law) of tolerance, the value of an ecological factor that is optimal for an organism lies within the tolerance range bounded by the extreme values the organism can withstand. The bell-shaped curve describing an organism's response to a condition is usually drawn symmetrically, though this is by no means obligatory; in the figure above I deliberately departed from symmetry. [IMG_2] Wikipedia authors who write that "the law of tolerance extends Liebig's law of the minimum" or that "any factor present in excess or deficiency limits the growth and development of organisms and populations" are confusing resources and conditions. This is a widespread error. I should add that I do not wish to disparage Wikipedia. It is a good starting point for beginning to understand a problem. But it is foolish to attempt to use it as the final authority for rendering a verdict in a dispute. Can resources not also limit through excess? Imagine a plant suffering from nitrogen deficiency caused by a low concentration of nitrate salts in the soil. Add saltpetre and you obtain a clear, appreciative response from the plant, confirming that this resource was indeed the limiting factor. But if too much saltpetre is added, the soil becomes salinised and the plant will have difficulty extracting water from the soil brine. Is this an example of limitation by resource excess? No. Soil salinisation is not a resource. At this point one may adopt one of two formal positions. One may consider that the same factor (nitrate salt content) functions as a resource in one range of values and as a condition in another. But I prefer the alternative: to consider that two different factors are associated with the same molecules in the soil. The first is nitrogen compounds (both nitrate salts and ammonium salts) as a source of mineral nutrition (a resource); the second is salts (both nitrate and, for example, chloride) as a source of soil salinisation (a condition). Some conditions limit development both through excess and through deficiency (temperature, for example), while others limit only through excess (soil salinisation, or, for instance, the toxic action of plutonium). Let us now try to understand what happens at the edges of the tolerance range for a condition (I have "enlarged" one such point on the graph). The factor value increases, conditions worsen for the organisms. But then — what, all of them die at once? Of course not. Contrary to widespread belief, toxicologists do not determine the lethal dose of poisons. They determine the semi-lethal dose (LD50) — the dose at which half of the experimental organisms will die within a specified period. The experimental conditions must be stated precisely. Such-and-such a dose of a given poison causes 50 percent mortality in mice of a given strain within, say, 48 hours. What happens if the LD50 is determined over 72 hours, or using a more sensitive strain? The LD50 value will be lower (the reason is clear, is it not?). Whether a given individual survives or not is influenced by many factors; this process can be regarded as stochastic. The more homogeneous the individuals, the smaller the scatter — yet there can be no such threshold as: below it everyone is alive, above it everyone instantly dies. How is this to be represented on a graph? By showing both the positive and negative effects of the factor on the organism. If the action of a condition increases an organism's productivity or probability of survival, one may speak of stimulation; if it decreases them — of inhibition. Let us construct such a figure, for ionising radiation by way of example. [IMG_3] Ionising radiation (X-rays, gamma rays, etc.) ionises tissues. As an electromagnetic quantum passes through a cell, it can transfer energy to the surrounding molecules. Free radicals are generated — molecular fragments with high reactivity. If this process proceeds intensively, normal cellular processes are disrupted and radiation sickness develops (point 4 on the figure). At background, natural levels of radiation, its effect may be regarded as neutral (point 2). However much this may distress the reader mentioned at the start of the column, the stimulating action of low doses of radiation (point 3) is a phenomenon well-demonstrated in many experiments. One may (and should!) debate its mechanisms, but its existence is no longer in doubt. I have observed it myself (I will describe how shortly). And finally, point 1. To the best of my knowledge, when the level of ionising radiation is reduced substantially below background (which is difficult to achieve experimentally — powerful radiation shielding is required), cell division is impaired. In general, an intracellular environment in which no free radicals arise is something so unusual that organisms have had neither the opportunity nor the reason to adapt to it. Apparently, certain stages of cell division require radicals that are always present in the environment, and in their absence problems arise. What curve passes through the points we have plotted on the graph? The simplest assumption is as follows. [IMG_4] It was precisely this hypothesis that we set out to test, studying the effect of radiation in the intermediate dose range (I have finished the introduction and now turn to the substance of our work, carried out between 1989 and 1991). A few words on the experimental design. To assess the effect of a given treatment, one must analyse the dynamics of some numerical parameter. It is best if the process under study is linear, and one that can be evaluated as positive for the organism. Growth is a good option. But one must choose a growth model in which there are no significant restructurings, so that size serves as an adequate measure... We used the growth of the tail-fin regenerate in fish (mosquitofish, Gambusia). Half the caudal fin of the fish was carefully excised. Over a period of time, a "bud" forms and reorganises, from which the regenerate grows, and then a period of linear growth begins. By measuring the length of the regenerate at regular intervals, one can assess the rate of this process — and the effect of various factors upon it. A particular challenge was the homogeneity of the experimental material. We travelled to the warm-water discharge of a power station where, in Soviet times, enormous numbers of Gambusia lived — small South American fish that were once introduced for mosquito control. We caught Gambusia with nets and selected healthy, vigorous virgin females of uniform size. These were randomly assigned to groups, their fins were excised, they were irradiated with X-rays, and the rate of regeneration was measured. The stimulation at low doses was reliably recorded. Inhibition at high doses was as well. But with intermediate doses the results were strange — we recorded sometimes accelerated and sometimes retarded regeneration. In the intermediate dose range, small changes in experimental conditions caused inhibition to alternate with stimulation or vice versa. We ultimately concluded that the dose-response relationship looked approximately as follows. [IMG_5] We cannot assert that there are exactly two maxima and two minima in the intermediate dose range, but it appears that this range is characterised by an alternation of minima and maxima. Moreover, we hypothesised that this kind of pattern is characteristic of the majority of damaging factors. How is it to be explained? By the hormesis effect. An adverse signal activates a protective system that more than compensates for the signal's action. The presence of multiple peaks is a consequence of the existence of several protective systems differing in their capacity. A separate question — which I will not have space to discuss here — is what cost is paid for the activation of such systems. I will describe just one of the circumstances associated with the idea outlined above. Following our experiments I developed a filter through which I now perceive publications that examine, in one way or another, the effects of intermediate doses of damaging factors. Conscientious authors often acknowledge that their results turned out to be experimentally "noisy". If the experimental groups were heterogeneous, intermediate doses cause a sharp increase in within-group variance (some individuals fall into the "+" zone, others into the "–" zone). Where data points align into a neat curve, the data have most likely been edited or falsified. And a few words regarding the Wikipedia quotation cited by the critical reader. In matters of safety it sometimes makes sense to err on the side of caution. When it is unclear how intermediate doses of radiation act, it is entirely logical to treat them as undesirable and harmful. As a means of understanding the nature of processes induced by radiation, the linear model does not correspond to the current state of knowledge. However, as a means of accounting for potentially hazardous exposures (the dips into "–" on the graph have not been abolished!) it proves quite applicable. And how did our experiments end? We approached the limit of the "resolving power" achievable with the experimental setup of that time. We lacked the resources to continue. More than twenty years have now passed. Periodically I recall that work and dream: if only one could muster the strength to continue! If only I could obtain clonal tadpoles by crossing half-clones of water frogs and return to those old ideas, using particularly homogeneous experimental animals...