The Clock That Starts When It Stops

I.The First Known Thing — the mineral that dates its own closing

geochronology · closure temperature

A radiometric date rests on a parent that decays at a known rate into a daughter that accumulates, and the date is read from the ratio of the two. The difficulty, which the first half-century of the method got wrong in an instructive way, is that the daughter is not always kept. Argon produced from potassium, helium from uranium and thorium, lead from uranium, are foreign to the crystal that holds them, and at high temperature they diffuse out of it about as fast as they are made. The crystal is, in that state, a leaking vessel whose ratio records nothing. As the rock cools, diffusion slows — exponentially, by the usual law — and there comes a range of temperature over which the loss falls from complete to negligible. Below it the daughter is retained and the clock runs. Above it the clock is continuously reset. The date that the method returns is therefore not the date the crystal formed, and for a slowly cooled rock it is not the date of any event at all in the ordinary sense: it is the date at which the crystal passed through the temperature at which it stopped exchanging with its surroundings.

the closing depends on the cooling

Martin Dodson's contribution in 1973 was to show that this moment is well defined and to say what it depends on. He defined the closure temperature of a system as the temperature the rock was at, at the time its apparent age records, and derived it from the diffusion parameters of the mineral, the size and shape of the grain, and the rate at which the rock was cooling. The last of these is the surprising one. A crystal cooled quickly closes at a higher temperature than the same crystal cooled slowly, because in a fast cooling the window over which the daughter is partly lost is passed in less time and less is lost; and since the closing is defined by the cooling and the cooling is what the date is used to measure, the two must be solved together, by iteration, rather than one read off the other. The dependence is logarithmic and so not large, but it means that the closure temperature is not a constant of the mineral. It is a joint property of the mineral and of the history it was in. Grain size enters in the same way: a large crystal keeps its daughter longer than a small one of the same kind, and so closes hotter and earlier, and two grains of one mineral from one rock can return different dates for no reason other than their size.

many clocks, one path

The consequence that built a subfield is that different mineral-and-daughter systems close at very different temperatures. Uranium-lead in zircon closes at something over nine hundred degrees, near the crystallisation of most rocks that carry it. Argon in hornblende closes around five hundred; in muscovite and biotite, somewhere in the three to four hundreds. The fission-track damage in apatite anneals away above roughly a hundred and ten degrees, and helium diffuses out of apatite above about seventy. A single rock therefore carries a set of clocks that each started at a different temperature, and their dates, laid against their closure temperatures, are not competing estimates of one age but successive points on the rock's own time–temperature path — the record of when it cooled through each of those isotherms, and from that, of how fast it was brought to the surface. This is thermochronology, and its working assumption inverts the one the method began with: the dates from one rock are expected to disagree, the pattern of the disagreement is the datum, and a rock whose clocks all agree is a rock that cooled fast enough for its history to have no readable shape. Two further facts belong here. A rock reheated above a system's closure temperature has that clock reset, so the date records the last cooling and not the first, and nothing in the date says which it was. And a rock held for a long time inside the temperature range where loss is partial — the partial retention zone — returns a date that is neither the entry to that range nor the exit, and is meaningful only with a model of the residence.

what the discipline makes of it

The field has spent fifty years on the machinery — diffusion parameters, grain-size corrections, damage accumulation, the modelling of paths from sets of dates — and it treats the closing as a property to be calibrated for each system, not as a principle about recorders in general. It is in the habit of reading a cooling rate from a spread of dates. It has never had reason to ask what that habit would mean for a recorder that is not a mineral, or for a body whose temperature is not what it wishes to know.

II.The Second Known Thing — the marker that reports the past

drug discovery · biomarkers and patient stratification

A biomarker, in the use that matters here, is a measured quantity that stands in for a disease process too slow, too deep or too diffuse to be measured directly, and stratification is the practice of dividing a trial population, or a treated one, by the value the marker takes at a visit — above a cut-point or below it, positive or negative, high or low — so that the effect of a drug can be estimated within the divisions, or the drug given only to one. The division is made from the marker at a single time. It is understood to be a division by state: how much disease, how much of the target, how far along.

every marker has a window

Almost every marker of this kind is, on inspection, not a reading of the present but an average of the recent past over a window set by its own turnover. Glycated haemoglobin is the plain case. Glucose attaches to haemoglobin irreversibly, the red cell lives about four months, and the measured fraction is the mean glucose over the cells' lifetimes, weighted towards the most recent weeks. Fructosamine, the glycation of serum proteins, mostly albumin, averages the same glucose over two or three weeks, because that is how long the proteins last; glycated albumin likewise; a fingerstick glucose averages nothing. In oncology the tumour DNA circulating in plasma is cleared with a half-life of the order of an hour and so reports the tumour of this morning, while the protein markers — carcinoembryonic antigen, the prostate-specific antigen, the CA series — are cleared over days and report the tumour of last week, and a scan reports the tumour of the moment but is taken every two or three months. Each of these is a recorder in exchange with the process, and each stops exchanging, and so stops recording, at a lag fixed by its own turnover. The field knows this well and uses it in one direction only: for monitoring. A fructosamine is ordered when a change in control needs to be seen sooner than the haemoglobin will show it; a circulating-DNA response is read weeks before the scan can confirm it. The window is treated as a matter of which marker answers fastest.

what is done with two of them at once

Where two markers of the same quantity with different windows are measured at the same visit, their disagreement has been noticed and has been named. In diabetes the difference between a patient's glycated haemoglobin and the value predicted from their fructosamine is the glycation gap, and it has been studied for twenty years. It is fairly stable within an individual over years, it differs between individuals, it predicts nephropathy and mortality beyond the haemoglobin alone, and it is attributed to what varies between people — the lifespan of their red cells, their propensity to glycate, the enzymes that undo it. It is read, in short, as a trait. That it might also carry, in a patient whose glucose was moving when the sample was drawn, the direction and speed of that movement, and that the stable part and the moving part are separable in principle, is not part of how it is used. In oncology the corresponding pair — circulating DNA and a protein marker on the same day — is not combined into anything; each is compared with its own previous value. Rate, where the field wants it, is taken from serial measurement of one marker: the PSA velocity, the change in haemoglobin over three months, the molecular response between cycles. A rate from a single visit is not a concept the field has, and stratification by rate at baseline, before any second sample exists, is not a thing that is done.

what the field controls and what it counts

The stratifying cut-point is validated with care — on its reproducibility, its association with outcome, its interaction with treatment. The window of the marker behind it is not part of the validation. A population divided at a single visit on a marker with a three-month window has been divided on the patients' state a month or two ago; a population divided on a marker with a window of hours has been divided on their state now; and a trial that stratifies on the first and measures response by the second has changed clocks between its baseline and its endpoint without saying so. No measure in use distinguishes a patient whose slow marker and fast marker agree, and who is therefore at rest, from one whose fast marker has run ahead of the slow one, and who is therefore moving, though the two may sit on the same side of every cut-point the trial uses.

III.The Bridge

no thermochronology paper cites a glycation gap; no biomarker review cites a closure temperature

The halls do not meet. One is a branch of geochronology whose literature is diffusion parameters, mineral systems and the exhumation of mountain belts; the other is clinical and translational science whose literature is assay validation, cut-points and outcomes. No review spans them and the words they share — half-life, clearance, reset — are shared by every field that has a rate in it. Three neighbours in this catalogue should be set aside. It is not the hiatus incorporation of the specimen on sediment, in which a rate measured over a span averages the dormancy the span contains and so falls the longer one looks; that concerns how a single rate depends on the span it is taken over, whereas this concerns how two recorders of one process, each with its own span, disagree at one instant. It is not the discharge order of the specimen on depots, which concerns the sequence in which a store gives back what entered it; here nothing is stored and given back — the recorder is overwritten. And it is not the convergence fadeout of the specimen on catch-up, in which a measured difference decays because the comparator arrives; there the two trajectories are two arms of a trial, whereas here they are two instruments on one patient, and their difference is not an effect that fades but a reading that is meant.

X: the record is dated by the closing, and the closing by the change

Call it closure lag. Where a recorder is in exchange with a quantity that changes, and the exchange is what lets the recorder follow it, the recorder does not report the quantity as it is but as it was at a lag — and three things follow about that lag, none of which is that it is a constant. The first: the lag is set by the recorder's own exchange constant, so that a body carrying several recorders of one quantity carries a set of readings of that quantity at a set of past times, and the disagreement among them, read at a single instant, is a measurement of the quantity's rate of change over the span the lags cover, while their agreement is a finding that the quantity is at rest. The second: the lag is not a property of the recorder alone but of the recorder and the change together — a quantity moving quickly is recorded at a shorter lag than one moving slowly, because a recorder with a fixed exchange constant that averages an exponentially changing quantity reports it at the lag that would have been exact for a steady change, shorter than that when the quantity is rising and longer when it is falling, so that a rate read from the disagreement by assuming the lags fixed understates the fastest movers, and the correction is a function of the very rate being read and must be solved with it. The third: because the recorder can be reset by an event that renews its material, its reading dates from the last such event, not from the origin of the quantity, and nothing in the reading says which. Read into the clinician's hall, each has a consequence the hall does not state. A patient's fast and slow markers of one quantity, drawn at one visit, contain a velocity, and stratifying at baseline on the difference between them, scaled by the difference in their windows, sorts patients into those whose disease was moving and those whose disease was still — a division no cut-point on either marker makes, and one that is available before any second sample. A patient's stable offset between two markers, the trait the diabetes field has named, is what remains of that difference when the velocity is subtracted, and the two are separable by the single fact that one of them changes sign when the trajectory does and the other does not. And the conversion from difference to rate, if it is done by a fixed factor, will place the fastest patients too near the resting ones, and place a falling process further from its markers than a rising one of equal speed — a bias with the shape of a closure temperature, and with the same remedy.

IV.The Question That Becomes Possible

neither discipline would ask this alone

The clinician's hall asks which marker answers fastest and, when it wants a rate, takes a second sample. The geochronologist's hall has no patients, but it has half a century of reading the rate of a process from the spread of readings taken at one instant by recorders that close at different times, and of correcting the reading for the fact that the closing itself depends on the rate. Neither hall asks whether a population can be stratified by velocity from one visit.

the closure lag hypothesis

For a disease process tracked by two markers of the same underlying quantity whose exchange windows differ — glycated haemoglobin against fructosamine or glycated albumin; circulating tumour DNA against a serum protein marker of the same tumour — does the discordance between the two at a single visit, converted to a rate through the difference in their windows, predict the rate of change of the process subsequently observed by serial measurement; does stratifying a population at baseline on that single-visit rate separate patients by outcome and by treatment effect beyond either marker's level alone and beyond the stable individual offset between them; and does the conversion require, as closure temperature does, that the lag be solved together with the rate, so that a fixed-factor conversion systematically underplaces the fastest-moving patients and misplaces a falling process relative to a rising one?

why it would matter

Because a trial that could separate moving patients from resting ones at enrolment, from samples it already draws, could stratify on a quantity that plausibly governs response — a disease accelerating into a trial is not the disease that is drifting into it, whatever the level — without a run-in period or a second visit, and could do so in exactly the populations where run-in is hardest to afford. It would give the glycation gap, and whatever its counterparts in other diseases turn out to be, a decomposition into a part that is the patient and a part that is the moment, and a reason to record the second. It would tell a trial that stratifies on a slow marker and reads its endpoint on a fast one how much of its apparent heterogeneity is a change of clocks. And if the rule fails — if the single-visit discordance is all trait and no motion, or predicts nothing a second sample does not predict better — then the marker's window is a matter of monitoring convenience, exactly as the field treats it, and the cooling rock has nothing to say to the clinic.

V.How It Could Be Proven — or Broken

a candidate must be breakable, or it is merely poetry

An intercognix candidate earns nothing until it names its own test. This one is unusually cheap, because the data it needs have been collected many times over for other reasons, and its first break condition can be reached from a single existing cohort.

the honest status

Note the narrowness. The claim concerns pairs of markers that are both averages of one underlying quantity over known and different windows, and says nothing about markers of different things, about markers that are thresholds rather than averages, or about the great majority of stratifying markers, which are genotypes and expression states that do not move at all. It does not say that the glycation gap is not a trait; it says it may be a trait plus a velocity, and that the two are separable by their behaviour under a change of direction, which is a testable claim and may be false. It does not say the field's serial velocities are wrong; it says a velocity may be had one visit earlier than they can supply it, at the price of a conversion that is harder than division. It is worth saying what does not transfer. The rock's clocks record temperature, which the geologist wants; the patient's markers record a process the clinician wants only as a proxy for something further off, so a velocity in the marker is one step further from the thing that matters than a date in the rock. The rock's several clocks are read once and never again, and the whole discipline exists because there is no second visit; the clinic has second visits, and the claim survives only if the single-visit rate is worth something the second visit is not — earliness, or the absence of a run-in, or the stratification of a trial at the door. And the rate-dependence of the lag, which is the part of the bridge that is not merely a difference of half-lives, is derived here for a marker that is an exponentially weighted average of the process; a marker whose weighting is of another shape has a different correction, and the diabetes markers in particular are known to weight the recent past more heavily than a single exponential would. The whole thing rests on one cohort with a baseline pair and a serial follow-up, which exists, and on a comparison against a two-visit slope, which is the comparison most likely to end it. If it ends there, this is an elegant way of saying that a second sample is worth taking, and should be said so. Until that comparison is made, this remains exactly what its stamp says: a candidate. A structural echo between two halls of the library, waiting for someone with the tools of both to walk the corridor.