Bjorntorp: You measured these things every second minute, and then you have a pulse of say LH. This then has to reach the testosterone-producing site, causing testosterone secretion. This then has to feedback. Is this actually happening? I can understand the nervous circuit, because this is quick, but the circulatory circuit is slower.

Veldhuis: Yes, there is feedback. One of the things that is strangely lacking is the exact kinetics of the feedback time delays. I have spent a year reading 600 papers and cannot find exact time delays. We are going to use the drug ketoconazole, which blocks cytochrome P450 activity at high doses and thus steroidogenesis. One dose of this drug lowers testosterone concentrations overnight from 25 nM to about 3 nM. Now you have a testosterone-withdrawn state in which you can clamp feedback. At midnight, we start a constant testosterone infusion that is about one-third of the expected amount produced endogenously over the same time interval. At 8 a.m. the next morning we pulse in a 6 min waveform of testosterone and monitor feedback timing in young and older men. Currently, we are guessing feedback timing on the basis of cross-correlation data, which means that we take 15 older men and 15 younger men, and sample for LH and T simultaneously for 24 h. We then have paired series. We ask the question, 'whenever T goes down, how long does it take for LH to go up?' In the human, this negative feedback has about a 60—90 min delay in the young and 0—60 min delay in the older male. Feedback is occurring, but this is the only way that we have estimated how long it takes for the system to react.

Bjorntorp: You are not saying that the decrease of the LH peak is dependent on an immediate feedback.

Veldhuis: No, that is a good point— it is unlike the cortisol—adrenocorticotropic hormone (ACTH) axis where there is some evidence for that. This is not so rapid.

Bjorntorp: So the LH peaks are sort of automatic?

Veldhuis: That is what we believe, but we think the pulse generator frequency is under T control in the human.

Handelsman: It is a wonderfully subtle illustration of entropy. The power of the approach is enormous. I just wondered whether you have thought about this another way.

Veldhuis: This is the advantage of the current formulation by Steve Pincus, which we used in Pincus et al (1996). It is a lag-independent cross-approximate entropy (ApEn) metric. One of the disadvantages of simple linear cross-correlation is that it is assumed that each subject has roughly the same relationship between the two hormones in time, and also that within any one person there is a similar relationship across the day and night. This may not be true. When we run windows of cross-correlation, we find that the strength of feed-forward coupling varies across 24 h. It sounds intuitively obvious, but it is very clear for ACTH—cortisol and LH—T. The beauty of cross-ApEn is that it is lag-independent. It basically asks the question, given standardized z-score transforms of the original time series to make them scale independent, if there are some wiggles in the first series of hormones, do they ever happen in the second? If they never do, they are not very synchronous. If they do happen a lot together, they are fairly synchronous. If they are happening almost all the time, they are highly synchronous. It matches templates up- and downstream independently of location.

Handelsman: One of the beauties of this technique is that it is model-independent. However, the difficulty is that it makes entropy seem such an abstract notion. To be a bit more concrete, in the studies where you deliberately gave LH pulses, how does that look under your model? Can you override the apparent age-related increase in entropy by administering clear and coherent LH pulses?

Veldhuis: We intend to look at this. When we use the GnRH pump in older men, we see a result that at first is counterintuitive. There is a more random output of LH in younger and older men under perfectly regular 90 min experimentally enforced pulsatile GnRH drive (Mulligan et al 1999). Why is this? We are actually monitoring minute-to-minute feedback activity between T and/or LH under the GnRH stimulus and not the 90 min pulse. This is a microanalysis that is checking feedback adjustment (Veldhuis 1999a). When the system is forced with fixed input, this abolishes feedback. Thus, ApEn of LH actually goes up on the GnRH pump in young men. The axis essentially becomes a clamped system with a non-dynamic quality of feedback. The feedback elegance is abolished by the clamp.

Handelsman: The physiological pharmacodynamic models of Jusko and colleagues are very similar; they are constructed of components like that. Are your thoughts going in this direction?

Veldhuis: This is the idea. We have a couple of papers out using testosterone, which took us five years to write, because there are surprisingly large subtleties in how to build a dose—response curve and prove that the set of equations is realizable mathematically (Keenan & Veldhuis 1998, 2001, Keenan et al 2000). There are some things that are produced only in the square root of minus one, which is an answer that has no utility to us as clinicians, being an undefined term. We have now done this for ACTH and we are just getting there for GH (Farhy et al 2001). The idea is only to take the core components. The first time we did this for GH, we tried to do it comprehensively (Straume et al 1995). We ended up with 87 parameters, and it may take a few dozen years for computers to be developed with the power to optimize this collection of parameters. Now we are down to 12 parameters for GH and about 10—12 for LH. Without infusing LH, I'd like to know that the older Leydig cell of the mouse, human or rat is unresponsive to LH. How do I do that? I have to watch LH and T move together in young and older men and calculate the endogenous dose—response curve, without ever seeing it. I can't do that without a correct statement of how the dose—response curve primarily operates. If I can do that, I can tell you the dose—response curve without injecting anything.

Robertson: I'm not as familiar with chaos theory applied to the endocrine system as I am for example with its application to heart rate. But looking at your data I

would never have guessed you would be able to account for nearly everything that you see by the interactions of these two variables. What percentage of influences do you think are outside this paradigm?

Veldhuis: That is a gorgeous question: I just wish you had been a reviewer. A reviewer once said that we didn't need any stochastic, random element that is unexplained, but that we should just draw the correct feedback loop. My response was that nothing is absolutely constant. If I stand up, my LH distribution volume is slightly different. If I walk, my testis bloodflow is changed. Everything is changing slightly outside the idealized dose—response. The aggregate uncertainty can be instilled in a stochastic differential equation. Our stochastic term is only 2—3% of the data, but it is critical. Where is the stochastic element? Firstly, the pulse generator doesn't fire exactly as a clock ticks. We allow it some variability (Veldhuis 1999a, Urban et al 1988). Second, we say that the feedback equations we are talking about are idealized equations. They are never observed. The feedback equations are dancing slightly, but at all times. We put in a little stochastic term to allow the parameters of the feedback equations to jiggle by 2—3%. This gives our realistic data profiles. Otherwise one observes gorgeous curves that you and I only see one in 20 profiles.

Handelsman: This is such a highly deterministic system. One feature is that you can explain virtually all T secretion by LH pulsatility as shown by the fact that you can switch it completely off with antagonists or steroids. This makes it reasonable to say that you can predict nearly all the components, because we can easily identify proximate determinants that can switch it completely off. This isn't true for most other physiological systems, where there is a very lower proportion of variance explained.

Veldhuis: It is strongly deterministic with just 2—3% stochastic. This fits with the fact that we are not a couple of molecules reacting in free solution.

Giustina: One point we know from the ageing GH axis is that ageing is interacting with obesity in creating a loss of GH secretion. What about your model of LH and testosterone in obesity?

Veldhuis: All we know is that in general the literature agrees that LH pulse amplitude is damped in some manner by visceral obesity in particular. Most studies show this effect to be quite strong, and at least as strong as the age effect in middle age. What isn't clear to me is what is mediating this effect. It could be the insulin levels.

Shalet: Where does oestradiol fit in to this?

Veldhuis: That is a frightening question because the situation is getting more and more complicated. The oestrogen receptor knockout or the aromatase gene-defective animal have about a doubling of LH output. We find the same with the drug anastrozole, an aromatase inhibitor. In situ aromatase activity appears to be important in negative feedback. It isn't clear whether this is controlling only amplitude or frequency. We have had to study 31 men to try to get a clear answer. We have used three different pulse methods to see whether we can get a consistent opinion on it. The amplitude clearly changes, so there is amplitude drive. I had been puzzled why men show an increased LH pulse frequency on clomifene or tamoxifen, both antioestrogens, but when you infuse peripheral oestrogen in the human, you can almost never demonstrate a suppression of LH pulse frequency (Veldhuis et al 1984, Veldhuis & Dufau 1987, Urban et al 1988). The exception is a study in which we put an oestrogen-containing silastic ring intravaginally in postmenopausal women, delivering oestradiol (Veldhuis et al 1987). There, on day 5, LH pulse frequency fell with amplitude and then recovered. In the monkey, one can infuse peripheral oestrogen, which decreases hypothalamic multiunit firing within minutes. But, excluding those exceptions, people cannot readily demonstrate oestradiol negative feedback on frequency in the male. This is puzzling. Is it the in situ hypothalamic oestradial that suppresses the pulse generator frequency? As far as I can tell, this would explain the tamoxifen/ clomifene and anastrozole data. These drugs would block oestradiol produced in the hypothalamus. This would also explain the fact that peripheral oestradiol infusion, in almost everybody's hands, mainly blocks GnRH-driven LH amplitude at the pituitary level. The aromatase inhibitor study will be key to try to dissect whether that is true.

Laron: What down-regulates prolactin?

Veldhuis: I would love to know. Older men are hypoprolactinaemic (Iranmanesh et al 1999). So are type I diabetic patients (Iranmanesh et al 1990). There are a collection of curious situations where there is reversible hypoprolactinaemia. But I don't know other data that give us clear evidence for dopamine excess.

Müller: There could be an up-regulation of the dopamine receptor.

Veldhuis: That would be beautiful.

Müller: We have data from experiments in older rats showing increased pituitary sensitivity to the prolactin-lowering effect of bromocriptine (Cocchi et al 1984). Moreover in aged female rats presenting with marked alterations in the tuberoinfundibular dopaminergic neuronal function, pituitary binding sites for [3H] spiroperidol, a neuroleptic, are increased (Govoni et al 1980).

Laron: This relates to my first question: how much of the dose—response is actually linked to the number of receptors?

Veldhuis: The data in the rat do not consistently show loss of GnRH receptor or GnRH activity with ageing.

Wang: The GnRH responsiveness is normal in old rats.

Veldhuis: In our hands it is also normal to enhanced in the human (Mulligan et al 1999, Zwartet al 1996).

Morley: Johannes, you have done a great job of trying to take the complex and make it intelligible. Unfortunately, I prefer complexity. As I look at the literature, when we start to look closely, young and old are not young and old: there are at least four separate phases. There is the 20—32 year old who we could call normal young. Somewhere after 32 we start to lose some testosterone in almost all studies. When you get to early middle age (40—55), there are some hints that there is excess opioid secretion at this stage and these people are very responsive to opiate antagonism in their LH levels. Then we get the group you have been talking about, the 60—75 year olds. In longitudinal studies by ourselves and others, when you get to 80+ the LH suddenly takes off and gets to 25—30IU/L. These are clearly a different group. I guess the question is, how do you put this together with the entropy and what causes that sudden release in very old age to going from a quasi secondary hypogonadism to a primary hypogonadism?

Veldhuis: That is why I was so excited by Christine Wang's data suggesting that there may be some fixed GnRH defect. I had assumed that the late LH rise was due to end-stage Leydig cell failure (Veldhuis et al 1999b). Of course, no one has done the kind of near-physiological drive of the Leydig cells that modern tools allow us to do. The idea of formalizing several levels in the axis that are points of lesioning in ageing is that you can then test them and their implications. Certain nodes clearly don't lead to exactly what you predict. The reason is that if there is a non-linear interactive, time-delayed system, intuition is stymied (Keenan & Veldhuis 1998, 2001, Keenan et al 2000). However, what we thought we would do is create a model in which we let the computer run overnight, producing a seven year lifespan. We let it gradually trickle down one of the feedback constants, and then introduce a couple of lesions on top of that. This gives an idea of whether it is possible to unmask the phases. The other real challenge is the between-individual variability. There you have individuals who appear to be absolutely normal in their entropy scores, and yet their pulse generator looks awfully good.

Morley: Could you go back and look at the people you studied a long time ago? This is probably the key to understanding all this.

Veldhuis: Believe it or not, since you like complexity, I will soon have data of 10 min LH ApEn analyses collected for four consecutive days, to watch the pulse generator unfold and fluctuate over the day and night. We intend to compare this in older and young men. We postulate that as one gets into these metastable conditions (by which I mean that they are not absolutely normal, but they are not pathological), the stability of the pulse generator over four days will be degraded (Pincus et al 1996). We may be wrong, and it may prove to be even more stable in the elderly, which would be a more exciting paper.

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