In many biological systems, information is transferred by hormonal ligands, and it is assumed that these hormonal signals encode developmental and regulatory programs in mammalian organisms. In contrast to the dogma of endocrine homeostasis, it could be shown that the biological information in hormonal networks is not only present as a constant hormone concentration in the circulation pool. Recently, it has become apparent that hormone pulses contribute to this hormonal pool, which modulates the responsiveness of receptors within the cell membrane by regulation of the receptor synthesis, movement within the membrane layer, coupling to signal transduction proteins and internalization. Phase space analysis of dynamic parathyroid hormone (PTH) secretion allowed the definition of a (in comparison to normal subjects) relatively quiet ‘‘low dynamic’’ secretory pattern in osteoporosis, and a ‘‘high dynamic’’ state in hyperparathyroidism. We now investigate whether this pulsatile secretion of PTH in healthy men exhibits characteristics of nonlinear determinism. Our findings suggest that this is conceivable, although on the basis of presently available data and techniques, no proof can be established. Nevertheless, pulsatile secretion of PTH might be a first example of nonlinear deterministic dynamics in an apparently irregular hormonal rhythm in human physiology.

1.
L. Glass and M. C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, NJ, 1988).
2.
H. Degn, A. V. Holden, and L. F. Olsen, Chaos in Biological Systems (Plenum, New York, 1987).
3.
L.
Glass
,
A. L.
Goldberger
,
M.
Courtemanche
, and
A.
Shrier
, “
Nonlinear dynamics, chaos, and complex cardiac arrhythmias
,”
Philos. Trans. R. Soc. London Ser. 1 A
413
,
9
26
(
1987
).
4.
A.
Babloyantz
and
A.
Destcxhe
, “
Is the normal heart a periodic oscillator?
”;
Biol. Cybernet.
58
,
203
211
(
1988
).
5.
A.
Babloyantz
and
A.
Destexhe
, “
Low-dimensional chaos in an instance of epilepsy
,”
Proc. Natl. Acad. Sci. USA
83
,
3513
3517
(
1986
).
6.
A. Goldbster and Y. X. Li, “Frequency coding in intercellular communication,” in Cell to Cell Signaling: From Experiments to Theoretical Models, edited by A. Goldbeter (Academic, London, 1989), pp. 415–432.
7.
C.
Schöfl
,
A.
Sanchez-Bueno
,
G.
Brabant
,
P. H.
Cobbold
, and
K. S. R.
Cuthbertson
, “
Frequency and amplitude enhancement of calcium transients by cyclic AMP in hepatocytes
,”
Biochem. J.
273
,
799
802
(
1991
).
8.
D. J.
Waxman
,
N. A.
Pampori
,
P. A.
Ram
,
A. K.
Agrawal
, and
B. H.
Shapiro
, “
Interpulse interval in circulating growth hormone patterns regulates sexually dimorphic expression of hepatic cytochrome P450
,”
Proc. Natl. Acad. Sci. USA
88
,
6868
6872
(
1991
).
9.
J.
Isgaard
,
L.
Carlsson
,
O. G.
Isaksson
, and
J. O.
Jansson
, “
Pulsatile intravenous growth hormone (GH) infusion to hypophysectomized rats increases insulin-like growth factor I messenger ribonucleic acid in skeletal tissues more effectively than continuous GH infusion
,”
Endocrinology
123
,
2605
2610
(
1988
).
10.
E.
Knobil
, “
The neuroendocrine control of the menstrual cycle
,”
Rec. Prog. Horm. Res.
36
,
53
88
(
1980
).
11.
G.
Brabant
,
K.
Prank
,
U.
Ranft
,
T.
Schuermeyer
,
T. O. F.
Wagner
,
H.
Hauser
,
B.
Kummer
,
H.
Feistner
,
R. D.
Hesch
, and
A.
von zur Miihlen
, “
Physiological regulation of circadian and pulsatile thyrotropin secretion in normal man and woman
,”
J. Clin. Endocrinol. Metab.
70
,
403
409
(
1990
).
12.
J. D.
Veldhuis
,
A.
Iranmanesh
,
G.
Lizarralde
, and
M. L.
Johnson
, “
Amplitude modulation of a burstlike mode of Cortisol secretion subserves the circadian glucocorticoid rhythm
,”
Am. J. Physiol.
257
,
E6
-
E14
(
1989
).
13.
W. F. Crowley and J. G. Hofler, The Episodic Secretion of Hormones (Wiley, New York, 1987).
14.
G.
Brabant
,
K.
Prank
, and
C.
Schöfl
, “
Pulsatile patterns in hormone secretion
,”
Trends Endocrinol. Metab.
3
,
183
190
(
1992
).
15.
H. M.
Harms
,
K.
Prank
,
U.
Brosa
,
E.
Schlinke
,
O.
Neubauer
,
G.
Brabant
, and
R. D.
Hesch
, “
Classification of dynamical diseases by new mathematical tools: Application of multi-dimensional phase space analyses to the pulsatile secretion of parathyroid hormone
,”
Eur. J. Clin. Invest.
22
,
371
377
(
1992
).4l6
16.
C. S.
Tarn
,
J. N.
Heersche
,
T. M.
Murray
, and
J. A.
Parsons
, “
Parathyroid hormone stimulates the bone apposition rate independently of its resorptive action: Differential effects of intermittent and continuous administration
,”
Endocrinology
110
,
506
512
(
1982
).
17.
R.
Podbesek
,
C.
Edouard
,
P. J.
Meunier
,
J. A.
Parsons
,
J.
Reeve
,
R. W.
Stevenson
, and
J. M.
Zanelli
, “
Effects of two regimes with synthetic human parathyroid hormone fragment on bone formation and the tissue balance of trabecular bone in greyhounds
,”
Endocrinology
112
,
1000
1006
(
1983
).
18.
C. C.
Liu
,
D. N.
Kalu
,
E.
Salerno
,
R.
Echon
,
B. W.
Hollis
, and
M.
Ray
, “
Preexisting bone loss associated with ovariectomy in rats is reversed by parathyroid hormone
,”
J. Bone Min. Res.
6
,
1071
1080
(
1991
).
19.
M.
Parisien
,
S. J.
Silverberg
,
E.
Shane
,
L.
de la Cruz
,
R.
Lindsay
,
J. P.
Bilezikian
, and
D. W.
Dempster
, “
The histomorphometry of bone in primary hyperparathyroidism: Preservation of cancellous bone structure
,”
J. Clin. Endocrinol. Metab.
70
,
930
938
(
1990
).
20.
H.
Harms
,
U.
Kaptaina
,
W. R.
Külpmann
,
G.
Brabant
, and
R. D.
Hesch
, “
Pulse amplitude and frequency modulation of parathyroid hormone in plasma
,”
J. Clin. Endocrinol. Metab.
69
,
843
851
(
1989
).
21.
N.
Kitamura
,
C.
Shigeno
,
K.
Shiomi
,
K.
Lee
,
S.
Ohta
,
T.
Sone
,
S.
Katsushima
,
E.
Tadamura
,
T.
Kousaka
,
I.
Yamamoto
,
S.
Dokoh
, and
J.
Konishi
, “
Episodic fluctuation in serum intact parathyroid hormone concentration in men
,”
J. Clin. Endocrinol. Metab.
70
,
252
263
(
1990
).
22.
M. H.
Samuels
,
J.
Veldhuis
,
C.
Cawley
,
R. J.
Urban
,
M.
Luther
,
B.
Bauer
, and
G.
Mundy
, “
Pulsatile secretion of parathyroid hormone in normal young subjects: assessment by deconvolution analysis
,”
J. Clin. Endocrinol. Metab.
76
,
399
403
(
1993
).
23.
J.
Theiler
, “
Estimating fractal dimension
,”
J. Opt. Soc. Am. A
7
,
1055
1073
(
1990
).
24.
J. P.
Eckmann
and
D.
Ruelle
, “
Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
,”
Physica D
56
,
185
187
(
1992
).
25.
A. R.
Osborne
and
A.
Provenzale
, “
Finite correlation dimension for stochastic systems with power-law spectra
,”
Physica D
35
,
357
381
(
1989
).
26.
J.
Theiler
, “
Some comments on the correlation dimension of 1/f noise
,”
Phys. Lett.
155
,
480
493
(
3991
).
27.
J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J. D. Farmer, “Using surrogate data to detect nonlinearity in time series,” in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubank (Addison-Wesley, Redwood City, CA, 1992), pp. 163–188.
28.
F. Mitschke, “Acausal filters for chaotic signals,” Phys. Rev. A41,1169–1171 (1990).
29.
N. H.
Packard
,
J. P.
Crutchfield
,
J. D.
Farmer
, and
R. S.
Shaw
, “
Geometry from a time series
,”
Phys. Rev. Lett.
45
,
712
716
(
1980
).
30.
F. Takens, “Detecting strange attractors in turbulence,” in Dynamical Systems and Turbulence, edited by D. A. Rand and L. S. Young, Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898, pp. 366–381.
31.
P.
Grassberger
and
I.
Procaccia
, “
Characterization of strange attractors
,”
Phys. Rev. Lett.
50
,
346
349
(
1983
).
32.
L. A.
Smith
, “
Intrinsic limits on dimension calculations
,”
Phys. Lett. A
133
,
283
288
(
1988
).
33.
P.
Grassberger
and
I.
Procaccia
, “
Estimation of the Kolmogorov entropy from a chaotic signal
,”
Phys. Rev. A
28
,
2591
2593
(
1983
).
34.
A.
Wolf
,
J. B.
Swift
,
H. L.
Swinney
, and
J. A.
Vastano
, “
Determining Lyapunov exponents from a time series
,”
Physica D
16
,
285
317
(
198S
).
35.
F.
Mitschke
and
M.
Dámmig
, “
Chaos versus noise in experimental data
,”
Int. J. Bifurcation Chaos
3
,
693
702
(
1993
).
36.
G.
Mantica
and
A.
Sloan
, “
Chaotic optimization and the construction of fractals: Solution of the inverse problem
,”
Complex Syst.
3
,
37
62
(
1989
).
37.
M. C.
Mackey
and
J. G.
Milton
, “
Dynamical diseases
,”
Ann. NY Acad. Sci.
504
,
16
32
(
1987
).
38.
T.
Shinbrot
,
E.
Ott
,
C.
Grebogi
, and
J. A.
Yorke
, “
Using small perturbations to control chaos
,”
Nature
363
,
411
417
(
1993
).
39.
M.
Doebeli
, “
The evolutionary advantage of controlled chaos
,”
Proc. R. Soc. London Ser. B
254
,
281
285
(
1993
).
40.
A.
Garfinkel
,
M. L.
Spano
,
W. L.
Ditto
, and
J. N.
Weiss
, “
Controlling cardiac chaos
,”
Science
257
,
1230
123S
(
1992
).
41.
A. L.
Goldberger
,
V.
Bhargava
,
B. J.
West
, and
A. J.
Mandell
, “
Some observations on the question: Is ventricular fibrillation ’chaos’?
,”
Physica D
19
,
282
289
(
1986
).
42.
A. L.
Goldberger
,
L. J.
Findley
,
M. R.
Blackburn
, and
A. J.
Mandell
, “
Nonlinear dynamics in heart failure: Implications of long-wavelength cardiopulmonary oscillations
,”
Am. Heart. J.
107
,
612
615
(
1984
).
43.
R. D. Hesch, “Classification’of cell receptors,” in Current Topics in Pathology. Cell Receptors, edited by G. Seifert (Springer-Verlag, Berlin, 1991), pp. 13–51.
44.
K. Prank, H. Harms, C. Kayser, G. Brabant, and R. D. Hesch, “The dynamic code: Information transfer in hormonal systems,” in Complexity, Chaos and Biological Evolution, edited by E. Mosekifde and L. Mosekiide (Plenum, New York, 1992), pp. 95–118.
This content is only available via PDF.
You do not currently have access to this content.