ABSTRACT:
This a model from the article:
Parathyroid hormone temporal effects on bone formation and resorption.
Kroll MH. Bull Math Biol
2000 Jan;62(1):163-88 10824426
,
Abstract:
Parathyroid hormone (PTH) paradoxically causes net bone loss (resorption) when
administered in a continuous fashion, and net bone formation (deposition) when
administered intermittently. Currently no pharmacological formulations are
available to promote bone formation, as needed for the treatment of
osteoporosis. The paradoxical behavior of PTH confuses endocrinologists, thus, a
model bone resorption or deposition dependent on the timing of PTH
administration would de-mystify this behavior and provide the basis for logical
drug formulation. We developed a mathematical model that accounts for net bone
loss with continuous PTH administration and net bone formation with intermittent
PTH administration, based on the differential effects of PTH on the osteoblastic
and osteoclastic populations of cells. Bone, being a major reservoir of body
calcium, is under the hormonal control of PTH. The overall effect of PTH is to
raise plasma levels of calcium, partly through bone resorption. Osteoclasts
resorb bone and liberate calcium, but they lack receptors for PTH. The
preosteoblastic precursors and preosteoblasts possess receptors for PTH, upon
which the hormone induces differentiation from the precursor to preosteoblast
and from the preosteoblast to the osteoblast. The osteoblasts generate IL-6;
IL-6 stimulates preosteoclasts to differentiate into osteoclasts. We developed a
mathematical model for the differentiation of osteoblastic and osteoclastic
populations in bone, using a delay time of 1 hour for differentiation of
preosteoblastic precursors into preosteoblasts and 2 hours for the
differentiation of preosteoblasts into osteoblasts. The ratio of the number of
osteoblasts to osteoclasts indicates the net effect of PTH on bone resorption
and deposition; the timing of events producing the maximum ratio would induce
net bone deposition. When PTH is pulsed with a frequency of every hour, the
preosteoblastic population rises and decreases in nearly a symmetric pattern,
with 3.9 peaks every 24 hours, and 4.0 peaks every 24 hours when PTH is
administered every 6 hours. Thus, the preosteoblast and osteoblast frequency
depends more on the nearly constant value of the PTH, rather than on the
frequency of the PTH pulsations. Increasing the time delay gradually increases
the mean value for the number of osteoblasts. The osteoblastic population
oscillates for all intermittent administrations of PTH and even when the PTH
infusion is constant. The maximum ratio of osteoblasts to osteoclasts occurs
when PTH is administered in pulses of every 6 hours. The delay features in the
model bear most of the responsibility for the occurrence of these oscillations,
because without the delay and in the presence of constant PTH infusions, no
oscillations occur. However, with a delay, under constant PTH infusions, the
model generates oscillations. The osteoblast oscillations express limit cycle
behavior. Phase plane analysis show simple and complex attractors. Subsequent to
a disturbance in the number of osteoblasts, the osteoblasts quickly regain their
oscillatory behavior and cycle back to the original attractor, typical of limit
cycle behavior. Further, because the model was constructed with dissipative and
nonlinear features, one would expect ensuing oscillations to show limit cycle
behavior. The results from our model, increased bone deposition with
intermittent PTH administration and increased bone resorption with constant PTH
administration, conforms with experimental observations and with an accepted
explanation for osteoporosis.
This model was taken from the CellML repository
and automatically converted to SBML.
The original model was:
Kroll MH. (2000) - version=1.0
The original CellML model was created by:
Catherine Lloyd
c.lloyd@auckland.ac.nz
The University of Auckland
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To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
Camille Laibe 
