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Файл:Age endocrinology. Study aid for students of medical universities
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One of the striking features of beta cells is that within the islets they exhibit a
close synchronization of regular fluctuations in electrical activity, while isolated cells
fluctuate irregularly. This phenomenon has been modeled mathematically by
considering the islet as a network of beta cells. In accordance with the hypothesis of
heterogeneity, variability in individual cells is “smoothed out” by intercellular
interactions, so that the network can be considered as the average number of cells in
it. This led to the idea that the islets are essentially syncytium, with no single cell
determining the overall response of the network. However, this view has been
challenged by new optogenetic experiments, which have shown that the suppression
of the activity of one (specific) cell can disrupt electrical rhythms throughout the
islet. The presence of these so-called nodal cells can be understood by applying the
theory of computational graphs to the island. Graph-theoretic models emphasize the
presence and nature of interactions within islets rather than the dynamics of
individual beta cells. Such models highlight the dependence of these interactions on
extracellular glucose concentration and that heterogeneous connectivity can give rise
to networks that support nodal cells, functions that would be difficult to understand
without a basic model. Despite the success of using graph theory in this system, there
is currently no experimental or mathematical model to explain the results of the node
cell silence experiment, but it is likely that this will require combining the two
approaches.
Along with secretory insufficiency, insulin resistance is one of the main
mechanisms associated with the development of type 2 diabetes mellitus. To
investigate this phenomenon, a phenomenological model has been proposed that
describes the whole-body response to insulin resistance, including an increase in
beta-cell activity in short and medium time intervals and changes in beta-cell mass
over longer time intervals. Importantly, the model predicts the effect of temporary
weight gain and loss, as well as medical interventions such as gastric bypass. The
study introduces the concept of an insulin sensitivity threshold: a small decrease can
be effectively compensated for, as opposed to a more pronounced one. In particular,
the model highlights how feedback mechanisms to counteract insulin resistance may
contribute to the development of diabetes once the threshold has been crossed. The
concept of personal fat thresholds is already being used to develop diet plans for
diabetics; mathematical modeling has the potential to further support such
interventions. It is important to note that the analysis of the mechanisms of the model
that establishes the threshold explains why it is much easier to prevent diabetes
mellitus than to reverse it.
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Artificial pancreas
The ultimate goal of diabetes management is to achieve glycemic control; that
is, maintaining the concentration of glucose in the blood within a certain range.
Patients with type 1 diabetes mellitus with reduced insulin secretion due to
autoimmune destruction of the beta cells of the islets of Langerhans, exogenous
insulin is usually administered in a basal bolus regimen. Currently, the dose of insulin
administered is calculated by estimating the carbohydrate content of the food. In
addition, these people should monitor their glucose levels throughout the day with
glucometers to prevent hypo- or hyperglycemia. Advances in technology such as
continuous glucose monitors and adjustable dose insulin pumps offer the possibility
of closed-loop control of blood glucose levels through their integration into an
artificial pancreas. Previous trials of the artificial pancreas have been promising, and
the prospect of using mathematical models to understand the dynamics and feedback
between glucose, insulin, glucagon, and other hormonal systems offers a powerful
tool to support advances in biomedical engineering. Importantly, mathematical
models can reveal inherent time frames in biological systems, the understanding of
which is critical to effective control. To this end, mathematical models of blood
glucose and insulin dynamics can be used to develop controls that are predictive as
well as responsive to changes in fasting and postprandial blood glucose levels. The
possibility of further development of control methods using Kalman filters opens up
opportunities for tailoring the parameters of the underlying models to the individual
with the ultimate goal of achieving an individualized treatment plan.
Hypothalamic-pituitary-adrenal (HPA) axis:
hormonal secretion rhythms and stress response
The body's response to stress is mediated by several hormones, the most
significant of which is cortisol. Cortisol belongs to the group of glucocorticoid steroid
hormones with a wide range of context-dependent effects. Because glucocorticoid
steroid hormones are rapidly secreted in response to physical and psychological
stressors, they are commonly known as stress hormones. In the clinic, synthetic
glucocorticoids are widely used due to their anti-inflammatory effect, as well as
hormone replacement therapy. The levels of circulating glucocorticoids – cortisol in
humans, corticosterone in rodents (COR T) — are dynamically controlled by the
activity of the HPA system (Pic. 2), which is characterized by the rhythmic secretion
of corticotropin-releasing hormone (CRH) and arginine-vasopressin (AV) by the
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paraventricular nuclei of the hypothalamus (PNH), adrenocorticotropic hormone
(ACTH) by the pituitary gland and CORT by the adrenal glands. Despite the
cumulative evidence showing the importance of CORT secretion rhythms for
immunological, cognitive, reproductive and metabolic functions, little attention has
been paid to the development of dynamic aspects of glucocorticoid therapy. From a
theoretical standpoint, understanding how the HPA axis maintains rhythmic activity
while eliciting rapid, transient, and proportionate responses to stressors is a major
challenge.
Endogenous glucocorticoids (CORTs) are vital hormones involved in many
physiological processes that are key to homeostasis and survival (eg, mediation of the
stress response, anti-inflammatory and immunosuppressive effects, regulation of
carbohydrate metabolism). Circulating levels of CORT are controlled by the HPA
axis. Corticotropin-releasing hormone (CRH) and arginine vasopressin (AV)
stimulate the release of adrenocorticotropic hormone (ACTH) by the pituitary gland.
ACTH, in turn, stimulates the adrenal glands to produce CORT, which further
regulates its own synthesis via an intra-adrenal feedback loop. Within the HPA axis,
CORT inhibits ACTH in the pituitary and CRH and AV in the hypothalamus,
creating a double negative feedback loop. These impulses have been shown to play
an important role in the optimal response of neuronal processes sensitive to
glucocorticoids. However, under pathological conditions (eg, inflammation, chronic
stress, neurological dysfunction) or aging, this pulsatile dynamic changes and the
tight synchrony between ACTH and CORT is significantly disrupted.
One of the key steps in understanding the dynamic activity of the HPA axis
relates to the causal relationship between ACTH and CORT secretion. An innovative
mathematical model addressed this question by taking into account several stages of
the signaling pathway: activation of the putative ACTH receptor in the membrane of
steroidogenic cells of the adrenal cortex, its transmission through c AMP in the
cytosol, mitochondrial import of cholesterol (substrate for CORT), and the synthesis
and secretion of CORT.
The model was adapted to the rate of adrenal cortisol secretion and blood
ACTH concentrations measured in dogs treated with intravenous ACTH. Importantly,
this model predicted changes in adrenal sensitivity to small and large ACTH
impulses, a phenomenon that was later identified and investigated in other mammals.
Subsequent models considered feedback loops of glucocorticoid influence at the level
of the pituitary and hypothalamus. These models have proposed qualitative
predictions of feedback-generated ultradian fluctuations in CORT levels and possible
ways to enable circadian modulation.
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Pic. 2. Hypothalamic-pituitary-adrenal (HPA) axis2
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Thus, the scientists showed that the combination of a feedback mechanism with
a central nervous system-controlled pulse generator provides both ultradian and
circadian variability in hormone secretion. These models also aimed to explain
specific physiopathological changes such as stress, administration of synthetic
glucocorticoids, and adrenalectomy. Interestingly, the Gupta model S., (2007) also
proposed a bistability mechanism that could explain the operation of the HPA axis
under chronic stress in the allostatic mode.
Although Bairagi 's mathematical models N. (2008) and Gupta S. (2007)
demonstrate the possibility of ultradian oscillations generated by negative feedback,
the predicted frequency of these oscillations differing significantly from the nearhourly oscillations observed in humans. A number of authors have noted that the
mechanisms underlying ultradian oscillations have been correctly predicted to
originate from negative feedback loops between the pituitary and adrenal glands,
while the hypothalamic impulse provides the source of circadian modulation. This
model predicted circadian fluctuations in ACTH and CORT secretion maintained in
vivo, even in the presence of a constant hypothalamic CRH signal. Subsequent
experiments confirmed that the hypothalamic “pulse generator” is not essential for
generating ultradian oscillations of glucocurticoids.
Mathematical models of the HPA axis have now been created, linking
glucocorticoid dynamics and mental health, as well as describing the response to
stress and inflammation. Understanding how healthy adrenal glands achieve rapid
secretion of CORT while preventing its uncontrolled release in response to stressors
is key to explaining the dysregulation seen in endocrine diseases such as Addison's
disease and Cushing's syndrome. In this direction, a number of works have combined
experimental physiology and mathematical modeling, explaining how bursts of
ACTH can be decoded by the adrenal glands, suggesting that the control mechanism
may involve an intra-adrenal negative feedback loop mediated by the glucocorticoid
receptor. The organization of the molecular mechanisms involved in such
intraadrenal regulation occurs through slow genomic and fast non-genomic signaling
pathways. These mechanisms were mathematically modeled as a regulatory network
that not only predicted the transient dynamic responses seen during the stress
response, but also explained how the adrenal glands could decode ACTH impulses of
various magnitudes, including those seen during inflammation.
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The hypothalamic-pituitary-gonadal axis: unraveling the mechanisms
of pulsation of gonadotropin releasing hormone (GRH)
Hormonal signals in the hypothalamic-pituitary-gonadal (HPG) axis (Pic. 3)
are critical to reproductive function, with the key regulatory process being the
pulsatile release of GRH from the hypothalamus to the pituitary gland. Mathematical
models have made it possible to understand how GRH pulsation controls the
synthesis and secretion of the gonadotropic hormones luteinizing hormone (LH) and
follicle-stimulating hormone (FSH)] by the pituitary gland. Early experimental work
in primates revealed a dependence of gonadotropin secretion on GRH frequency,
showing that a pulsatile but not constant rhythm of release from exogenous GRH
depots can restore gonadotropin secretion in animals with hypothalamic lesions. It is
now clear that gonadotropin secretion is suppressed when GRH frequency is either
too high or too low, and this effect is mediated by complex signaling networks that
allow cells to regulate LH and FSH synthesis differently in response to GRH
frequency. Several mathematical models have been proposed showing GRH
signaling. The mechanistic model of this pathway demonstrated the fact that the nonlinear relationship between gonadotropin secretion and GRH pulse rate is most likely
due to the convergent architecture of the feedforward network. The model suggests
that frequency decoding is primarily achieved through the synergistic effect of
several signaling pathways, e.g., the extracellular signal-regulated kinase (ERK)
pathway and the activated T cell nuclear factor (NFAT) pathway] on the expression
of gonadotropin-associated genes. This somewhat contradicts the concept of negative
feedback bottom-up interaction, which was previously thought to play a crucial role
in frequency decoding. Instead, the model shows that feedback plays a different role,
allowing the pituitary system to deal with intercellular heterogeneity and process
GRH information more reliably.
Gonadotropin-releasing hormone (GRH), secreted by GRH neurons located in
the hypothalamus, stimulates the release of gonadotropin hormones [luteinizing
hormone (LH) and follicle-stimulating hormone (FSH)] from the pituitary gland. The
release of gonadotropins depends on the pulsatile dynamics of GRH, which is driven
by neuronal networks in the hypothalamus. Gonadotropins act on the gonads,
initiating the processes involved in gametogenesis and ovulation, and triggering the
release of sex steroids (estradiol, testosterone, progesterone), which feed back to the
brain and pituitary gland, modulating the dynamics of GRH and LH / FSH secretion.
Mathematical models have offered insight into how hypothalamic neurons coexpressing kisspeptin, neurokinin-B, and dynorphin control the pulsatile dynamics of
GRH secretion and how these pulsatile signals are decoded by individual pituitary
cells.
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Pic. 3. Hypothalamic-pituitary-gonadal axis (HPG)3
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At the hypothalamic level, the coarse-grained neuronal population model has
advanced our understanding of how GRH firing is maintained and regulated. The
model relies on experimental work that demonstrates the key role of neuropeptide
signaling in the arcuate nucleus kisspeptin population for GRH impulse generation.
The model supports the idea that kisspeptin regulates GRH impulses, acts as a
relaxation oscillator through negative and positive feedback neuropeptidergic
interactions mediated by neurokinin B and dynorphin, respectively. In addition, the
model predicts that pulsatile dynamics depend on basal activity levels in the
kisspeptin population and highlights the critical behavior of the system as basal
activity increases. Using optogenetics, these model predictions have been validated in
vivo, showing that impulses can be directly controlled in estrous mice by selectively
firing kisspeptin neurons in the arcuate nucleus with continuous low frequency (1 Hz
and 5 Hz) light stimulation. Thus, this is another example of how even simple
phenomenological models can lead to useful and experimentally verifiable
conclusions.
Mathematical modeling has also been used to understand the macroscopic
processes involved in follicle development. Although gonadotropins are known to
control the development of ovarian follicles and their secretory activity, little
attention has been paid to the study of sex steroid secretion and how they revert to the
ascending components of the HPG axis, modulating GRH and gonadotropin
secretion. These feedbacks underlie the ovarian cycle and play a critical role in
female physiology and reproductive health, thus presenting a unique opportunity for
experimental physiologists, clinicians, and mathematical modellers.
Hybrid systems:
a new paradigm for determining how parts affect the whole
Like the alpha and beta cells of the pancreas, the five types of anterior pituitary
endocrine cells (cells that secrete LH, FSH, ACTH, STH, prolactin) generate
electrical activity in bursts. Electrical activity delivers Ca
2+
to cells through ion
channels, which triggers hormone secretion. In the absence of hypothalamic signals,
pituitary gonadotropes release few hormones at a slow rate. On the contrary,
lactotrophs and somatotrophs release hormones in a bolus in a pulsed mode,
providing more time for Ca
2+
to penetrate into cells. Therefore, lactotrophs and
somatotrophs have a high basal rate of hormone release. In addition, the cells of the
pituitary gland differ in the number of potassium (VC) channels of high conductivity.
Lactotrophs and somatotrophs have a high density of BK channels, while
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gonadotrophs have a low density. This is paradoxical because BK channels are
repolarizing channels (in neurons and other cell types). BK channels usually open
rapidly during an action potential, shortening its duration. However, in pituitary cells
such as somatotrophs and lactotrophs, BK channels seem to increase the duration of
impulses, converting monotonous secretions into impulse boluses.
The mathematical model predicted that the assimilation of BK channels into
the electrical activity of gonadotropes can change the dynamics of their excitation
from peak to explosive. Opening rapidly at the beginning of the action potential, VC
channels limit the activation of other, slower K channels. + channels, which in turn
prevents cell repolarization. Analysis of the model suggests that this effect is resistant
to changes in the expression of other ion channels (Pic. 4).
Experimental Hybrid System. Traditionally, mathematical models have been
integrated with experiments through an iterative process: the predictions of the
models are checked against the results of the corresponding experiments, and then the
models are updated to eliminate any discrepancies between them. Although many
studies follow this scenario, nevertheless, hybrid experiments allow you to combine a
mathematical model and an experiment interactively, in real time. Hybrid systems
allow us to manipulate the values of key parameters with the freedom of a
mathematical model. At the same time, the effects of these manipulations are
observed in real biological systems. One example of a hybrid system is the dynamic
clamping protocol for electrically excitable cells. This system uses a mathematical
model to send a command signal to the cell from which the electrical recording is
made. It is important to note that since the cell's membrane potential can be fed to a
real-time model, it can be used to input signals that mimic ionic currents that may or
may not be present in a real cell. Thus, the parameters associated with these currents
can be manipulated, or completely different channels can be included in the cell.
Dynamic clamping has been instrumental in establishing the role of BK
channels by linking a model-based mathematical mechanism to real pituitary cells. It
illustrates the ability of hybrid systems to combine experiments and mathematical
modeling. Another interesting example of such a system was developed by
Dhumpa R. (2014) and showed that the islets of Langerhans can synchronize their
insulin secretion through feedback from the liver. To do this, they introduced islets
loaded with a Ca2+ fluorescent indicator into a microfluidic chamber and coupled the
total Ca2+ signal from the islet population with a mathematical model of hepatic
glucose release in response to insulin. The simulated glucose level was then delivered
back to the islet chamber. Without feedback from the liver, the islets produced
independent oscillations.
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Pic. 4. Dynamic Clamp: Simultaneous Mathematical Simulation and Real-Time4
However, once the feedback was turned on, the islets began to synchronize, as
evidenced by the resulting total concentration of Ca
2+
fluctuations, out of phase with
the net glucose fluctuation.
This fact showed that the liver can act as a coordinator of activity in the islet
population, which made it possible to test the effectiveness of this coordination, since
the feedback rate of the liver was different. Thus, hybrid systems allow us to define
the role played by each component of a biological system in real time.
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