Emergent Patterns of HPA Hormone Pulsatility and Diurnal Variability in silico: Part 1 of 3

Jay Michael Otero and Hans B. Sieburg*

Laboratory for Biological Informatics and Theoretical Medicine
Department of Psychiatry, Department of Mathematics
University of California, San Diego
La Jolla, California 92093-0112 USA
Tel: +1-619-534-6949
FAX: +1-619-492-1137
E-mail: hsieburg@ucsd.edu

*Author to whom all correspondence should be addressed.

http://www.netsci.org/Science/Bioinform/feature02.html

Summary

This study used a computerized hypothalamic-pituitary-adrenal (HPA) axis simulator to model dynamic interactions and patterns of hormone secretion. We defined the structure of our model HPA axis using several parameters: a central pulse generator, gland sizes, hormone secretion rates, hormone life spans, feedback inhibition, and constitutive (baseline) hormone secretion. We found that constitutive CORT secretion from small adrenal glands produced pulsatility and diurnal variability in CRF and ACTH secretion, but large adrenal glands suppressed secretion due to feedback inhibition. Simulations using small HPA glands, low CORT secretion, intermediate CRF and ACTH secretion, constitutive CRF secretion, and hypothalamic (long) feedback inhibition additionally produced pulsatility and diurnal variability in CORT secretion. Suppression of CRF and ACTH by larger adrenal glands in silico parallels known clinical disease states (e.g., Cushing's syndrome). Diurnally variable CORT levels in simulations without pituitary feedback inhibition may parallel HPA hormone circadian rhythms in vivo influenced by changes in pituitary feedback sensitivity. We propose that shifts in pituitary sensitivity may serve to regulate circadian rhythm. The reported work suggests that in silico research, conducted in parallel with in vivo research, may permit investigators to generate hypotheses more rapidly from available data.

Keywords -- Computer simulation; HPA axis; Feedback inhibition; Pulsatility; Diurnal variability; In silico research.

Introduction

The hypothalamic-pituitary-adrenal (HPA) axis is an important control system and dynamic interface for multiple physiological systems. Biochemically interconnected, its major glands generate rhythmic hormone secretion. The respective hormones, corticotrophin releasing factor (CRF), adrenocorticotropic hormone (ACTH), and principle glucocorticosteroids (CORT; e.g., cortisol in man, corticosterone in rats), modulate their own secretion through feedforward and feedback mechanisms within the HPA axis and exert physiological effects in target organs outside the HPA axis.

In healthy humans, HPA hormones, particularly ACTH and CORT, exhibit diurnal variability in serum levels and tend to be secreted in pulsatile fashion. CRF stimulates the pituitary corticotroph, and pulsatile secretion appears to be a basic characteristic with approximately 18-40 ACTH pulses per day in humans (Gallagher, Yoshida et al. 1973; Negro-Vilar, Spinedi et al. 1987; Sherman, Schlecte et al. 1987; Veldhuis, Iranmanesh et al. 1990). Studies of CORT have shown a range in pulsatility with approximately six to 15 secretory episodes per day (Refetoff, Van Cauter et al. 1985; Sachar, Hellman et al. 1973; Sherman, Schlecte et al. 1987). Humans with normal sleep-wake patterns commonly show a circadian pattern of CORT secretion featuring a surge in the early morning hours later reaching a peak at around 0800 (McCutcheon and Oldfield ). Sustained levels throughout the day gradually declining in the late evening or early morning hours typically follow the mid-to-late morning surge (Krieger 1979). Levels begin to steadily rise again after midnight. Changes in feedback sensitivity during the day appear to modulate variability in CORT level. The hypothalamus and pituitary seem to be most sensitive to negative feedback at midnight and least sensitive in the morning (McCutcheon and Oldfield ). However, the diurnal variability in ACTH levels appears to be independent of CORT feedback inhibition (McCutcheon and Oldfield ).

Because the HPA axis provides a link among multiple physiological pathways, synergistic influences arise producing non-linear dynamics. We have previously described a software thinktank, the Cellular Device Machine Development System (CDM-DS), for building simulators with the capacity to predict complex non-linear dynamics [Sieburg, 1990 #7; Sieburg, 1990 #8; Sieburg, 1991 #6; Sieburg, 1991 #9; Sieburg, 1993 #1; Sieburg, 1993 #3; Sieburg, 1994 #122; Sieburg, 1994 #144; Baray, 1993 #79]. We have applied this system to explore some of these interactions.

In our simulations, we have found that configurations using a constitutively secreting pituitary respond in a less predictable manner than systems using a constitutively secreting hypothalamus (Sieburg, Otero et al. 1994). Specifically, we predicted that two HPA axis configurations possessed sufficient regulatory and information-processing capacity to serve as control systems for the body. In one model, the hypothalamus and adrenal gland, both constitutively secreting and driving the pituitary, served as pacemakers for the HPA axis. In the other model, the pituitary gland secreted constitutively driving the adrenal gland. The feedback type did not appear to be a determinant of the system dynamic in these two models of the HPA axis. Circadian rhythmicity in vivo may represent a shift between two dynamical states; i.e., a hypothalamic/adrenal pacemaker may diurnally alternate with a pituitary pacemaker. Our findings in silico suggest that a system alternating between two configurations may exhibit "ordered" secretion patterns while shifting through intermediate chaotic states.

Physiological and psychological stressors such as surgery, insulin-induced hypoglycemia, and depression show increased levels of HPA hormones (Avgerinos, Schuermeyer et al. 1987; Musselman and Nemeroff 1993). The magnitude of ACTH levels during surgery or insulin-induced hypoglycemia is large relative to levels produced by CRF infusions. This hints of concomitant involvement of other extrapituitary mechanisms (Fehm, Holl et al. 1988). Conversely, isolated anterior pituitary cells in vitro secrete in a pulsatile fashion, which suggests that pulsatility may be a feature of the HPA axis independent of higher brain centers (Gambacciani, Liu et al. 1987). Because the suprachiasmatic nucleus plays an important role in "pacing" the secretion of CRF (Buijs, Markman et al. 1993), our neuroendocrine simulator is driven by a model pulse generator that stimulates the HPA axis to secrete with variable frequency and amplitude. The pulsatile behavior emerging in silico may serve as the basis for more complex and clinically valid analyses of higher neuroendocrine functioning, such as the relationship between the glands of the HPA axis and higher brain centers. In this paper, we further explore the dynamics of more complex simulation paradigms using regular pulse stimulation, and report the emergence of HPA hormone pulsatility and diurnal variability in silico.

Materials And Methods

The Cellular Device Machine Development System (CDM-DS) consists of a fully portable subset of the UNIX operating system, the programming language SLANG (Simulator LANGuage), and modules for evaluating spatio-temporal simulations. CDM-DS simulators are available on the Internet World Wide Web (URL http://bitmed.ucsd.edu/).

The CDM-DS neuroendocrine simulator may be thought of as a virtual biomedical instrument that uses software to model physiological interactions within the HPA axis (Fig. 1). Researchers manipulate parameters of interest and explore possible outcomes arising from various hypothetical configurations. Processing of input is preprogrammed in accordance with known information from clinical or in vivo investigation; and physiological output is stored as time series data for display or statistical manipulation.

[Figure 1]

Figure 1 Cartoon of the CDM-DS neuroendocrine simulator. Using SLANG, the CDM-DS allows the creation and development of biomedical simulators within a virtual (i.e., computer software) environment. As the cartoon suggests, the user manipulates parameters relevant to the physiological system under investigation in order to provide input to the simulator. Processing of input is preprogrammed in accordance with known information from clinical or in vivo investigation. Physiological output is stored as time series data that may be manipulated for display or statistical manipulation. See below for discussion of user-defined parameters and simulation processing.

Cells are models of transducers capable of recognizing and processing input (external information) in order to produce some output (Fig. 2).

[Figure 2]

Figure 2. Characteristic cell physiology. Cellular models share several basic features regardless of the specific cell types they represent. Input (INPUT) in a variety of forms impinges on the cell which modifies it according to intrinsic rules. Processing of individual signals may be initially accomplished at the cell membrane by affording a weight (W) to the intake site. For example, a modulator attached to a high affinity receptor may exert influence on the cell for longer periods than the same modulator bound to a low affinity receptor. The cell's response (ACTIVATION) is a function of the summated activity of individual inputs (SIGMA INPUT). Depending on cell type, levels of cyclic adenosine monophosphate may rise in cells employing second messenger systems or neurons may produce action potentials. This overall effect may be further processed resulting in increased messenger ribonucleic acid, or synaptic vesicle movement toward the membrane (TRANSFER). Finally, the cell carries out its ultimate function (OUTPUT) according to its specialization. As an example, secretion of hormone by a glandular cell (or release of neurotransmitter into the synaptic cleft) occurs.

For example, neurotransmitter absorption at a dendritic spine (input) leads to localized ionic influx and depolarization or hyperpolarization. The graded potentials arising from multiple dendritic sites are continuously summed over the neuronal soma. Above some threshold, depolarization at the axon hillock leads to all-or-nothing action potentials that propagate essentially unmodified down the axon. Further signal processing occurs at the axon terminal, where, generally depending on action potential frequency, neurotransmitter secretion occurs (output). The firing neuron may then become refractory to continuous neurotransmitter release until additional processing occurs (e.g., electrical potential restoration through anionic efflux). This process of modulator absorption (input), intracellular processing (transduction), and cellular action (output) is fundamental to all models of cellular functioning.

Cells or hormone molecules within a CDM-DS simulation can be thought of as pieces occupying positions on a virtual gameboard (such as "Go"; Fig. 3).

[Figure 3]

Figure 3. Virtual gameboard. Objects, such as cells or hormone molecules, occupy sites on a virtual gameboard. More than one object may occupy a site at any time. Cells are fixed in location, whereas hormones are free to move about randomly one site at a time.

The number of positions on the board is fixed prior to experimentation. Cells are randomly distributed to positions on the board at the start of each simulation. Multiple cells may occupy a given site. In this manner, elements representing hypothalamic, pituitary, and adrenal cells are distributed throughout the gameboard and not discretely (anatomically) localized. For the neuroendocrine simulator, the positions of cells are fixed. The user specifies the size of each gland (small, medium, or large). The defined size is proportional to the number of cells of that type that will be randomly assigned to the gameboard. The effects and interactions of variable-sized glands can be modeled with this feature ( e.g., how does a system behave using a large adrenal gland with small hypothalamic and pituitary populations; how does a system behave using a medium pituitary gland with large hypothalamic and small adrenal populations?).

During a simulation, sites on the game board are randomly chosen one-by-one for updating. One generation cycle (iteration) occurs when the total number of chosen sites equals the number of positions on the gameboard. Because sites are selected randomly, a site may be chosen more than once (or not at all). A site may be empty, occupied by a single cell, occupied by a single hormone "molecule," or occupied by more than one cell or hormone effector.

Once the simulation is underway, cells "secrete" hormone so that sites may be populated by non-cellular effectors. Hormone elements representing CRF, ACTH, and CORT are free to move about randomly into adjacent sites (Brownian motion). Hormones may only exist for a finite time. The life span or eigenlife for each hormone is set by the user. Eigenlife may be thought of as the virtual counterpart to hormone half-life in vivo. When a hormone element has existed for its specified eigenlife duration, it disappears from the gameboard. The virtual structure and interactions of elements within the CDM-DS neuroendocrine simulator correspond to those occurring in animal/human HPA axes (Fig. 4).

[Figure 4]

Figure 4. Virtual HPA axis. The virtual HPA axis is modeled after human or animal HPA axes. There are three cell types represented in the virtual gameboard: hypothalamic, pituitary, and adrenal. These cells are randomly distributed and not anatomically localized. A software boost signal (from a virtual "pulse generator") to resting hypothalamic cells orders them to begin secreting CRF "molecules" onto the virtual gameboard. The number of molecules secreted depends on the secretion rate. Each cell type has its own secretion rate specified by the user at the start of the simulation. Resting pituitary cells may absorb CRF molecules and change their state to active. Resting pituitary (and/or hypothalamic) cells may also absorb CORT molecules and change their state to inhibited. Activated pituitary cells secrete ACTH molecules onto the virtual gameboard. These ACTH molecules move about. If a resting adrenal cell absorbs them, the adrenal cell becomes active. (ACTH has NO inhibitory activity in the virtual HPA axis.) Active adrenal cells secrete CORT. The length of time a boost pulse or hormone molecule exists after entering the virtual gameboard depends on its eigenlife.

The "pulse generator" is a software instruction set by default or entered by the user. During a specified simulation iteration, a specified percentage (or number) of hypothalamic cells are randomly selected to become active. This boost percentage may range from 0% to "100%" of hypothalamic cells per generation cycle. Therefore, a selected hypothalamic cell has a certain probability or "odds" of being instructed to secrete CRF during a single cycle. Selected hypothalamic cells are also instructed to continue secreting over a specified number of generation cycles. This duration is referred to as pulse eigenlife. Hypothalamic cells receive additional boost signals at specified intervals according to the boost frequency.

"Secretion" by an activated cell is characterized by the appearance of a hormone element adjacent to the activated cell upon its selection (Figs. 5a).

[Figure 5a]

Figure 5a. Secretion in silico. An activated cell (square) is randomly selected and "secretes" its hormone (circle) into any one of the adjacent spaces. Because the hormone has a defined eigenlife, the hormone will "disappear" after a certain number of generation cycles. The hormone is free to move about randomly one space at a time (Brownian motion) during its eigenlife. Under certain circumstances it may be absorbed (see Fig. 5b).

Hormone is removed from the gameboard when "absorbed" by an adjacent cell (Figs. 5b).

[Figure 5b]

Figure 5b. Absorption in silico. A resting cell (square) is randomly selected. Its immediate adjacent environment is scanned for hormone (circle; e.g., a pituitary cell "looks" for a CRF molecule in its immediate vicinity). Having found its appropriate excitatory or inhibitory hormone, the cell absorbs it (i.e., the hormone disappears), and the cell changes its state. The cell may now be stimulated (activated) to secrete or be inhibited from secreting. The duration of activation or inhibition is set by software instruction and typically ranges from one to five generation cycles.

Continue with part 2 of Emergent Patterns of HPA Hormone Pulsatility



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