Emergent Patterns of HPA Hormone Pulsatility and Diurnal Variability in silico:
Part 2 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
E-mail: hsieburg@ucsd.edu

*Author to whom all correspondence should be addressed.

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

Hypothalamic cells may secrete CRF and absorb CORT (their inhibitory effector) . Pituitary cells may secrete ACTH and absorb CRF (their excitatory effector) or CORT (their inhibitory effector). Adrenal cells may secrete CORT and absorb ACTH (their excitatory effector). Each cell type may also spontaneously secrete its hormone-type at a baseline rate (constitutive secretion). Sample SLANG code for hypothalamic cells is shown below:

Hypothal_Rules:

if Inhibitable_Hypothal then
{
    if rec Small_CO then
    {
        Uptake_Small_CO;
        Become_Inhibited_Hypothal;
        return;
    }
}
if Inducible_Hypothal then
{
    if rec Small_ES then
        {
            Uptake_Small_ES;
            Become_Active_Hypothal;
            gosub Release_CR;
            return;
        }
    else
        {
            let temp = reg[Constit_H_reg] .* 0x10000000;
            if (% < temp) then
                Release_Small_CR;
            return;
        }
}
else if Inhibited_Hypothal then
{
    Increase_Inhib_Hypothal_Counter;    // count the inhibition states
    if Recovered_Hypothal then              // if inhibited long enough...
        Become_Inducible_Hypothal;
    return;
}
else if Active_Hypothal then
{
    Increase_Active_Hypothal_Counter;    // count the active states
    gosub Release_CR;                              // signal
    if Completed_Hypothal then               // if finished signalling
        Become_Inducible_Hypothal;
    return;
}

return;

Release_CR:

if Hypo_Large_CR_Model then
    Release_Large_CR;
else if Hypo_Medium_CR_Model then
    Release_Medium_CR;
else
    Release_Small_CR;

return;


The user determines which inhibitory (negative) feedback loops (if any) to be used and the cell types (if any) to secrete constitutively. CORT is the only inhibitory hormone element in the virtual HPA axis. Short feedback is defined as pituitary inhibition only; long feedback as hypothalamic inhibition only; and dual feedback is defined as both hypothalamic and pituitary inhibition. Figure 6 shows the types of secretion/absorption available and their effects (constitutive secretion is not shown).

[Figure 6]

Figure 6. Patterns of stimulation and inhibition. When randomly selected, resting cells change their states depending on the presence of adjacent excitatory or inhibitory effectors.

The user is able to set the secretion rate for each hormone. Secretion rate determines the number of hormone elements that will appear in positions adjacent to the secreting cell. As an example, if the CORT secretion rate is set to two, CORT elements will appear at two sites adjacent to an active adrenal cell when that cell's site is selected. Table I shows the parameters specified by the user during each simulation.

SIMULATION DURATION
GENERATION CYCLES

PULSE STIMULATION
BOOST %
BOOST FREQUENCY
EIGENLIFE

GLAND SIZES
SMALL ... MEDIUM ... LARGE
HYPOTHALAMUS
PITUITARY
ADRENAL

SECRETION RATES
LOW ... MEDIUM ... HIGH
CRF
ACTH
CORT

CONSTITUTIVE SECRETION
YES ..... NO
CRF
ACTH
CORT

EIGENLIFES
GENERATION CYCLES
CRF
ACTH
CORT

FEEDBACK INHIBITION
SHORT ... LONG ... DUAL

Table I. User-defined parameters for running endocrine simulations. The user specifies the structure of a simulation by indicating the desired simulation duration, pulse stimulation, gland sizes, secretion rates, constitutive secretion, eigenlifes, and feedback inhibition (see text).

During a simulation, the program randomly selects a site on the gameboard. If a site is occupied by a cell, the program asks:

  • What type of cell is present (i.e., is it a hypothalamic, pituitary, or adrenal cell)?

  • What is the cell's state (i.e., is the cell resting, active, or inhibited)? [Whenever a resting cell becomes activated or inhibited, it maintains this state for a specified duration (see below). In general, cells remain active for five generation cycles and inhibited for three. (Each cell has an "internal clock" and "knows" how long it has existed in its current state.)]

  • What are the contents of the sites immediately adjacent to the cell (i.e., is CRF, ACTH, or CORT nearby)?

With these questions answered, several things happen:

  • A resting (inactive) hypothalamic cell may be reassigned as an active hypothalamic cell according to the probability set by the pulse generator.

  • An active cell will be instructed to secrete its appropriate hormone into one of the (randomly chosen) adjacent sites (see Figures 5a and 6; e.g., a hypothalamic cell secretes a CRF element; a pituitary cell secretes an ACTH element; an adrenal cell secretes a CORT element).

  • If a resting cell is adjacent to its stimulatory hormone, the hormone will be absorbed (removed from the gameboard; Fig. 5b) and the resting cell will be reassigned as active. For example, a pituitary cell adjacent to a CRF molecule will "absorb" the CRF element (i.e., the CRF element will be removed from the gameboard) and the state of the pituitary cell changes from inactive to active. This newly-defined active cell will not actually secrete until the next time its site is randomly selected.

  • If a resting cell is adjacent to its inhibitory hormone, the hormone will be absorbed (removed from the gameboard; Fig. 5b) and the resting cell will be reassigned as inhibited. For example, a pituitary cell adjacent to a CORT molecule will "absorb" the CORT element (i.e., the CORT element is removed from the gameboard) and the state of the pituitary cell changes from resting to inhibited.

  • An active cell will have its "internal clock" incremented by one. If its duration of activation is reached, it will change its state to resting the next time it is randomly selected.

  • An inhibited cell will have its "internal clock" incremented by one. If its duration of inhibition is reached, it will change its state to resting the next time it is randomly selected.

If a site is occupied by a hormone molecule, the program asks:

  • What type of hormone is present (i.e., is it CRF, ACTH, or CORT)?

  • How many times has this particular hormone been selected? If this number is less than or equal to the defined eigenlife, the hormone "ages" by one generation cycle. If this number is greater than the defined eigenlife, the hormone disappears from the gameboard.

  • Where should the hormone molecule "move"? The hormone may remain stationary or move into a randomly selected adjacent site (Brownian motion).

Having done all this, the program increments its counter and randomly selects another site, repeating the procedure. Obviously, if selected sites contain no objects, the program increments its counter and randomly selects another site.

Since approximate half-lives have been established in vivo for HPA hormones (Iranmanesh, Lizarralde et al. 1993; Kaplan 1992; Saphier, Faria et al. 1992), these values were used to assign eigenlifes for each in silico hormone. Eigenlifes for CRF, ACTH, and CORT were 30, 17, and 80 generation cycles, respectively. Circadian hormonal secretion was modeled by permitting simulations to run for 1440 generation cycles. This is equivalent to the number of minutes per day and allows direct utilization of half-life data and clinical observations of hormonal pulsatility and diurnal variation. In our simulations, after each generation cycle or "minute," the number of molecules for each hormone on the gameboard was recorded. Using Microsoft Excel¨ (Ver. 4), simulation data for each hormone was graphically represented as a time series plot. Because we were interested in the relative changes in hormone level during a simulation rather than absolute magnitudes, time series values for in silico hormone concentrations were "normalized" on an arbitrary concentration scale from 0 to one.

Our HPA simulations using the CDM-DS (version 3.4.1) were run on a Macintosh personal computer (simulations may also be run on UNIX and PC- compatible machines). A regular stimulation pulse was delivered to each hypothalamic cell (i.e., "100%" Boost ) every 63 generation cycles or minutes. Since we assumed direct hypothalamic stimulation on the pituitary, the 63 generation cycle boost pulse period was chosen based on clinical literature review indicating approximately 23-40 ACTH pulses per day in humans (Negro-Vilar, Spinedi et al. 1987; Sherman, Schlecte et al. 1987; Veldhuis, Iranmanesh et al. 1990). The eigenlife duration for each hypothalamic boost stimulation pulse was 1 minute. Table II shows parameter settings for our simulations.

EXP # SIZE SECRETION CONSTITUTIVITY FEED-
  H P A CRF ACTH CORT CRF ACTH CORT BACK
1 S S S M M M N N N D
2 S S S M M L C C N D
3 S S S M M L N C N D
4 S S S M M L C N N D
5 S S S M M L C C N D
6 S S S M M L C N N Ln
7 S S S M M L N N N Sh
8 S S S M M L N N N No
9 S S S M M L N C C D
10 S S S M M L N N N Sh
11 S S S L L L N N N No
12 S S S M M L N N C D
13 S S S M M L N N C Sh
14 M S S M M L N N C D
15 S M S M M L N N C D
16 S S M M M L N N C D
17 M M S M M L N N C D
18 Lg M S M M L N N C D
19 Lg Lg S M M L N N C D
20 S S M M M L N N C D
21 S S S M M L N N N D
22 M S S M M L N N N D
23 S M S M M L N N N D
24 S S M M M L N N N D
25 M M S M M L N N N D
26 S S M M M L N N C D
27 S S M M M L N N C D
28 S S M M M L N N C D
29 S S M M M L N N C D
30 S S M M M L N N C D
31 S S M M M L N N C D
32 S S M M M L N N C D
33 S S M M M L N N C D
34 S S M M M L N N C D
35 S S M M M M N N C D
36 S S M M M L N N C D


Table II. User-defined parameters for HPA simulations. We established the structures of virtual HPA axes by setting parameters at the start of each simulation. Columns represent experiment number (EXPERIMENT NUMBER), gland sizes (SIZE), secretion rates (SECRETION), constitutive secretion (CONSTITUTIVITY), feedback inhibition (FEEDBACK). Modifiers code for hypothalamic cells (H), pituitary cells (P), adrenal cells (A), corticotrophin releasing factor (CRF), adrenocorticotropic hormone (ACTH), glucocorticoid (CORT), small gland size (S), medium gland size (M), large gland size (Lg), low secretion rate (L), medium secretion rate (M), high secretion rate (H), non-constitutive secretion (N), constitutive secretion (C), dual feedback inhibition (D), hypothalamic (long) feedback inhibition (Ln), and pituitary (short) feedback inhibition (Sh), no feedback inhibition (No). All simulations were run for 1440 generation cycles (equivalent to 1440 "minutes" -- the number of minutes in one day). Eigenlifes for CRF, ACTH, and CORT were 30, 17, and 80 generation cycles, respectively. Boost % stimulation was set at "100%" hypothalamic cells, boost frequency every 63 generation cycles, and boost eigenlife of one cycle.

Continue with part 3 of Emergent Patterns of HPA Hormone Pulsatility



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