Måned: august 2022

Summaries 1.1 to 1.4 – 1

Af

While working on this page, I came across a saving opportunity in R – save.image. It was a fantastic possibility till it was not anymore. After opening R and pressing save.image left me with an empty workspace and hours of lost work. Hence this page is not complete yet.

These tables show the complex (theoretical) interplay between the hormones.

Equilibrium solutions

Time-dependent solutions

Equilibrium stable all one
Time-dependent all one
s1/FT4(0.1,1,10) – 1.3, 1.5, 2.2
s1/FT3(0.1,1,10) – 1.0, 1.4, 3.3
s1/TSH(0.1,1,10) – 0.9, 1.0, 1.6
s1/TRH(0.1,1,10) – 0.1, 0.5, 1.5

There is still a marginal variation in FT3 all over the range – see the histograms. But it is in the 9th decimal

Increase FT4, FT3, TSH, TRH

s1_10 (analytical equilibrium solutions of system (1))
TRH1.6556002607617
TSH1.82116028683787
FT41.82116028683787
FT33.3166247903554
Decrease the TH values
= All One
Decrease FT4, FT3, TSH – increase TRH
Increase FT4, FT3, TSH, Decrease TRH
Increase TRH, Decrease TSH, FT4, FT3
Decrease TRH, Increase TSH, FT4, FT3
Increase FT4, FT3, TSH decrease TRH
Decrease FT4, FT3, TSH – increase TRH
Increase TSH,
= All One
Decrease TRH, TSH, FT4 – increase FT3
Increase TRH, TSH, FT4 – decrease FT3
?
?
Increase TRH, TSH, FT4, FT3
Equal to the table above
Decrease TRH, Increase TSH, FT4, FT3
Increase TRH, decrease TSH, FT4, FT3
Decrease TRH, TSH, increase FT4, no change FT3
Increase TRH, TSH, decrease FT4, , no change FT3
Decrease TRH, TSH, increase FT4, no change FT3
Decrease TRH, TSH, FT3, increase FT4

Below are three different parameters 0.1 or 10 – to show the movement experimental not physiological

Principles: FT3

Af

Two parameters may change the value of FT3 in the mathematical model (Ref.1);
k423 – positive feedforward of TSH and FT4 onto FT3 (downstream, activating)
a4 – the FT3 elimination rate constant.

Only examples of the effect of the parameter –

Principles: FT4

Af

In the mathematical model (Ref. 1) two parameters may change the outcome of FT4:
k32 – positive feedforward of TSH onto FT4 (downstream, activating) and
a 3 – the FT4 elimination rate constant.

Sense?

Only examples of the effect of the parameter –

  1. Hoermann R, Pekker MJ, Midgley JEM, Larisch R and Dietrich JW (2022) Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change. Front. Endocrinol. 13:825107. doi: 10.3389/fendo.2022.825107 https://www.frontiersin.org/articles/10.3389/fendo.2022.825107/full

Principles: TSH

Af

Four parameters regulate TSH (in the mathematical model (ref.1)):
k21 – (positive feedforward of TRH onto TSH (downstream, activating)),
c2 – (the secretory capacity constant),
k234 -negative feedback of FT4 and FT3 onto TSH (upstream, repressing) and
a2 – (the TSH elimination rate constant.).

Be aware that the colours for the hormones are different in the rows below.

Positive feedforward of TRH onto TSH (downstream, activating)):

Level compared to the equilibrium calculation

Negative feedback of FT4 and FT3 onto TSH (upstream, repressing)

The TSH elimination rate constant.

The secretory capacity constant

Only examples of the effect of the parameter –

  1. Hoermann R, Pekker MJ, Midgley JEM, Larisch R and Dietrich JW (2022) Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change. Front. Endocrinol. 13:825107. doi: 10.3389/fendo.2022.825107 https://www.frontiersin.org/articles/10.3389/fendo.2022.825107/full

Principles: TRH

Af

Hoerman et al (Ref.1) have developed a mathematical model with 14 different parameters that influence the HPT axis (hypothalamus – pituitary – thyroid axis). I will describe the effects in the following.

There are different parameters which can change the hormones in this mathematical model.

S1 is an input signal with an effect on TRH. As seen in the description above, changes in S1 affect the other hormones as well. The article describes how this knowledge can be used in combination with different parameters.

The first part of the above presentation describes the three different equilibrium solutions for s1=1, 0.1 and 10 and the second part describes the time-dependent solution.

You need not be good at mathematics to see the connection between the used equations and the conceptual drawing of the HPT axis (Ref.1). What is important is the complexity – and flexibility compared to a fixed TSH value as the understanding of the HPT axis.

Overview of the four equations
Fig.1 from ref.1 : Network of the hypothalamic-pituitary-thyroid axis regulation

The first part of the second presentation describes the three different equilibrium solutions for k134 =1, 0.1 and 10 and the second part describes the time-dependent solution.

This is theoretical and only serves as an example of how the hormones are changed by the parameter. K134 is the negative feedback of FT4 and FT3 onto TRH (upstream, repressing).

Finally the a1 parameter ( a1 is the TRH elimination rate constant):

a1 parameter

Look at equation 1.1:

We have looked at the effects of s1, k134 and a1 on TRH and the other hormones.

One thing to observe is the FT3 and FT4 curves. In the plot left is shown what the authors call “The perfect homeostasis”. Here the two curves follow each other with a certain distance. In the plots above this pattern is disrupted. We will get back to these observations later.

  1. Hoermann R, Pekker MJ, Midgley JEM, Larisch R and Dietrich JW (2022) Principles of Endocrine Regulation: Reconciling Tensions Between Robustness in Performance and Adaptation to Change. Front. Endocrinol. 13:825107. doi: 10.3389/fendo.2022.825107 https://www.frontiersin.org/articles/10.3389/fendo.2022.825107/full