Edit2: Prečo komplexované? Viď Edit1: https://www.namaximum.sk/magnezium-8-complex-kapsuly?parameters%5B2%5D=68&utm_source=chatgpt.com
Edit1:
Dnes sme diskutovali o osteo poróze a podľa mojej chemikárky z 9tej triedy ZŠ sme navrhli vyzrážať varom Ca2+ a K+ , aby kosti netvrdli a neredli. Toto bola pointa. Potom bola naša ďalšia otázka, či je lepšie cvrknúť si do tejto vody štipku Na+ alebo Mg2+ https://hrubos.tech/blogy/content/images/20260901191838-Snímka obrazovky 2026-09-01 o 18.29.48.png
No á napadla ma známa analógia: Ak je alkohol kvalitnejší, opíja vás dlhšie, teda Metaxa 501 by mala byť lepšia ako Vodka 80%, lebo ide na vás pomaly. No á toto je v skratke moja simulácia v krvnej plazme. Pozrite sa, za koľko Vás opije magnézium a za koľko sodík:
Teda na sodík 1.27-1.8 sekundy na dosiahnutie rovnováhy v krvnej plazme pri reakcii. Á teraz si pozrite KOMPLEX z tabuľky vyššie, ktorý je termodynamicky výhodnejší:
Teda vidíme, že Magnézium ma "opije" za TROJNÁSOBOK ČASU, ako tá Metaxa 501 oproti Vodka 80%
No á aby som to nenaťahoval, simulácia v JuliaLang bola:
# ============================================================
# MG2+ vs Na+ V KRVNEJ PLAZME
#
# Dynamicka simulacia navratu k rovnovaznemu stavu
#
# 4 panely:
#
# [1,1] Mg2+ - koncentracia
# [1,2] Na+ - detail viazanej koncentracie
# [2,1] Mg2+ - percentualne zastupenie
# [2,2] Na+ - detail viazanej frakcie
#
# Spolocny cas pre vsetky panely.
#
# Casova zvisla ciara = aktualny frame videa.
# Gulicky = aktualny stav systemu.
#
# ============================================================
# ============================================================
# 1. BALIKY
# ============================================================
using Pkg
Pkg.add("DifferentialEquations")
Pkg.add("CairoMakie")
Pkg.add("FFMPEG")
using DifferentialEquations
using CairoMakie
# ============================================================
# 2. FYZIOLOGICKE REFERENCNE HODNOTY
# ============================================================
# ------------------------------------------------------------
# Mg2+
# ------------------------------------------------------------
Mg_total = 0.85 # mmol/L
Mg_free_fraction = 0.65
Mg_protein_fraction = 0.27
Mg_complex_fraction = 0.08
@assert isapprox(
Mg_free_fraction +
Mg_protein_fraction +
Mg_complex_fraction,
1.0
)
# ------------------------------------------------------------
# Na+
# ------------------------------------------------------------
Na_total = 140.0 # mmol/L
# Modelova reprezentacia velmi malej viazanej frakcie
#
# 0.02 % = 0.0002 ako podiel
Na_bound_fraction = 0.0002
Na_free_fraction =
1.0 - Na_bound_fraction
@assert isapprox(
Na_free_fraction +
Na_bound_fraction,
1.0
)
# ============================================================
# 3. ROVNOVAZNE KONCENTRACIE
# ============================================================
Mg_free_eq =
Mg_total * Mg_free_fraction
Mg_protein_eq =
Mg_total * Mg_protein_fraction
Mg_complex_eq =
Mg_total * Mg_complex_fraction
Na_free_eq =
Na_total * Na_free_fraction
Na_bound_eq =
Na_total * Na_bound_fraction
println()
println("================================================")
println(" MG2+ vs Na+ V KRVNEJ PLAZME")
println("================================================")
println()
println("Mg2+")
println("-----------------------------------------------")
println(
"celkove Mg2+ = ",
round(Mg_total, digits=4),
" mmol/L"
)
println(
"volne Mg2+ = ",
round(Mg_free_eq, digits=4),
" mmol/L (65 %)"
)
println(
"proteinovo Mg2+ = ",
round(Mg_protein_eq, digits=4),
" mmol/L (27 %)"
)
println(
"komplexovane Mg2+ = ",
round(Mg_complex_eq, digits=4),
" mmol/L (8 %)"
)
println()
println("Na+")
println("-----------------------------------------------")
println(
"celkove Na+ = ",
round(Na_total, digits=4),
" mmol/L"
)
println(
"volne Na+ = ",
round(Na_free_eq, digits=6),
" mmol/L (99.98 %)"
)
println(
"viazane Na+ = ",
round(Na_bound_eq, digits=6),
" mmol/L (0.02 %)"
)
println()
# ============================================================
# 4. KINETICKE PARAMETRE Mg2+
# ============================================================
# Tieto tau su MODELOVE CASOVE KONSTANTY.
#
# Neznamenaju experimentálne namerany cas
# "navratu krvi do rovnovahy".
Mg_tau_protein = 1.8
Mg_tau_complex = 0.9
Mg_k_fp =
1.0 / Mg_tau_protein
Mg_k_pf =
1.0 / Mg_tau_protein
Mg_k_fc =
1.0 / Mg_tau_complex
Mg_k_cf =
1.0 / Mg_tau_complex
# ============================================================
# 5. Na+ - KINETIKA
# ============================================================
# Chceme, aby modelova rovnovaha bola:
#
# [Na_bound] / [Na_total] = 0.0002
#
# teda 0.02 %.
#
# Pre reakciu:
#
# Na_free <-> Na_bound
#
# v rovnováhe platí:
#
# k_forward * free =
# k_backward * bound
#
# Preto:
#
# bound/free =
# k_forward/k_backward
#
# ------------------------------------------------------------
Na_tau = 0.5
Na_k_backward =
1.0 / Na_tau
# Rovnovazny pomer bound/free
Na_equilibrium_ratio =
Na_bound_fraction /
Na_free_fraction
Na_k_forward =
Na_equilibrium_ratio *
Na_k_backward
println(
"Na+ K rovnovazny pomer bound/free = ",
Na_equilibrium_ratio
)
println(
"Na+ k_forward = ",
Na_k_forward
)
println(
"Na+ k_backward = ",
Na_k_backward
)
println()
# ============================================================
# 6. DIFERENCIALNY MODEL Mg2+
# ============================================================
function mg_model!(du, u, p, t)
free =
u[1]
protein =
u[2]
complex =
u[3]
# --------------------------------------------
# free <-> protein
# --------------------------------------------
forward_protein =
Mg_k_fp * free
backward_protein =
Mg_k_pf * protein
# --------------------------------------------
# free <-> complex
# --------------------------------------------
forward_complex =
Mg_k_fc * free
backward_complex =
Mg_k_cf * complex
# --------------------------------------------
# rovnice
# --------------------------------------------
du[1] =
-forward_protein +
backward_protein -
forward_complex +
backward_complex
du[2] =
forward_protein -
backward_protein
du[3] =
forward_complex -
backward_complex
end
# ============================================================
# 7. DIFERENCIALNY MODEL Na+
# ============================================================
function na_model!(du, u, p, t)
free =
u[1]
bound =
u[2]
forward =
Na_k_forward * free
backward =
Na_k_backward * bound
du[1] =
-forward +
backward
du[2] =
forward -
backward
end
# ============================================================
# 8. NARUSENIE ROVNOVAHY - Mg2+
# ============================================================
# Presunieme 20 % komplexovaneho Mg2+
# docasne do volneho poolu.
Mg_perturbation =
0.20 * Mg_complex_eq
Mg_initial_free =
Mg_free_eq +
Mg_perturbation
Mg_initial_protein =
Mg_protein_eq
Mg_initial_complex =
Mg_complex_eq -
Mg_perturbation
Mg_u0 = [
Mg_initial_free,
Mg_initial_protein,
Mg_initial_complex
]
# ============================================================
# 9. NARUSENIE ROVNOVAHY - Na+
# ============================================================
# Presunieme polovicu velmi malej viazanej frakcie
# do volneho Na+ poolu.
Na_perturbation =
0.50 * Na_bound_eq
Na_initial_free =
Na_free_eq +
Na_perturbation
Na_initial_bound =
Na_bound_eq -
Na_perturbation
Na_u0 = [
Na_initial_free,
Na_initial_bound
]
# ============================================================
# 10. CAS SIMULACIE
# ============================================================
t_start = 0.0
t_end = 10.0
tspan =
(t_start, t_end)
# ============================================================
# 11. ODE PROBLEMY
# ============================================================
Mg_prob =
ODEProblem(
mg_model!,
Mg_u0,
tspan
)
Na_prob =
ODEProblem(
na_model!,
Na_u0,
tspan
)
# ============================================================
# 12. VYRIESENIE ODE
# ============================================================
Mg_sol =
solve(
Mg_prob,
Tsit5(),
saveat = 0.01
)
Na_sol =
solve(
Na_prob,
Tsit5(),
saveat = 0.01
)
# ============================================================
# 13. DATA Mg2+
# ============================================================
time =
Mg_sol.t
Mg_free =
[u[1] for u in Mg_sol.u]
Mg_protein =
[u[2] for u in Mg_sol.u]
Mg_complex =
[u[3] for u in Mg_sol.u]
Mg_free_percent =
100 .* Mg_free ./ Mg_total
Mg_protein_percent =
100 .* Mg_protein ./ Mg_total
Mg_complex_percent =
100 .* Mg_complex ./ Mg_total
# ============================================================
# 14. DATA Na+
# ============================================================
Na_free =
[u[1] for u in Na_sol.u]
Na_bound =
[u[2] for u in Na_sol.u]
Na_free_percent =
100 .* Na_free ./ Na_total
Na_bound_percent =
100 .* Na_bound ./ Na_total
# ============================================================
# 15. KONTROLA KONECNEHO STAVU
# ============================================================
println("================================================")
println("KONTROLA ROVNOVAHY")
println("================================================")
println()
println("Mg2+ konec:")
println(
" free = ",
round(Mg_free[end], digits=6)
)
println(
" protein = ",
round(Mg_protein[end], digits=6)
)
println(
" complex = ",
round(Mg_complex[end], digits=6)
)
println()
println("Ocakavane:")
println(
" free = ",
round(Mg_free_eq, digits=6)
)
println(
" protein = ",
round(Mg_protein_eq, digits=6)
)
println(
" complex = ",
round(Mg_complex_eq, digits=6)
)
println()
println("Na+ konec:")
println(
" free = ",
round(Na_free[end], digits=8)
)
println(
" bound = ",
round(Na_bound[end], digits=8)
)
println()
println("Ocakavane:")
println(
" free = ",
round(Na_free_eq, digits=8)
)
println(
" bound = ",
round(Na_bound_eq, digits=8)
)
println()
# ============================================================
# 16. FIGURE
# ============================================================
fig =
Figure(
size = (1800, 1200),
fontsize = 20
)
# ============================================================
# 17. Mg2+ KONCENTRACIA
# ============================================================
ax_Mg_conc =
Axis(
fig[1, 1],
title =
"Mg2+ — koncentracia",
xlabel =
"cas [s]",
ylabel =
"mmol/L",
limits =
(
0,
10,
0,
Mg_total * 1.15
)
)
lines!(
ax_Mg_conc,
time,
Mg_free,
linewidth = 4,
label = "volne Mg2+"
)
lines!(
ax_Mg_conc,
time,
Mg_protein,
linewidth = 4,
label = "proteinovo viazane"
)
lines!(
ax_Mg_conc,
time,
Mg_complex,
linewidth = 4,
label = "komplexovane"
)
hlines!(
ax_Mg_conc,
[Mg_free_eq],
linestyle = :dash
)
hlines!(
ax_Mg_conc,
[Mg_protein_eq],
linestyle = :dash
)
hlines!(
ax_Mg_conc,
[Mg_complex_eq],
linestyle = :dash
)
axislegend(
ax_Mg_conc,
position = :rt
)
# ============================================================
# 18. Na+ KONCENTRACIA - ZOOM
# ============================================================
ax_Na_conc =
Axis(
fig[1, 2],
title =
"Na+ — detail redistribucie",
xlabel =
"cas [s]",
ylabel =
"viazany Na+ [mmol/L]",
limits =
(
0,
10,
0,
max(
Na_bound_eq * 3,
0.001
)
)
)
lines!(
ax_Na_conc,
time,
Na_bound,
linewidth = 4,
label = "viazany Na+"
)
hlines!(
ax_Na_conc,
[Na_bound_eq],
linestyle = :dash
)
axislegend(
ax_Na_conc,
position = :rt
)
# ============================================================
# 19. Mg2+ PERCENT
# ============================================================
ax_Mg_percent =
Axis(
fig[2, 1],
title =
"Mg2+ — relativne zastupenie",
xlabel =
"cas [s]",
ylabel =
"podiel [%]",
limits =
(
0,
10,
0,
75
)
)
lines!(
ax_Mg_percent,
time,
Mg_free_percent,
linewidth = 4,
label = "volne"
)
lines!(
ax_Mg_percent,
time,
Mg_protein_percent,
linewidth = 4,
label = "proteinovo viazane"
)
lines!(
ax_Mg_percent,
time,
Mg_complex_percent,
linewidth = 4,
label = "komplexovane"
)
axislegend(
ax_Mg_percent,
position = :rt
)
# ============================================================
# 20. Na+ PERCENT - ZOOM
# ============================================================
ax_Na_percent =
Axis(
fig[2, 2],
title =
"Na+ — detail viazanej frakcie",
xlabel =
"cas [s]",
ylabel =
"viazany Na+ [%]",
limits =
(
0,
10,
0,
max(
0.06,
Na_bound_fraction * 100 * 3
)
)
)
lines!(
ax_Na_percent,
time,
Na_bound_percent,
linewidth = 4,
label = "viazany Na+"
)
hlines!(
ax_Na_percent,
[Na_bound_fraction * 100],
linestyle = :dash
)
axislegend(
ax_Na_percent,
position = :rt
)
# ============================================================
# 21. SPOLOCNY CAS
# ============================================================
current_time =
Observable(0.0)
# ============================================================
# 22. CASOVE CARY
# ============================================================
function create_time_line(
axis,
ymin,
ymax
)
x =
Observable(
[0.0, 0.0]
)
y =
Observable(
[ymin, ymax]
)
lines!(
axis,
x,
y,
linewidth = 3,
linestyle = :dash
)
return x, y
end
MgConcX, MgConcY =
create_time_line(
ax_Mg_conc,
0.0,
Mg_total * 1.15
)
NaConcX, NaConcY =
create_time_line(
ax_Na_conc,
0.0,
max(
Na_bound_eq * 3,
0.001
)
)
MgPercentX, MgPercentY =
create_time_line(
ax_Mg_percent,
0.0,
75.0
)
NaPercentX, NaPercentY =
create_time_line(
ax_Na_percent,
0.0,
max(
0.06,
Na_bound_fraction * 100 * 3
)
)
# ============================================================
# 23. GULICKY Mg2+
# ============================================================
Mg_dot_time =
Observable(0.0)
Mg_dot_free =
Observable(Mg_initial_free)
Mg_dot_protein =
Observable(Mg_initial_protein)
Mg_dot_complex =
Observable(Mg_initial_complex)
scatter!(
ax_Mg_conc,
Mg_dot_time,
Mg_dot_free,
markersize = 18
)
scatter!(
ax_Mg_conc,
Mg_dot_time,
Mg_dot_protein,
markersize = 18
)
scatter!(
ax_Mg_conc,
Mg_dot_time,
Mg_dot_complex,
markersize = 18
)
# ============================================================
# 24. GULICKY Na+
# ============================================================
Na_dot_time =
Observable(0.0)
Na_dot_bound =
Observable(Na_initial_bound)
scatter!(
ax_Na_conc,
Na_dot_time,
Na_dot_bound,
markersize = 18
)
# ============================================================
# 25. GULICKY Mg2+ %
# ============================================================
Mg_dot_free_percent =
Observable(
100 *
Mg_initial_free /
Mg_total
)
Mg_dot_protein_percent =
Observable(
100 *
Mg_initial_protein /
Mg_total
)
Mg_dot_complex_percent =
Observable(
100 *
Mg_initial_complex /
Mg_total
)
scatter!(
ax_Mg_percent,
Mg_dot_time,
Mg_dot_free_percent,
markersize = 18
)
scatter!(
ax_Mg_percent,
Mg_dot_time,
Mg_dot_protein_percent,
markersize = 18
)
scatter!(
ax_Mg_percent,
Mg_dot_time,
Mg_dot_complex_percent,
markersize = 18
)
# ============================================================
# 26. GULICKA Na+ %
# ============================================================
Na_dot_bound_percent =
Observable(
100 *
Na_initial_bound /
Na_total
)
scatter!(
ax_Na_percent,
Na_dot_time,
Na_dot_bound_percent,
markersize = 18
)
# ============================================================
# 27. HLAVNY CASOVY TEXT
# ============================================================
time_label =
Observable(
"t = 0.00 s"
)
Label(
fig[3, 1:2],
time_label,
fontsize = 30,
tellwidth = false,
halign = :center
)
# ============================================================
# 28. MP4
# ============================================================
output_file =
"mg2_vs_na_plasma_equilibrium.mp4"
println()
println("================================================")
println("START RENDEROVANIA MP4")
println("================================================")
println(
"Subor: ",
output_file
)
println(
"Pocet framov: ",
length(time)
)
println()
# ============================================================
# 29. ANIMACIA
# ============================================================
record(
fig,
output_file,
1:length(time);
framerate = 30
) do i
# ========================================================
# JEDEN SPOLOCNY CAS
# ========================================================
t =
time[i]
current_time[] =
t
time_label[] =
"t = $(round(t, digits=2)) s"
# ========================================================
# CASOVE CARY
# ========================================================
MgConcX[] =
[t, t]
MgConcY[] =
[
0.0,
Mg_total * 1.15
]
NaConcX[] =
[t, t]
NaConcY[] =
[
0.0,
max(
Na_bound_eq * 3,
0.001
)
]
MgPercentX[] =
[t, t]
MgPercentY[] =
[0.0, 75.0]
NaPercentX[] =
[t, t]
NaPercentY[] =
[
0.0,
max(
0.06,
Na_bound_fraction * 100 * 3
)
]
# ========================================================
# Mg2+ KONCENTRACIA
# ========================================================
Mg_dot_time[] =
t
Mg_dot_free[] =
Mg_sol.u[i][1]
Mg_dot_protein[] =
Mg_sol.u[i][2]
Mg_dot_complex[] =
Mg_sol.u[i][3]
# ========================================================
# Na+ KONCENTRACIA
# ========================================================
Na_dot_time[] =
t
Na_dot_bound[] =
Na_sol.u[i][2]
# ========================================================
# Mg2+ PERCENT
# ========================================================
Mg_dot_free_percent[] =
100 *
Mg_sol.u[i][1] /
Mg_total
Mg_dot_protein_percent[] =
100 *
Mg_sol.u[i][2] /
Mg_total
Mg_dot_complex_percent[] =
100 *
Mg_sol.u[i][3] /
Mg_total
# ========================================================
# Na+ PERCENT
# ========================================================
Na_dot_bound_percent[] =
100 *
Na_sol.u[i][2] /
Na_total
end
# ============================================================
# 30. KONIEC
# ============================================================
println()
println("================================================")
println("HOTOVO")
println("================================================")
println(
"Vystupny subor:"
)
println(
abspath(output_file)
)
println()
Za pomoc ďakujem: Mojej mamine za prednášku, ako sa mám opíjať pomaly á za simuláciu podľa príkazov ďakujem GPT a Ideogram AI :)
Comments “Dnes sme diskutovali, či je lepšie dať si do destilovanej vody štipku Na+ alebo Mg2+ Á napadla ma známa analógia: Z ktorého alkoholu sa opijete lepšie? No z toho, ktorý Vás opíja DLHŠIE/POMALŠIE, čiže Metaxa 501 je kvalitnejšia ako Vodka 80% Ukážem prečo: Mg2+ je lepšie ako Na+ na krvnej plazme v simulácií:”