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Marty Carlson
Figure 1. Energy production and usage.
Introduction
At the time I took the photo above, I was taking a biochemistry
class. During this class I was awestruck at the glimpse I
received into what we are. Our energy, our health, our lives,
everything about us, directly derives from the chemistry that
happens within us. Though it has been studied for decades,
and its outlines mapped, the human metabolic system is still
a mystery in many ways.
In addition to this, for some time I've been interested in
using the computing power on my desk top to illustrate graphically
what happens in a dynamic process. In this article I'll introduce
that system and described how I've applied it to a very limited
part of the human metabolic system; the TCA cycle.
Brief overview of the TCA cycle
The direction of nature is toward increasing entropy, increasing
disorder. This is the crux of Newton 's Second Law of Thermodynamics.
Countering this natural direction is work, and work requires
energy. The application of Newton 's law to the human body
means that in order to keep our bodies from quickly returning
to the disorder from which they originated, considerable energy
is constantly required.
In the UK in 1953, Sir Hans Adolph Krebs, discovered a cycle
of chemical reactions that goes on within us that is responsible
for the production of molecules that the body uses for energy
needed to drive reactions forward. This cycle is referred
to as the Krebs Cycle, or the tricarboxylic acid cycle, and
this is a part of a much larger system of chemical reactions
known as the "Metabolic Pathways".
The Tri Carboxylic Acid (TCA) cycle occurs in every cell in
the human body. It is the main process by which these cells
derive the energy needed for survival. Figure 2 is a diagram
of this cycle.
Figure 2. TCA cycle image (Wikipedia).
The diagram shows a circular series of reactions that has
the effect of moving a "substrate" molecule through
a series of conversions, and finally back into itself. The
other net result of this cycle is the conversion of lower
energy molecules into higher ones. Some of these higher energy
molecules; GTP, FADH 2 and NADH go on to other sets of reactions
in the to be used to drive other reactions. These molecules
are the goal of the TCA cycle.
Click here
for Wikipedia's description of the TCA cycle or go here
for one using Flash.
First Run
Now I'll jump right to the first run of this system. We can
use anything we want to as starting concentrations for the
chemical components of the system. For my first run I'll use
0.001 Mol/L for each of the "major molecules" in
the cycle (i.e., acetyl CoA, citrate, isocitrate,
etc.) and 0.0001 Mol/L for the "minor molecules"
(i.e., all the rest except for water) and 55 Mol/L
for water. Of these values, water is the only concentration
value that's even close, so we will see a lot of movement
of the system as it finds its equilibrium position. You can
see this in Figs. 3 and 4.
Figure 3. Start of run.
Figure 4. End of run.
From the graphics here you can see a very robust reaction.
Initially the top arrow is obvious, signifying that it is
where most of the "chemical pressure" (if you will
allow me to use that term) is. Quickly the second and seventh
reactions become the longest arrows, and the first arrow shortens
up, then disappears. From this we can say that the "pressure"
has moved to these positions, and therefore the third through
sixth positions pose no opposition to this system's flow.
Then the second and seventh arrows fade in color, suggesting
that they are running out of all the right components for
a vigorous reaction. Something has run out, but what? From
the plot in Fig. 5, we can see that the oxaloacetate (symbol
"OXA" on the cycle graphic) is what has run out.
Figure 5. Graph of run at standard concentrations.
Second run
Next I found in vivo values for as many of the components
as I could. These values would be the values in the actual
conditions this cycle will operate, that is, in the body.
Here are the values and sources.
The result is a beginning component mixture that is close
to where it should be to begin with, and so it doesn't change
nearly as radically as the standard concentrations used in
the first run. Because of this I had to amplify the red in
this video to see what's happening. In it we see that SUC
(succinate) is building up, and that the reaction again slows
to a halt. However this time the pH decreases greatly, that
is, an increase in H+ which is a by-product of the cycle moving
in the forward direction. It appears to be working correctly!
Figure 6. Start of run.
Figure 7. End of run.
If we take a look at the data output from these calculations
again, and this time normalize some of the components so we
can compare them as in Fig. 8, we see plainly that FAD (the
component in black) was the component that ran out.
Figure 8. Graph of run at concentration found in vivo.
Since we are using in vivo starting values, this result is
close to what happens in the body. But now we must make an
important leap of understanding of the chemical system in
which this chemical system is operating.
Buffers
The normal pH of blood at rest is 7.37. That is, a hydrogen
ion concentration of 4.27E-08 is maintained by the body. We
know that in chemistry buffers are used to maintain the pH
of a system. We also know that the body maintains a pH that
is quite constant. Buffer? Yes, but not in the same sense
that a chemist normally thinks of one.
In the body the components are kept constant, or, regulated,
by the action of elegant mechanisms. This is what bowled me
over in the dawning of my understanding in biochemistry class.
Take the CO2 levels for example. If the TCA cycle
were allowed to run unchecked, CO2 would increase
to a high level, poisoning us. Instead, CO2 is
picked up by the Hemoglobin and transferred to the lungs for
removal through inhalation. At the same time, the heme is
protected on its trip back to the lungs to get more oxygen.
Nothing is wasted.
In another example, the excess H+ are spirited away through
ATP synthase, which creates adenosine triphosphate, the number
one energy molecule in the body. Each of the energy molecules
produced directly by the TCA cycle; GTP, NAHD and FADH 2,
go to processes that use the energy stored in their bonds.
These processes then return their degraded components for
yet another cycle. In these ways all components are a part
of some extremely efficient system of regulation.
So for our artificial system we will add regulation. We will
maintain the in vivo values for our components, by putting
excess, as it is created, into artificial containers, And
we will remove from these artificial containers what is necessary
to maintain the levels. We will measure the amount into and
out of the containers. Remember, the amounts into and out
of these "containers" relate to the other systems
whose end results are overall this regulation. The system
is one.
Results
Now, adding in this regulation, we no longer get an interesting
TCA cycle graphic since all small molecules save water are
constant. But we do we see several other interesting things
happening. Figures 9 and 10 show the result.
Figure 9. Start of run.
Figure10. End of run.
Our imaginary containers are on the bottom of Fig. 10. They
are red when they are losing volume, and green when gaining.
Most change with the familiar non-linear rates we expect from
dynamic systems like this. But the production of FADH 2 at
a rest increases with a constant slope!
Figure 11 plots the in vivo concentrations,
considering buffers.
Figure 11. In vivo concentrations, considering buffers.
If nothing is wasted, as I asserted earlier, then we may assume
that there is a reason for everything in this elegant system,
even this linear output of FADH2. Perhaps FADH 2 has the linear
output shown in Fig. 11 because it is useful as an energy
source for some low-level maintenance of this part of the
metabolic system?
I like to think of this cycle as an analogy of a hydraulic
pump, specifically a Vane
pump . It moves around in a circle via the major molecules,
and produces a pressure of the outputted energy molecules.
In Fig. 11 you can see one of these molecules being pumped.
As with all good research approaches, this approach asks more
questions than it answers. I believe that one who loves science
is interested in those questions as well as the answers gleaned
from the experiment.
In the future
Why am I so excited about this? While this is a research tool
in the short run, in the long it has the potential to be something
else.
My Mom was recently diagnosed and hospitalized with gallstones.
These developed because of high concentrations of bilirubin,
cholesterol and bile salts. These, in turn, were because…
etc. A similar model of the chemical equilibria that describe
that sub-system would have shown these conditions long ago.
They would have shown conditions that were ripe for precipitation
of solids, another chemical equilibrium equation.
This program was written quickly, using Visual Basic, and
it covers just a very narrow focus of the metabolic pathway.
As buffer inputs it has general data from the Internet. Imagine
a model of the whole system, with the "buffer
inputs" in real time from the patient . Moore
's Law will soon have us there in terms of computing power.
Such a system will know the positions of our metabolic equilibria.
It will "see danger signs" and give us dietary,
lifestyle or pharmaceutical advice that will get us back in
line. Our lives will be extended greatly. This may be the
future of medical diagnosis, and another turn in medical history.
For details on the calculations this is based on, how
I assembled it, and where I got the data, you may take a look
here. You can write
if you have more questions on how to build a system for your
own experimentation.
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