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CHM 112: Arrhenius equation

According to collision theory, molecules must do a couple of things in order to react. They are:

  1. Collide
  2. Collide in the correct orientation
  3. And Collide with enough energy

Anyways, this is the Arrhenius equation: k = A*e^((-Ea)/(R*T))

  • k is rate constant
  • A is frequency factor or “pre-exponential factor”
    • A includes frequency of collisions
    • A includes orientation of collisions
  • e^((-Ea)/(RT)) is the fraction/number of collisions with enough energy to react
    • You may symbolize all of e^((-Ea)/(RT)) as f
  • so f depends on activation energy (-Ea), which is in joules per mole
  • R is the gas constant
  • T is the temperature in Kelvin

arrhenius equation.PNG

So let’s see how changing the activation energy, or temperature, how it affects the the fraction/number of collisions with enough energy for a reaction to occur.

Example: Ea = 40kJ/mol | T = 373 K

f = e^((-40*1000)/(8.314*373)) = 2.50E-6 or 2.5 * 10^-6

Note that 2.5/1,000,000 is 2.50E-6. That means that for every 1 million collisions in our reaction, only 2.5 collisions have enough energy to react.

Now let’s change the activation energy to a smaller number: Ea = 10kJ/mol | 373 K

When activation energy is decreased, reaction rate increases.

When temperature is increased, reaction rate of exothermic reaction is increased.

Images of neurons show ~5-20 synapses, but descriptions say each neuron has ~10,000 or more. Which is correct?

Images of neurons show ~5-20 synapses, but descriptions say each neuron has ~10,000 or more. Which is … by Paul King

Answer by Paul King:

Cartoon drawings of neurons may show only 5 – 20 synapses in order to make the cartoon easier to understand, but images of real neurons in the cerebral cortex show thousands of synapses, up to 10,000.

A cartoon neuron:

A real neuron from the visual cortex:

The tiny black dots are synapses. The neuron is actually 3-dimensional, so in this 2-dimensional slice, you are seeing less than 10% of the neuron.

More than 99% of the neurons in this image are transparent, as only one neuron is stained black, which is why you don’t see the hundreds of neurons on the transmitting side of these synapses.

Images of neurons show ~5-20 synapses, but descriptions say each neuron has ~10,000 or more. Which is correct?

I recently started taking a magnesium supplement everyday and I feel amazing. Can anyone explain why?

I recently started taking a magnesium supplement everyday and I feel amazing. Can anyone explain w… by Steven Fowkes

Answer by Steven Fowkes:

Magnesium is an essential nutrient. Any essential metabolic pathway could be involved in why you feel better.

One of magnesium’s roles is in the action of ATP, the energy molecule. ATP is not really an energy molecule in the scientific meaning of energy. It might be more accurately described as an anti-entropy molecule. But the take-home message is that ATP drives the enzymes in your body that make your body work. The muscles that make you move and pump your blood, the enzymes that digest your food and repair your body, the electrical signaling pathways of your brain and nerves, all are made dynamic by the action of ATP.

Magnesium is at the heart of the ATP reaction. The ATP molecule is very negatively charged, and it wraps itself around a positively charged magnesium ion. This ATP-magnesium complex than fits into an enzyme to transform its potential energy (negentropy) into action. Change chemical A to chemical B. Move the fiber in muscle one notch further along. Pump a calcium ion out of a neuron so it can fire again. Many different kinds of action, indeed!

Deficiencies of nutrients impair function. From a position of impairment, you are more likely to notice improvement of function.

This is not a linear system. In other words, more will not necessarily make you feel better. It is an issue of sufficiency or adequacy in terms of normal function, and an issue of optimization for peak performance. It is easier to notice the difference between impaired function and normal function. But distinguishing optimal function from normal function is difficult and usually requires a sophisticated measuring system. In athletics, for example, peak performance can be a matter of a difference of seconds.

I would say that the most likely explanation is that your were magnesium deficient before supplementing.

Good luck if you should undertake further biohacking efforts.

I recently started taking a magnesium supplement everyday and I feel amazing. Can anyone explain why?

What is Phosphorylation?

What is Phosphorylation? by Steven Fowkes

Answer by Steven Fowkes:

Phosphorylation is the process of adding a phosphate group (PO4) to a hydroxy position on a molecule, protein or enzyme. The two primary residues on enzymes or proteins that are phosphorylated are tyrosine and serine.

The initial hydroxy group is small and slightly positively charged due to part-time protonation in its aqueous environment, but the phosphate group is large and quite anionic (negatively charged), which can change the shape of the protein or enzyme that has been phosphorylated. This can increase its enzymatic activity, or decrease it.

Dephosphorylation (removal of a phosphate group) by phosphatases is the opposite process.

Kinases can add phosphate groups to both kinases and phosphorylases.

Phosphorylases can remove phosphate groups from both kinases and phosphorylases.

This means that kinases and phosphorylases can increase and/or decrease the activities of both kinases and phosphorylases.

This is actually put to use in a major way in the human brain, which is stabilized in function by a metastable 90-second cycle of over-phosphorylation and under-phosphorylation. As the cycle begins, the kinases phosphorylate both kinases and phosphorylases to increase the activity of kinases and decrease the activity of phosphorylases. Then, when phosphorylation ultimately proceeds towards saturation, the phosphorylation sabotages the activities of key kinases and enhances the activities of key phosphorylases. The wholesale phosphorylation begins to reverse. As phosphate groups are stripped off by the ascendent activities of phosphorylases, the activities of phosphorylases are enhanced and kinases suppressed. This rapidly swings the brain into a dephosphorylated state. But some key phosphatases are decreased in activity by their dephosphorylation, and some key kinases are activated by their dephosphorylation. So the system again reverses.

This is one reason why the human brain has so high a metabolic rate. Although only 3% of the body’s mass, it consumes 20% of the body’s energy.

In Alzheimer’s disease, the collateral inhibition of sulfhydryl-based enzymes causes critical destabilization of at least two kinases and four phosphatases that control the meta-stable “flipping” of the over-phosphorylated state into phosphatase dominance. As a result, the brain stays in a hyper-phosphorylated state. This manifests in (a) the precipitation of hyper-phosphorylated tau protein into neurofibrillary tangles, and (b) destabilization of the brain’s cytoskeletal infrastructure maintenance.

Others may provide different examples of the role of phosphorylation and dephosphorylation in control of enzymatic regulation. But this example is, I think, a good example of the importance and complexity of such systems.

I hope my explanation is comprehensible.

Great question.

What is Phosphorylation?

What is mitochondrial uncoupling?

What is mitochondrial uncoupling? by Steven Fowkes

Answer by Steven Fowkes:

Uncoupling is a loss of output efficiency for any given input to a process. Mitochondrial uncoupling is the loss of ATP production from the input of protons into the inter-membrane space. This can be protein driven as part of a natural feedback loop for the regulation of energy and temperature, and it can be chemical / toxin driven.

I think 2,4-dinitrophenol is the classic uncoupling toxin for much of the research in this area. You also mention aspirin, which also has an uncoupling effect.

If you measure energy by ATP formation, uncoupling can decrease energy. But not necessarily always. Thermogenic agents like caffeine and ephedra can increase both ATP and fuel consumption to compensate for uncoupling inefficiencies.

If you measure energy by fuel consumption (a caloric perspective), uncoupling can increase energy production. This is most conspicuous in brown-fat tissues exposed to cold, but it might also play a strong role in the generation of fever responses to sepsis.

Thanks for the question.

What is mitochondrial uncoupling?

What kind of disease it is when you can’t eat carbohydrates?

What kind of disease it is when you can't eat carbohydrates? by Steven Fowkes

Answer by Steven Fowkes:

The “can’t eat carbohydrates” message is NOT literal. Even obligate carnivores get carbohydrates in their natural diet by eating meat. What eat-no-carbohydrates likely means is (1) avoiding refined carbohydrate-foods entirely, like bread, flour, beer, cookies, cakes, soda, etc. and (2) minimizing foods which have an especially high carbohydrate content, like grains, starchy vegetables, root vegetables and fruits. These treat diseases of energy metabolism, which can include epilepsy, dementias, chronic fatigue syndromes, chemical sensitivity syndromes, depressions, autoimmune diseases, diabetes and some neurodegenerative conditions.

Simple carbohydrate restriction induces beta-oxidation and ketosis. Beta-oxidation is the metabolic process of burning fat for energy. Our bodies can burn carbs and fat for energy, and some diseases are essentially linked to disorders of carb-burning systems (insulin resistance, syndrome X, pre-diabetes). Fat-burning systems are the back-up energy pathway, so restricting carbs is the traditional therapy for activating fat-burning energy pathways. This can be highly therapeutic. For example, there are countless reports of intractable seizures in infants and children which resolve completely when carbohydrate foods are restricted. Carbohydrate restriction is a long-established therapeutic modality with plenty of scientific and medical literature behind it—despite what you might read here from other authors.

Ketosis is the process of taking beta-oxidation to a systemic level. When carbohydrate is restricted to a certain “set point,” which is unique to every individual and can also change over time, the liver goes into beta-oxidation “overdrive.” The high-flux metabolism of fatty acids in the liver into “ketone bodies” or ketone fuels get exported to the rest of the body through the blood stream. This provides fuel to body tissues that is not restricted by insulin resistance. Ketone fuels are actually carbohydrates, but they are 4-carbon carbs instead of 6-carbon carbs (glucose) and there is no restriction on their absorption into cells, and into mitochondria. So all the myriad of diseases which develop from energy constraints (low ATP and low NADPH) can begin to resolve in as little as a week.

If you search online, you will see two popularized (and hyped), carb-restriction-based approaches to resolving type-II diabetes. One is the raw vegan diet. The other is the low-carb paleolithic diet. Although these seem disparate in first appraisal, they have carb-restriction in common. Both diets can produce ketosis on a sustained basis.

I think it likely that there is also a non-carb component to your female friend’s lifestyle changes. That would be food restrictions for minimizing allergic, hypersensitive and inflammatory responses. The avoidance of milk tips me off. Milk is one of the five most common foods that causes delayed hypersensitivities in western societies (along with wheat, corn, eggs and yeasts). And the wheat and corn are doubly implicated as allergens AND carb-rich foods.

Although there are certainly ways in which carb-restriction and dietary restrictions can be promoted and practiced as fads, such practices are fundamentally part of a strategy of a “return to nature.” Carb foods in nature are never refined. Carb foods in nature are rarely available year round, usually involving seasons of availability. Seasonal food eating is mimicked by intermittent and selective fasting, and dietary rotation protocols. Many dietary protocols now focus on changes to the microbiome, adverse alterations of which are now being widely connected to disease occurrence.

It may take you a while to digest all of this, and become more at ease with your friend’s chosen therapeutic path. But you have time to look more into some of these topics and understand some of the less well known advantages of naturopathic medicine and functional medicine.

Good luck to you. I hope my long-winded answer helps answer some of your questions.

What kind of disease it is when you can't eat carbohydrates?

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