# Why do some chemical reactions require many steps?

I posted the following question in Physics SE and was advised to transfer it to Chemistry SE.

I studied physics in college ten years ago and I recently started to learn biochemistry. I enjoy finding out that some familiar concepts in physics play important roles in biochemistry such as entropy and the Gibbs free energy.

For example, as a (ex-)student of physics, I am happy to know that the Gibbs free energy determines the directions of chemical reactions. I feel this is a good example where a sort of fundamental law of physics determines how a phenomenon looks like.

However, I still can not understand why the chemical reactions in a body need to be so complex. Many chemical systems consist of more than several steps to achieve their purposes. According to Wikipedia, glycolysis takes ten steps through its process. Why are so many steps necessary?

I tried to find out a physical law that prohibit the glycolysis process from being achieved in one or two steps, but I could not find an answer. I would like to know (or discuss) whether there is a physical law that makes chemical systems so complex (many steps required).

My assumption is that some physical law prohibit the existence of an enzyme that realizes a one-step process of glycolysis.

• There is no such law. It is just that you need to carefully rearrange a lot of delicate things (chemical bonds). Can you, say, print a book in one hour? I don't think so. What physical law prohibits that? – Ivan Neretin Jun 19 '18 at 10:03
• My intuition is opposite to yours. – Ivan Neretin Jun 19 '18 at 11:01
• Do you think any book can be printed in one hour? – Ivan Neretin Jun 19 '18 at 11:47
• Is it not just a matter of where you start? If with the elements, say carbon, oxygen etc then even to make a small and specific molecule rathe than just any type of molecules several steps are needed as the reaction has to be directed towards your product. – porphyrin Jun 19 '18 at 12:21
• @IvanNeretin I joined just so I could comment,,, I work at a printing company, and many times we print multiple books (and finish them) within the span of an hour. I had my thesis printed (6 copies) and binded within 45 minutes. :) – SynerCoder Jun 20 '18 at 7:33

There is no fundamental law preventing simple chemical reactions: things are complex because of the combinatorial complexity of chemical compounds

The complexity of many chemical reactions is a byproduct of the fact that there is a very, very large variety of possible chemicals. Much of that complexity happens because of the almost infinite way even some simple elements can be combined together to give complicated structures (carbon being the archetypal example). Theoretically, for example (theoretical because not all of the examples can exist in 3D space) there are 366,319 ways to build different alkane compounds from just 20 carbon atoms and hydrogen atoms (see this question here and this entry in the Encyclopaedia of integer sequences). And this number drastically understates the real complexity as it ignores mirror images and more complicated ways of joining the carbon atoms together (like in rings, for example). The complexity just gets more mind boggling if you start adding other elements to the mix.

No physical law prevent us making any possible compound in one step. But the sheer complexity of the end products makes simple ways to reach many of them extraordinarily unlikely from the laws of probability alone, never mind the specific ways chemical components can be easily joined up to make more complex things.

Here is a simple analogy. Let's say you want to assemble a Lego model of the Star Wars Death Star weapon. There are 4,016 pieces of lego that have to be assembled in the right combination and the right order. There is no physical law that says you couldn't somehow do that in a single step. But no sane person's intuition would assume that this was easy or likely. It isn't physical law that prevents one step assembly: it is combinatorial complexity. Chemistry is, do I really need to say this, more complicated than Lego: not least because atoms can be joined up in many more complex ways than the simple, standard-sized physical pins that join Lego bricks together.

Both nature and synthetic chemists have explored many ways to achieve particular end products from simpler building blocks. Sometimes new chemical Death Star equivalents (like the geometrically beautiful hydrocarbon dodecahedrane, which, incidentally, has 20 carbons but isn't counted in the list of 20 carbon alkanes) are made only after long sequences of reactions. The original synthesis of dodecahedrane took 29 steps but others found better, higher yielding, routes that took only 20. Many important drugs are first synthesised in long sequences of reactions but are later found to be available via much shorter routes (there is nothing like the economics of manufacturing cost to encourage creativity).

So the reason many chemical reactions take multiple steps isn't physical laws but probability theory. There are just too many possible chemicals and too many ways to combine things for single step routes to most given products to be likely to work. Doing one thing at a time (just like you would if building the Lego Death Star) is the way to get what you want.

• Thank you very much! If I understand you correctly, you mean that there are significant number of routes for, say, Glucose to two molecules of pyruvic acid by the combinatorial complexity. The step size of each route is various. When one route is selected randomly, the probability of $step_size = 1$ is very few. That's why almost all complex chemical reaction takes more than one step. Is my understanding correct? – rkjt50r983 Jun 20 '18 at 8:54
• This and the other answer touches on the fact there is, in fact, a fundamental law: thermodynamics. To get, say, 25 atoms in the correct arrangement would require a colossal decrease in entropy. Individual steps lowers the entropic penalty, allowing reactions to take place. – awjlogan Jun 20 '18 at 14:03
• @rkjt50r983 Yes, I think your intuition is getting the right idea. – matt_black Jun 20 '18 at 18:18

I do not believe there is a fundamental law which prohibits complex reactions from taking place in a single step — it’s just extremely improbable.

# Collision Theory

## Gasses

This is especially relevant in gasses, but I will relate it to glycolysis later. Kinetic-Molecular Theory simplifies gasses to dimensionless points moving in constant, random, straight-line motion and colliding 100% elastically with each other. While none of this is exactly true, it is a good model.

For gases to chemically react, molecules must collide with the proper orientation and enough energy. Let’s look at the following reaction.

$$\ce{CH4 + Cl2 -> CH3Cl + HCl}$$

While it is theoretically possible for these particles to collide, it would most likely confuse the system rather than actually make the desired products. Let me propose a mechanism.

$$\ce{Cl2 -> 2Cl}$$

$$\ce{CH4 + Cl -> CH3+ + HCl}$$

$$\ce{CH3+ + Cl2 -> CH3Cl + Cl}$$

$$\ce{2Cl -> Cl2}$$

By using two intermediates (unstable substances created during a reaction which quickly rereact) and four steps, I have broken a complex reaction into a series of unimolecular and bimolecular collisions (favored by probability). Furthermore, it is far easier for the molecules in these steps to collide with a proper orientation. Let’s look at the second step. Methane has a tetrahedral electron-pair geometry, and when a monoatomic chlorine collides with enough energy 180 degrees opposite a hydrogen, the electron clouds may overlap, simultaneously forming a $\ce{C-Cl}$ bond and breaking a $\ce{C-H}$ bond.

## Glycolysis

Oversimplifying, but glycolysis turns a glucose molecule into two G3P molecules and two ATP. If methane is complicated with its five atoms, glucose is far more with its twenty-four. Not only would it be nearly impossible for one reaction to split this sturdy sugar ring but to rework the products as well into their forms that are comparable with the Krebs cycle, etc. would take insane luck. Instead, a carefully controlled process makes the essential reaction reliable.

Furthermore, enzymes are ‘invented’ by random mutations, so an enzyme to carry out this process may be feasible, but evolution would probably not invent it. And even if it did, it would probably not confer that much of a survival advantage and would pass out of the gene pool.

Hope this helps!

• (+1) While I like matt_black's answer a lot, I think this gets more to the point OP is confused about. Yes, there are a lot of things that could form if many atoms collided at once, but the bigger issue is that it becomes astronomically more unlikely to get 3, 4, ... things to collide in the proper orientation to produce anything at all and so most reactions proceed in steps involving a single collision. Even a very intricately designed enzyme would have little change of producing benzene from 6 carbon and 6 hydrogen atoms, it simply requires too much coordination. – Tyberius Jun 19 '18 at 18:30
• Not to mention, each enzyme in glycolysis has a specific function, and the metabolic intermedates often have functions by themselves. For example 2,3-BPG is "only" an intermedate in glycolysis, but it has vital functions on its own. – forest Jun 20 '18 at 2:40

Authors note: While there are some good answers already, I wish to help you understand by explaining in a different way. I do agree with the other posts that there is no physical or chemical law to prevent a different, more straight-forward process.

## Reason behind the glycolysis process

The reason why this process is as it is, is efficiency towards reaching the goal. And the goal is not to break down glucose to smaller molecules. The goal is to store energy in a carrier that can move through the body and is compatible with other biological processes.

The three bold words are key here. The body needs energy to perform various tasks such as muscle contractions (breathing, heart beat), cell growth, fighting bacteria and many more. It’s not handy to always generate the energy needed at the place where it is needed. Instead, we have energy carriers (most importantly ATP) that is produced in certain parts of our bodies and then distributed via the blood.

## Energy in the body

Before I continue, you need to understand a bit about Gibbs free energy. As you mentioned, it determines the most energy-efficient way for a process from beginning state to end state. However, if you provide energy, the process can go the reverse direction just fine. So looking at Gibbs free energy only shows the process that is most likely to spontaneously occur under normal circumstances, but not in all circumstances.

Second in-between background info is that the energy in the body is transported using adenosine triphosphate (ATP) and adenosine diphosphate (ADP). Adding a phosphate group to ADP (which then becomes ATP) costs energy that can later be extracted by the reverse process.

Third is that energy availability in the body is limited. We have two major sources of energy: ATP and body heat. An ATP molecule will always provide a specific amount of energy, while body heat can provide from 0 up until a certain limit, depending on body temperature (this maximum is lower than ATP’s energy). Any process that needs more energy than ATP can provide will have to be broken down into separate smaller steps.

## Back to glycolysis

With this background information in mind, we can explain the reason behind the (complex) glucolysis process better. From a Gibbs free energy point of view, we don’t need to go from high energy glucose to low-energy pyruvate as fast as possible. Instead, we need to do this in a way that has the most steps that provide the exact amount of energy needed to transform ADP into ATP.

As you can see in the image caption on the glucolysis page you linked, we need 1 glucose + 2 ATP, to generate 4 ATP. Why is the initial ATP needed? This is to get the specific break-down chain that allows 2*2 steps of energy extracting throughout the process. We need the initial energy investment to allow for in-between steps to happen, chemically speaking. Without this investment, you will not be able to form the intermediary molecules needed to give enough energy in order to store it in $\ce{ADP\bond{->}ATP}$.

## Comparison to nuclear fusion/fission

I normally don’t like to make comparisons to unrelated subjects, but I think this one fits well enough to mention and hope you will understand it better with your physicist background. In nuclear fission and fusion, you determine possible nuclear decays and fusions by looking at the available energy and energy levels of an atom. And if we ask your original question here, we get the same answers as in chemistry.

• Is there anything preventing 6 hydrogens atoms fusing into a carbon atom?
• Is there anything preventing U-235 into splitting into 20 different atoms in a single step?

To the first: no, but it’s very unlikely that 6 atoms meet at the exact same time and with the correct amount of energy. And even if they did, carbon is not a stable atom without neutrons, so where do they come from? You need multiple steps to go from hydrogen to carbon…

To the second: No, nothing prevents this. But splitting of atoms goes via a set of strict rules regarding the stability and energy of the atoms and their radiation products. The start and end point may be clear, but there are almost always multiple in-between steps (example: decay chain of thorium. In the same way, chemistry has many rules for reactions and atom/electron rearrangements within a molecule, limiting how molecules can break apart or combine.

The part where this comparison goes wrong is that biology does not always lean towards the most energy-efficient solutions. Sometimes nature takes a complex, unefficient route for a different purpose, as in glycolysis.

The chemical reactions that you learn about in chemistry classes are designed by humans. Although these can be sometimes quite complicated, there is a strong bias toward designing reactions that can be rationalized by the human brain. The reaction networks found by evolution are not constrained by what humans can understand and, therefore, can appear more complex.

In fact, evolution in some cases may favor complex reactions, because they can be more efficient. Have a look at the Krebs cycle (also known as the citric acid cycle), which converts most of the energy used by your body from sugars to a more usable form (as ATP, where the energy is stored in phosphate linkages). The RCSB Protein Data Bank has a good description (description of Krebs cycle with the enzyme structures) of the steps involved. The cycle is more energy efficient than other simpler options for converting energy from oxidation of acetate to ATP (paper by Krebs on the efficiency of the cycle).

Another thing to ponder is how these processes came to be. Evolution is the progenitor of basically all biochemical processes. Evolution doesn't [necessarily] care about efficiency, it cares about being effective (ie. creature stays alive). Sure, I can cut through someone's yard to get across the neighborhood, but taking the sidewalk keeps the neighbors from releasing the hounds on me.

Then there's energy. Everything in chemistry boils down to being energetically favored. You seem to understand that with Gibbs Free Energy. While not necessarily the case with glycolysis, but some chemicals will keep their bonds the same because it's so stable, unless a lot of energy is thrown at it. That's where proteins come in. The proteins bend or twist molecules so that the activation energy is much smaller and certain reactions are favored. (A tetrahedral carbon will not like having bond angles significantly less than 109.5 degrees so a change in bonding is likely to occur to return to that energy stability).

• Many of the specific sentences of this post are sensible and factual, but I'm afraid I don't see how this answers the question posted. – hBy2Py Jun 20 '18 at 4:06
• It's a generic answer to the title question. Will it get best answer? No, the previous answers definitely fit the bill better. However, it does explain why there isn't one singular reaction and provides some context to help the OP with rest of biochem. – Lux Claridge Jun 20 '18 at 12:57
• OP asked specifically about biochemistry. "Nothing in biology makes sense except in the light of evolution", so this answer adds an important perspective that is missing in the others. It could explain in more detail how unnecessary complexity would evolve, though. When there's a simple and a complex way to do it and a species has already evolved 90% of the complex way for other reasons then that's what you will end up with. – Cephalopod Jun 20 '18 at 13:33