“I don’t think there will be a return journey, Mr. Frodo”: how thermodynamic irreversibility makes life flourish

Original paper: Statistical Physics of Self-Replication

Content review: Adam Fortais
Style review: Andrew Ton


Understanding the origin of life is one of the most enduring and fundamental scientific challenges there is. Of all branches of science, physics is probably not the first place one would think to go to for enlightenment. Life seems too complicated and multi-layered to be captured by the simplistic frameworks of physics. Today’s paper tackles a small part of understanding the origin of life – the physics of self-replication.

This paper begins by considering two macroscopic states, shown in Figure 1A, which are “one bacterium in a petri dish” and “two bacteria in a petri dish”, and considers transitions between these states. The biggest challenge here is relating a macroscopic change — the replication of a cell or collection of complex molecules — to a set of microscopic operations, also known as chemical reactions.  But these reactions are tremendously complicated. How can we know what to expect from them? The answer lies within the art of thermodynamics. 

Figure 1. Some of the pathways considered in the process of cell division. The probability of cell division (A) occurring is much higher than that of the disintegration of a single cell (B), highlighting the irreversibility of this event. Image courtesy of the original article.

According to thermodynamics, the governing quantities in a typical chemical reaction are energy, heat, and entropy. During a reaction, they can gain or lose any of these three as long as the total energy is kept balanced. Entropy, however, is a bit more special than the other two. Roughly speaking, entropy is a way of counting the number of possible ways a system can be in a certain state. So if a reaction involves several small molecules binding together to form a larger molecule, that involves a big loss in entropy. This is because there are many more ways to organize a large number of molecules than ways to organize one. Thermodynamics tells us that heat must be released to “pay for” this change in entropy. This heat flow increases the entropy of the environment, leading to an overall increase. All other things being equal, systems tend towards states of high entropy, simply because there are more ways of being in those states. This is usually referred to as the Second Law of Thermodynamics.

These are abstract descriptions of thermodynamic processes — how does the author use these to construct more concrete, quantitative models? First, they derive a version of the Second Law which relates the heat released by the transition to the irreversibility of the transition: the harder it is to undo a process, i.e. the more irreversible it is, the more heat must be released. Combining this observation with a simple model of replication, England reaches an important result: for a self-replicating system, the more efficiently it uses the available energy, the more rapidly it will replicate. 

England uses thermodynamics as a set of rules to calculate whether cell division for a bacterium is physically possible. While we already know the answer, the author is seeking to understand if this simple theory contains enough details to make accurate estimates about bacterial replication. The hard part of this problem isn’t to calculate the heat or entropy released, but rather to put a physical constraint on the likelihood of the reverse process. After all, we don’t ever see bacteria spontaneously dissolve back into their constituents. But with some clever thinking, this problem can be circumvented. Instead of considering the probability of a bacterium dissolving, the author simply considers the probability of every single chemical bond inside it spontaneously breaking. This is an extremely unlikely event, and yet it’s not as unlikely as the cell spontaneously being unmade, as shown in Figure 1B, and so it can give us a lower bound for the irreversibility of cell division. Combined with careful estimates of heat and entropy transfers, this gives a full (and very approximate) thermodynamic accounting of the process of cell division.

What can we do with this? We can perform some comparisons: first of all, the irreversibility of a process turns out to be a much larger thermodynamic barrier than the entropic difficulty of organizing all the constituents of a daughter bacterial cell, which is a highly structured object! This is surprising at first, but hindsight is 20/20: living systems are doing a lot of work to make things that don’t dissolve back into water. Another surprising conclusion of this argument is that real bacteria are tremendously efficient! With the coarse estimates used here, the author gets a replication rate close to that of a real E. Coli bacterium. This is an astonishing result, since the process considered here is not nearly as irreversible as that of a real cell division. 

The takeaway here isn’t simply learning something about bacteria or replication. The real lesson is about the power of the methods of statistical physics. The division of a bacterium is frighteningly complicated, and no physicist could write down the chain of reactions necessary for the proper replication and division of this complex system. Despite this intricacy, biological processes must still follow the unambiguous laws of physics. And that implies one thing: more life, more complexity, and more entropy. While this is by no means an answer to the question “where does life come from?”, it gives us hope that physics will continue to play an important role in the story of answering this question.

Discovery of Liquid Crystals in Short DNA

Original paper: End-to-End Stacking and Liquid Crystal Condensation of 6- to 20- Base Pair DNA Duplexes


Ever since its discovery, scientists have known that the DNA molecule is present in every life form. It carries the genetic information of all living organisms and many viruses. Today, however, we will strip DNA of its genetic importance and look at it from a different perspective. We will discuss why DNA attracts attention even outside of the biological context: What is the connection between DNA and liquid crystals? What are end-to-end stacking interactions and why are they important? If you want to get answers on these questions (and many more), keep reading.

The chemical structure of DNA is intimately related to its geometry and physico-chemical properties. In water-based solutions, DNA is negatively charged. Since like charges repel, one DNA molecule pushes others away, effectively claiming  some  volume of space for itself [1]. Because electric repulsion decreases with distance, two DNA molecules cannot feel any kind of interactions when they are far away from each other. These features make it possible, together with DNA’s rod-like geometry, to model short DNA fragments (in this context, the term “DNA fragment” refers to an individual DNA molecule that’s much shorter than the length of a gene [2]) in a simplified way, as a hard repulsive rod (Fig.1.).

Fig1_png
Fig. 1. Structure of double-stranded DNA. Hydrophilic sugar-phosphate backbone is on the ‘outer’ side of the molecule, while hydrophobic nitrogenous bases are found on the ‘inner’ side. However, for simplicity, short DNA fragment is often modeled simply as hard repulsive rod (blue cylinder).

In the 1940s, researchers found that DNA molecules, when placed in solutions of water and salt, form liquid crystal (LC) phases. We all know the three phases of matter: gas, liquid and solid. LCs are substances that don’t fall into any of these categories. They are an intermediate phase that has properties of liquids as well as those of solid crystals — LCs can flow like liquids, but there is still some degree of order between the molecules. There are many types of liquid crystalline phases, the simplest of which is called the nematic phase. In the nematic phase, rod-like molecules (the “hard rods” of DNA in this case) point in the same direction on average [3]. This property gives nematic liquid crystals the ability to show colorful LC textures under a microscope equipped with a polarized light source (Fig. 2. b) [4].

According to theory, repulsive hard rods show the transition from a disordered fluid phase (called the isotropic phase) to the nematic LC phase only if they are sufficiently long and thin [1]. Almost 50 years later, Bolhuis and Frenkel confirmed this prediction by computer simulation [5].

In case of DNA, simulations predict that one shouldn’t expect to observe LCs for DNA fragments shorter than approximately 9 nm. So, when the authors of today’s paper observed LC textures in very short DNA fragments–  from approximately 2 to 7 nm — under a polarized-light microscope, it came as a real surprise.

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Fig. 2. a) With increasing concentration, a substance which shows liquid crystal behavior can undergo transitions between isotropic, nematic and columnar phase. b) Colorful textures of nematic liquid crystals visible under the microscope.

To understand this result,  let’s look in more detail at why hard rods in a solution begin to point in the same direction as their  concentration increases. In 1949, Lars Onsager published a paper in which he explained the entropic [1] origin of isotropic-nematic phase transition for hard rods. Entropy is usually understood as a measure of disorder. How then can the formation of liquid crystals lead to the increase of the total entropy in the system? To answer this question, we should understand the entropy as a measure of the number of possible configurations a system can have at a given state. According to Onsager, there is a balance between two contributions to the total entropy: while the number of different orientations available to each rod decreases in the process of ordering (decreased number of possible configurations), the centers of rods are able to move around more freely (Fig. 3.). The net effect is an increased number of possible configurations, which leads to an increase of total entropy in the system [6].

Fig3_png
Fig.3. Rods in a) parallel orientation and b) perpendicular orientation In the situation in (a), the rods are unable to rotate, but can translate (move in the way that all points of the rods move in the same direction and the same distance) freely, while in (b) the rods can rotate more feely but their translation is restricted.

The authors found that LC phases of short DNA share all the basic features of LC phases observed in long DNA fragments. As well as forming a nematic phase [3] at lower concentrations, with increasing concentration they undergo a transition to the columnar phase, where the molecules lie on top of each other in layers within which they often form hexagonal structure, as shown in Fig 2. a).

But how can LC ordering happen in  solutions of short DNA? It turns out that our simplified picture of DNA as a negatively charged rod was a bit too simple. To understand why, we need to learn a little more about the physico-chemical properties of the DNA molecule.  As shown in Fig. 1, the inside of DNA is made up of chemicals called nitrogenous bases. Like cooking oil or the surface of a teflon pan, these ‘water-fearing’ hydrophobic molecules tend to minimize their contact with water. However, at the terminal end of a short piece of DNA, some of the nitrogenous bases will be exposed to water. This is unavoidable — unless another DNA terminal end happens to be nearby. In that case, the ends tend to stick together to minimize their contact area with the surrounding water. This attraction between terminal ends of DNA is called the end-to-end stacking interaction and causes the formation of long, thin rods. And, as we already discussed, these rods are exactly the shape that gives rise to Onsager’s nematic phase.

If the main driving force for the formation of LCs in short DNA fragments is end-to-end stacking of terminal ends, the absence of these interactions should prevent LC ordering in the system. To disrupt end-to-end stacking interactions, authors chemically modify  their DNA fragments to disturb the attractive interactions between the terminal ends. By doing this, they can prevent the formation of LC phases in short DNA duplexes [7]. This experiment serves as another confirmation that end-to-end stacking interactions are indeed necessary to drive short DNA fragments to the formation of more ordered phases.

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Fig 4. End-to-end stacking of short DNA molecules  and the formation of nematic and columnar liquid crystal phases.

The research presented in this post provides a deeper understanding of the interactions that drive self-assembly of DNA and identifies a new type of interaction: hydrophobic end-to-end stacking between terminal ends of DNA. Identifying end-to-end stacking interactions represents another step towards better understanding of DNA as a generic (instead of genetic) building material and deciphering all of its unique properties.


[1] L. Onsager, Ann. N.Y. Acad. Sci. 51 (1949) 627-659

[2] For comparison, the smallest human genes, which are made up from DNA, are ‘only’ a few hundred nanometers long, while others are nearly a millimeter; every human cell contains approximately 2 meters of DNA in total.

[3] Double-stranded DNA is a chiral molecule with helical structure. For this reason, the nematic phase formed in solutions of DNA is called a  chiral nematic, and has different properties from a “plain-vanilla” nematic phase. However, this distinction is not relevant for us in this post.

[4]  Liquid crystals have the ability to change the direction of light polarization. This ability is called birefringence and it is responsible for the colorful textures of liquid crystals which we can observe under a microscope equipped with a polarized light source, but is also basic operating principle of modern TV and computer screens: Liquid Crystal Displays (LCDs).

[5] P. Bolhuis, D. Frenkel, J. Chem. Phys. 106 (1997) 666

[6] For further reading on this topic see: D. Frenkel, Nature materials 14 (2015) 9-12.

[7] M. Nakata, G. Zanchetta, B. D. Chapman, C. D. Jones, J. O. Cross, R. Pindak, T. Bellini, N. A. Clark, Science 318 (2007) 1276-1279