Tag: origins of life

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“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.

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Dividing Liquid Droplets as Protocells

Original paper: Growth and division of active droplets provides a model for protocells

In the beginning there was… what, exactly? Uncovering the origins of life is a notoriously difficult problem. When a researcher looks at a cell today, they see the highly-polished end product of millennia of evolution-driven engineering. While living cells are not made of any element that can’t be found somewhere else on earth, they don’t behave like any other matter that we know of. One major difference is that cells are constantly operating away from equilibrium. To understand equilibrium, consider a glass of ice water. When you put the glass in a warm room, the glass exchanges energy with the room until the ice melts and the entire glass of water warms to the temperature of the room around it. At this point, the water is said to have reached equilibrium with its environment. Despite mostly being made out of water, cells never equilibrate with their environment. Instead, they constantly consume energy to carry out the cyclic processes that keep them alive. As the saying goes, equilibrium is death[1]: the cessation of energy consumption can be thought of as a definition of death. The mystery of how non-equilibrium living matter spontaneously arose from all the equilibrated non-living stuff around it has perplexed scientists and philosophers for the better part of human history[2].

An important job for any early cell is to spatially separate its inner workings from its environment. This allows the specific reactions needed for life, such as replication, to happen reliably. Today, cells have a complicated cell membrane to separate themselves from their environment and regulate what comes in and what goes out. One theory proposes that, rather than waiting for that machinery to create itself, droplets within a “primordial soup” of chemicals found on the early Earth served as the first vessels for the formation of the building blocks of life. This idea was proposed independently by the Soviet biochemist Alexander Oparin in 1924 and the British scientist J.B.S. Haldane in 1929[3]. Oparin argued that droplets were a simple way for early cells to separate themselves from the surrounding environment, preempting the need for the membrane to form first.

In today’s paper, David Zwicker, Rabea Seyboldt, and their colleagues construct a relatively simple theoretical model for how droplets can behave in remarkably life-like ways. The authors consider a four-component fluid with components A, B, C, and C’, as shown in Figure 1. Fluids A and B comprise most of the system, but phase separate from each other such that a droplet composed of mostly fluid B exists in a bath of mostly fluid A. This kind of system, like oil droplets in water, is called an emulsion. Usually, an emulsion droplet lives a very boring life. It either grows until all of the droplet material is used up, or evaporates altogether. However, by introducing chemical reactions between these fluids, the authors are able to give the emulsion droplets in their model unique and exciting properties.

 

modelSchematic_fig1b
Fig. 1: Model schematic. A droplet composed mostly of fluid B (green) within a bath of fluid A (blue). Inside the droplet, B degrades into A. Outside the droplet, fluids C and A react to form fluids B and C’. Adapted from Zwicker and colleagues.

 

The chemical reactions in the model are fairly simple (see figure 1). Fluid B spontaneously degrades into fluid A and diffuses out of the droplet. While fluid A cannot easily turn back into fluid B (since spontaneous degradation implies going from a high energy state to a low one), fluid C can react with A to create fluids B and C’, and this fluid B can diffuse back into the B droplet.

$latex B \to A \quad \text{and} \quad A+C \to B+C’$

If C and C’ are constantly resupplied and removed, respectively, they can be kept at fixed concentrations. Without C and C’, the entire droplet would disappear by degrading into fluid A, reaching equilibrium. Here, C and C’ act as fuel that constantly drives the system away from equilibrium, creating what the authors dub an “active” emulsion. Active matter systems like this one have had success in describing living things because they, like all living matter, fulfill the requirement of being out-of-equilibrium.

Because the equations that describe how fluids A and B flow over time are so complicated, the authors solve their model using a computer simulation. When they do, something remarkable happens. Emulsions with no chemical reactions with their surrounding fluids never stop growing as long as there is more of the same material nearby to gobble up. This process is called Ostwald ripening[4]. The authors find that an active emulsion system, due to the fact that material is constantly turning over, suppresses Ostwald ripening and allows the emulsion droplet to maintain a steady size.

In addition to limited growth, the authors also find that the droplets undergo a shape instability that leads to spontaneous droplet division (see this movie). This occurs due to the constant fuel supply of C and C’. The chemical reaction A+C ? B+C’ creates a gradient in the concentration of fluids A and B outside the droplet. Just outside the droplet, there is a depletion of B and an abundance of A, while far away from the droplet, A and B reach an equilibrium concentration governed by the rate of their reactions with C and C’. The authors dub this excess concentration of B far away from the droplet the supersaturation. Where there exists a gradient in the concentration of a material, there exists a flow of that material, called a flux. This is the reason a puff of perfume in one corner of a room will eventually be evenly distributed around that room. The size of the droplet is dependent on the flux of fluid B into and out of the droplet.

Two quantities determine the evolution of the droplet. The first is the supersaturation that reaches a steady value once all fluxes stop changing in time, and the second is the rate at which the turnover reaction B?A occurs. For a given supersaturation and turnover rate, the authors can calculate how large the droplet will grow, and they find three distinct regimes. In one regime, the droplet dissolves and disappears as the turnover rate outpaces the flow of fluid B back into the droplet. Another has the droplet grow to a limited size and remain stable, since the turnover and supersaturation balance each other out and give a steady quantity of fluid B. The third and most interesting regime occurs if the droplet grows beyond a certain radius due to the influx of fluid B outpacing its efflux. Here, a spherical shape is unstable and any small perturbation will result in the elongation and eventual division of the droplet (Figure 2).

 

dropletStabilityDiagram_fig2b
Fig. 2: Stability diagram of droplets for normalized turnover rate $latex \nu_-/\nu_0$ vs supersaturation $latex \epsilon$. For a given value of $latex \epsilon$, the diagram shows regions where droplets dissolve and eventually disappear (white), grow to a steady size and remain stable (blue), and grow to a steady size and begin to divide (red). Adapted from Zwicker and colleagues.

 

And that’s it. If you have two materials that phase separate from each other, coupled to a constant fuel source to convert one into the other, controlled growth and division will naturally follow. While these droplets are more sophisticated than regular emulsion droplets, they are still a far cry from even the simplest microorganisms we see today. There is no genetic information being replicated and propagated, nor is there any internal structure to the droplets. Further, the droplets lack the membranes that modern cells use to distinguish themselves from their environments. An open question is whether a synthetic system exists that can test the model proposed by the authors. Nevertheless, these active emulsions provide a mechanism for how life’s complicated processes may have gotten started without modern cells’ complicated infrastructure.

Though many questions still remain, Zwicker and his colleagues have lent considerable credence to an important, simple, and feasible theory about the emergence of life: it all started with a single drop.

[1]: This isn’t exactly true. Some organisms undergo a process called anhydrobiosis, where they purposefully dehydrate and rehydrate themselves to stop and start their own metabolism. Also, some bacteria slow their metabolism to avoid accidentally ingesting antibiotics in a process called “bet-hedging”.

[2]: For example, ancient Greek natural philosophers such as Democritus and Aristotle believed in the theory of spontaneous generation, eventually disproven by Louis Pasteur in the 19th century.

[3]: Oparin, A. I. The Origin of Life. Moscow: Moscow Worker publisher, 1924 (in Russian), Haldane, J. B. S. The origin of life. Rationalist Annual 148, 3–10 (1929).

[4]: Ostwald ripening is a phenomenon observed in emulsions (such as oil droplets in water) and even crystals (such as ice) that describes how the inhomogeneities in the system change over time. In the case of emulsions, it describes how smaller droplets will dissolve in favor of growing larger droplets.