Following up on the @APSDBIO tweetorial on the bacterial flagellar motor, here are a few links to resources where you can learn more about this marvelous machine and its biophysics.

Reviews

Berg 2003

Sowa and Berry 2008

Nakamura and Minamino 2019

Beeby et al. 2020

Wadhwa and Berg 2022

Structures

Santiveri et al. 2020

Deme et al. 2020

Tan et al. 2021

Bi-directional rotation

Chang et al. 2020

Mechano-adaptation

Wadhwa et al. 2021

Wadhwa et al. 2019

Lele et al. 2013

Nord et al. 2017

Torque-speed relationship

Chen and Berg 2000

Yuan et al. 2010

Xing et al. 2006

Meacchi and Tu 2011

As you see, this is a rather brief list. If you know of other cool papers that you would like to see listed here, feel free to drop me a message.

This post first appeared on the website of MCB department at Harvard.

The bacterial flagellar engine has a bidirectional gearshift

Bacteria are a nanotechnological marvel. Consider the bacterium Escherichia coli as an example. Barely a millionth the size of a typical human (E. coli is a rod-shaped cell about 2 µm long and 1 μm wide), each cell is chock-full of molecular machinery that enables it to carry out life’s myriad functions. One of these, the flagellum, is the miniature propeller that allows E. coli to swim at astonishing speeds, covering up to 20 body lengths every second. A typical cell has four or five flagella, each capable of rotating in either direction – clockwise (CW) or counterclockwise (CCW).

The engine that drives rotation of the flagella is the flagellar motor, a highly complex nanomachine about 50 nm in diameter. Made up of tens of different proteins, the flagellar motor embeds in the E. coli cell envelope and turns the flagellum from its base. Like a car engine, the flagellar motor converts chemical energy into mechanical work. Protein complexes called stator units attach to the cell wall (thus remaining stationary) and apply a force on the rotor (which is free to rotate) to drive the rotation.

It turns out that this miniature engine of E. coli has some neat tricks up its sleeve. Just like modern cars can automatically change gears to adapt to changing terrains, the flagellar motor can also adapt to changes in the mechanical load. But unlike cars, which adjust the transmission from the engine to the wheels, E. coli modifies the engine itself. When load increases, the flagellar motor adds additional stator units to increase its torque output, and when load decreases, the motor releases stator units, decreasing torque output. So, E. coli constantly dismantles and rebuilds its engines as the mechanical demands of its external environment change.

We studied this process using electrorotation, a technique in which we apply a high frequency rotating electric field to E. coli cells attached to a surface by the flagellum. The electric field applies a large external torque on the cell. This torque instantaneously and reversibly changes the mechanical load on the motor, allowing us to carefully measure its adaptation response. We can also control the amount of external torque by adjusting the strength of the electric field. Our electrorotation rig is thus a feature-rich platform for probing the function of bacterial flagellar engines.

Using electrorotation, we previously measured the mechano-adaptation response in CCW rotating flagellar motors. We found that the extent and the speed of the motor’s response depends on the torque produced by the stator units. When we decrease the mechanical load, torque output decreases, and stator units leave. When load increases, torque also increases, and the stator units stay. Torque somehow tunes the stator units’ binding to the cell wall, enabling the adaptation response.

When we sought to test these ideas, we had to look no further than the CW rotating flagellar motor. For reasons not fully understood, the flagellar motor produces much less torque when spinning CW than it does when spinning CCW. So, to test our model of torque-dependent response, all we had to do was to use electrorotation to measure mechano-adaptation in CW rotating motors and compare the results with data from CCW rotating motors. That is exactly what we did, reporting our findings in a new paper just published in PNAS.

To our great satisfaction, we found that remodeling rates from CW and CCW rotating motors fall on the same curve if plotted against torque. So, mechanosensitive remodeling in the bacterial flagellar motor is independent of its direction of rotation and depends only on torque. This result not only confirms our model, but also provides strong constraints on the molecular mechanisms of mechano-adaptation in the flagellar motor. We are currently developing mathematical theories and new experimental methods to probe these mechanisms.

We remain enamored by the bacterial flagellar motor, which turns out to be one of nature’s most complex yet elegant nanomachines, making most human-made machines look primitive in comparison. Going forward, we plan to continue probing it with novel experimental approaches, in the hope that this will allow us to reveal more of its secrets.

This post first appeared on the blog of Biophysical Society. This was the third blog post in a 3-part series of blogs that I wrote about my favorite Biophysical Journal papers of 2019. You can read parts 1 and 2, here and here.

A new way of trapping bacteria

Araujo, G., Chen, W., Mani, S., & Tang, J. X. (2019). Orbiting of Flagellated Bacteria within a Thin Fluid Film around Micrometer-Sized Particles. Biophysical Journal, 117(2), 346-354. link to article

The field of biophysics owes its existence to the fact that the principles and approaches of physical sciences have been incredibly successful at elucidating biological phenomena. The reason behind this success is quite simple. At one level or another, most if not all biological processes can be broken down into physical interactions between two or more interacting partners. Once such interactions are identified, it can then often be straightforward to describe them using well-established physical laws.

A shining example of how to effectively marry physics and biology is found in the field of bacterial motility. Many bacteria swim through fluids by rotating rigid helical filaments driven by a sophisticated molecular nanomachine called the flagellar motor. Over the years, the study of flagella-driven bacterial motility has gained tremendously from using the tools of physics to attack this problem. Great progress has been made by combining careful experiments to observe bacterial motility with the application of hydrodynamics to rationalize the observations.

A recent study published in Biophysical Journal carries on this rich tradition. Araujo and colleagues reported a novel observation of trapping bacteria in thin liquid films. They grew a swarm of motile bacteria on top of an agar plate and dropped a suspension of micron-sized particles at the edge of the swarm. Within minutes, most of the liquid dropped by the researchers evaporated, leaving behind the deposited particles and small tents of fluid around them where surface tension pulled the meniscus away from the agar surface. When the researchers looked closer, they found bacteria trapped and swimming around in this tent. The most striking observation was that when viewed from above the meniscus, all the trapped bacteria were swimming in circles going clockwise!

An observation like that would get any scientist excited and eager to learn more. Why were the bacteria trapped? Why did they swim only clockwise? How long will they remain trapped if left untouched? Through a series of exploratory experiments, the researchers have revealed a rather peculiar situation in which the interplay between surface tension, evaporation, and the hydrodynamics of flagella-driven bacterial motility lead to the bacteria getting trapped and swimming in circles.

The fluid tent was formed because at the minute size scales relevant here, surface tension is the dominant fluid force around. This is why small insects can easily “walk” on water, because the force required to break through the water surface is much larger than what gravity can apply on such small organisms. Similarly, the surface tension at the fluid-solid interface between a micron-sized particle and the surrounding medium causes the meniscus to rise against gravity. Accordingly, when the researchers placed small particles on the agar surface, fluid was pulled away from the agar and small fluid-filled tents were formed, trapping bacteria within the bounds where the meniscus met the agar surface.

Thanks to another very useful principle of physics, such fluid tents were stable for hours at a time. Evaporation would normally deplete such a small volume of fluid within seconds. However, since the tent rested on top of a large reservoir of fluid (the agar gel), any loss of fluid to evaporation was supplanted by an inflow from the agar through wicking action. Surface tension for the win, again!

Why do the trapped bacteria swim clockwise when viewed from above? This is where the hydrodynamics of flagella driven motility kicks in. As mentioned before, many bacteria swim by rotating helical rigid filaments through the fluid. For bacteria such as Escherichia coli (one of the species studies by Araujo et al.), the flagellar filaments are left-handed helices. The cell swims forward by rotating the flagella counterclockwise (viewed from outside the cell), while the cell body counter-rotates clockwise to balance the torque. When the cell swims near the agar surface, the side closer to the agar experiences higher viscous drag. As a result, along with moving forward, the cell effectively rolls on its side, resulting in circular trajectories. For clockwise rotating cell bodies, this results in clockwise swimming when viewed from above.

There we have it. Grow some swarming bacteria on an agar plate and throw in some micron-sized particles, and you too can build your own bacterial traps. What you do with the bacteria you trap is up to you. Maybe you trap bacteria with other exotic modes of swimming. Maybe you play with the agar concentration to make it more or less stiff. You could even turn the agar plate upside down to give some extra challenge to surface tension. The possibilities are endless. As we have seen in the case of the Araujo et al. study, you can learn a lot by just observing.

This post first appeared on the blog of Biophysical Society. This was part 2 of a 3-part series of blogs that I wrote about my favorite Biophysical Journal papers of 2019. You can read part 1 here.

Gene regulation dynamics in single bacterial cells

Uphoff, S. (2019). A quantitative model explains single-cell dynamics of the adaptive response in Escherichia coli. Biophysical journal, 117(6), 1156-1165. link to article

Every living organism has three core missions in life – eat, survive, and reproduce. All these missions require the organism to interact with its environment at some level. The organism must continuously collect information from the environment – about resources, threats, mates – and respond in real time. The right response, be it timing, magnitude, or type, is critical for the organism’s success.

Very often, especially for unicellular organisms like bacteria, the response comes in the form of gene expression. The cell constantly monitors its internal state as well as the external environment. For example, in the presence of a new food source, the cell can turn on genes that allow it to consume the new food source. Similarly, if the cell senses a threat, say a chemical that causes DNA damage, it turns on genes that neutralize the threat and/or undo the damage.

While the big picture for gene expression is relatively easy to grasp, the real-world cases are often much more complicated. The expression of specific genes is often controlled by several competing factors, each of which in turn interacts with several different genes and proteins. This results in a complex web of interactions, often making it very challenging to understand and model the expression of single genes. Moreover, gene expression in itself isn’t sufficient for the cell to mount a response to a change in the environment. The transcribed RNA, in most cases, must be translated into a protein that carries out the function that forms the response. These complexities mean that in practice, it is not that likely to find a cellular process that can be described by only a few interacting parts in a way that is easily understood.

It is for this reason that it was a great pleasure to read the paper by Uphoff, which reports a simple model for the response of Escherichia coli to the DNA modifying methylation agent methyl methane-sulfonate (MMS). Indiscriminate alkylation of DNA has several negative effects, including problems associated with transcription, replication, as well as mutations. Bacteria must therefore react as soon as DNA methylation is detected. E. coli reacts through a protein called Ada, which repairs DNA methylation by transferring the methyl groups on to itself. The beauty of this response is that methylated Ada then activates its own transcription, leading to a positive feedback loop that increases the levels of Ada in the cell in the presence of methylation agents.

Uphoff wrote down a simple model for this process. The cell produces Ada at a small basal rate, which gets methylated in the presence of a methylation agent like MMS and activates the transcription of the Ada gene. Methylated Ada (meAda) can be inactivated (inAda) by proteolysis or other mechanisms and both Ada and meAda get diluted as the cell grows and divides. That’s it. The model can be written down as three coupled differential equations, one each for Ada, meAda, and inAda. Solving these equations for a given amount of MMS (which determines the rate of methylation of Ada to meAda) gives the total amount of Ada in the cell as a function of time, as well as the three individual species.

What’s even more remarkable is how well the model works. A single set of parameters obtained by fitting the steady state Ada response to varying MMS concentrations reproduced the whole family of response curves, including their time dependence. Even more instructive are the stochastic simulations of how single cells respond to MMS exposure. The noisy, seemingly random responses of individual cell in the simulations average out to produce the same clean curve produced by the coupled equations. This, to me, is a great demonstration of the power of differential equations even in cases when they are representing inherently stochastic processes.

The model also allowed Uphoff to rationalize a seemingly puzzling observation. Experiments had shown that even in the presence of high amounts of MMS, a subpopulation of cells did not show any response or had a long delay in the response. The solution to this puzzle might already be evident to many readers. Since the basal level of Ada production is small, many cells have no Ada molecules to initiate a response to DNA methylation. This subpopulation of cells simply must wait for the synthesis of the first Ada molecule, with the waiting times distributed exponentially as in a Poisson process. Uphoff confirmed this by comparing his simulations with the experimental observations of response times delay.

Finally, this work is also a great reminder of bacteria as a powerful model to study biology. Being “simpler” than their eukaryotic relatives, bacteria are a treasure trove of fundamental cellular processes that can be quantified and understood with mathematical precision. This gives us scientists a rare opportunity to truly and deeply understand the building blocks of life.

This post first appeared on the blog of Biophysical Society. This is part 1 of a 3-part series of blogs that I wrote about my favorite Biophysical Journal papers of 2019.

As we accelerate into the new year, it is natural and perhaps also useful to review what happened in the last one. 2019 saw the publication of a number of excellent papers, so I thought I would revisit three of my favorite Biophysical Journal papers from the year. This blog is the first of a three-part series in which I talk about these papers.

Now, you can imagine that this is an inherently subjective exercise and my favorite papers are unlikely to be the same set as anyone else’s. For one, I picked these papers because they contribute to my own field of interest – the biophysics of bacteria. A second factor that ties these papers together is that they all combine elegant experiments with simple theoretical models to learn something new. So, here is the first one.

The mechanics of the bacterial cell envelope

Wong, F., & Amir, A. (2019). Mechanics and Dynamics of Bacterial Cell Lysis. Biophysical journal, 116(12), 2378-2389. link to article

One might erroneously consider prokaryotes to be the primitive cousins of their more advanced counterparts, the eukaryotes. However, this notion will quickly disappear when you look closer at the architecture and the properties of the cell envelope of bacteria. Unlike eukaryotes, which have a single lipid bilayer separating the inside of the cell from the outside, bacteria have a complex multilayered structure which, apart from forming a boundary, provides bacterial cells with their characteristic shapes. The bacterial cell envelope is like the exoskeleton of arthropods (think insects, crustaceans) – it is a rigid structure which gives shape and mechanical integrity to the organism.

It should be of no surprise then that mechanics plays a key role in the function of bacterial cell envelopes. Mechanical defects in the cell envelope can be lethal to bacteria because they lead the cell to bursting open in a process termed lysis. In fact, many antibiotics kill bacteria by targeting the synthesis or maintenance of the cell envelope, resulting in mechanical defects in the envelope. It is therefore of significant practical interest to study the mechanical properties of the bacterial cell envelopes and to develop simple mathematical models for them.

This is exactly what Wong and Amir do in their paper. They set out to model the cell envelope mechanics of the bacterium Escherichia coli. The cell envelope of E. coli consists of three layers - inner and outer membranes consisting largely of phospholipids, and a rigid peptidoglycan wall sandwiched in between the two membranes. Wong and Amir develop a continuum model for the cell envelope by approximating the peptidoglycan cell wall as an elastic cylindrical shell with given material properties and reference size (the length and radius it would have if it didn’t interact with anything else), and the inner and outer membranes as fluid membranes. The equilibrium conformation of such a structure can be calculated by minimizing the total free energy arising from the bending and stretching of each of the layers and the entropy of the solutes inside the cell.

As an experimental test of their modeling approach, Wong and Amir turned to the same antibiotics that I mentioned above. These antibiotics, called β-lactams, cause defects in the peptidoglycan layer, causing the cell membranes to bulge out of cell followed by a slow swelling and an eventual rupture of the bulge. The authors tweaked their model to include bulge formation in it and compared their analytical and computational results with experiments in which they exposed bacteria to β-lactams. For reasonable values of parameters, the model does a good job of capturing the experimental results for both healthy cells as well as cells with bulge due to β-lactam exposure. In addition, the work by Wong and Amir provides evidence that swelling of the bulge takes place due to enlargement of the defect through which the bulge formed in the first place.

The work by Wong and Amir advances our understanding of the mechanical nature of the bacterial cell envelope. Also, it is a demonstration of the power of simple models. Linear approximations are often as good as full-scale numerical solutions. Many would have considered an elastic shell model too simple to represent the bacterial cell envelope with all its intricate composition and spatiotemporal regulation. The results from this work prove otherwise. Remember the old adage, “If it works, it works”.