A synchronised quorum of clocks
Clocks and their synchronisation are undeniably fundamental to our everyday lives. They are the invisible force that helps us structure our day-to-day activities and interactions in a timely and orderly fashion. Whether it’s setting up a meeting with colleagues, scheduling a flight across continents, or managing the steady flow of traffic at busy intersections, synchronised timekeeping ensures smooth operations. Without them, we’d likely descend into a state of disorder and confusion.
In this study, researchers engineered a gene network that can create synchronous oscillations within a growing cell population, and how we can modify parameters to modulate this output. The hope is that this synchronised genetic clock could pave the way for the development of large-scale biosensors and offers a specific model for understanding coordinated behaviour in cell colonies.
Key to the design of this synthetic oscillator are elements inspired from from the quorum sensing machinery found in two bacteria: Vibrio fischeri and Bacillus Thurigensis.
What is Quorum Sensing?
Quorum sensing is the mechanism by which cells “talk” to each other that bacteria use to coordinate group behaviours. This behaviour is dependent on the density of the bacterial population. Above a certain threshold of population density, the cells typically modify their behaviour to engage in a common group activity.
Vibrio fischeri, a species of bioluminescent bacteria, provides a classic example of quorum sensing. This bacterium forms a mutualistic symbiotic relationship with the Hawaiian bobtail squid. In exchange for a protected environment and nutrients, the bacteria provide bioluminescence that helps the squid to camouflage against predators. The bioluminescence is a group behaviour controlled by quorum sensing.
In the case of V. fischeri, the key players in the quorum sensing mechanism are LuxI, LuxR, and a molecule known as an Acyl-homoserine lactone (AHL). LuxI is an enzyme that produces AHL. As the bacterial population increases, so does the concentration of AHL in the environment because each bacterium is producing this molecule. AHL can freely diffuse across bacterial cell membranes, enabling it to move in and out of cells and spread through the bacterial population.
LuxR is a protein that binds to AHL. When the concentration of AHL in the environment is low (which corresponds to a low cell density), LuxR exists in an inactive state. However, as the population density increases, the concentration of AHL also rises. Once a certain threshold level of AHL is reached, it binds to LuxR, activating it.
The AHL-LuxR complex then acts as a transcription factor, binding to DNA and promoting the transcription of certain genes, including those involved in bioluminescence and further production of LuxI and LuxR. This results in a positive feedback loop that rapidly amplifies the response.
Synthetic Oscillator Design
In this design, three genes — luxI (from V. fischeri), aiiA (from B. Thurigensis), and yemGFP — are placed under the control of three identical copies of the luxI promoter. A promoter is a DNA sequence that controls gene transcription. This luxI promoter is therefore positioned in front of the respective genes, initiating the transcription of the following gene.
The luxI gene codes for the LuxI synthase enzyme, which produces acyl-homoserine lactone (AHL). Inside the cell, AHL binds to the constitutively produced LuxR protein, and the resulting LuxR-AHL complex activates transcription from the luxI promoter.
Conversely, AiiA acts as a negative regulator for the promoter. The aiiA gene comes from Bacillus thuringiensis and produces the AiiA enzyme, which catalyses the degradation of AHL. This arrangement of an activator (LuxR-AHL complex) controlling its own repressor (AiiA) is a common motif in both synthetic and natural oscillator designs, and is a key regulatory component in many circadian clock networks.
Finally, the yemGFP gene codes for a variant of green fluorescent protein (GFP). When this protein is produced, it emits green light, making it a useful marker to visually track gene expression.
As explained above, a certain cell density is typically required to generate coordinated behaviour. The cell density of the synchronised oscillator cells, referred to as TDQS1, were manipulated using microfluidic devices of different sizes. Microfluidic devices are systems used to manipulate or control fluids in networks of channels with dimensions from tens to hundreds of micrometres.
The specific device used for monitoring bulk oscillations consists of a nutrient-delivery channel (used to sustain the exponentially-growing colony) that feeds into a main chamber where the cells are growing. Once the cells are introduced, they grow in the chamber until they are pushed into the channel and flow to a waste port. After an initial adjustment period, the TDQS1 cells began to show stable synchronised oscillations that could be easily observed at the colony level.
Here’s how the dynamics of these oscillations work:
As the cells flow into the waste port, they wash AHL along with them. AHL is also internally degraded by the AiiA enzymes. Especially at a small colony size of individual cells producing AHL, this leads to insufficient inducer molecules (AHL) to bind to the LuxR protein and initiate the transcription from the luxI promoters. However, once the cell population reaches a critical density, there’s a ‘burst’ of transcription from the luxI promoters, causing increased levels of LuxI, AiiA and green fluorescent protein (GFP). As AiiA builds up, it starts to break down AHL, and after enough time has passed, the promoters return to their inactivated state. Production of AiiA is then reduced, which allows another round of AHL buildup and another transcriptional burst from the promoters.
At 90 min, the critical density of cells in the chamber is reached, commencing the stable oscillations.
To understand how the effective AHL dissipation rate impacts the period of the oscillations, a series of experiments was conducted at various channel flow rates. At high flow rates, the oscillations stabilise with a mean period of 90 ± 6 minutes and a mean amplitude of 54 ± 6 GFP arbitrary units. However, at a low flow rate, the period drops to 55 ± 6 minutes, and the amplitude decreases to 30 ± 9 GFP arbitrary units. Interestingly, the waveforms vary in shape depending on the rate: the slower oscillator drops near zero after activation, while the faster oscillator decays to levels above the original baseline.
Graph illustrating how amplitude and period vary with flow rate. The magenta line represents low-flow rate while the dark blue line represents a high flow-rate.
When the flow rate was gradually increased from 180 to 296 mm/min, an increase in oscillatory period from 52 to 90 minutes was observed. It was also found that the amplitude of the oscillations is proportional to their period, which aligns with observations from a previously reported intracellular oscillator showcasing ‘degrade-and-fire’ oscillations. In such a system, a component is degraded (broken down) and then suddenly fires (activates), causing an oscillation.
In the context of the experiment, the term “amplitude” refers to the “size” or “intensity” of the cycle — essentially, how much the fluorescent protein (GFP) levels go up during the ‘fire’ phase. The “period” is the length of the complete cycle — how long it takes from one ‘fire’ phase to the next. When the researchers say that the amplitude of the oscillations is proportional to their period, they’re observing that when the cycles take longer (longer periods), they also have larger ‘fire’ phases (higher amplitudes). In other words, the longer it takes for a cycle to complete, the more intense or “bigger” that cycle is.
So, by saying that their observations align with a “degrade-and-fire” oscillator, they’re essentially saying that they see a similar pattern — the longer it takes for a cycle to complete, the more intense that cycle is, just as you’d expect in a system where something is being degraded and then suddenly produced or activated.
Spatio-temporal dynamics
During these experiments at low flow rates, the researchers noticed that the glowing (fluorescent) signal was able to move across the chamber where the colony was growing, which was 100 micrometres wide. A micrometre is really, really tiny — about 1000 times smaller than a millimetre! To get a better look at this interesting movement, the scientists decided to make their trapping chamber bigger, expanding it to 2 millimetres.
As they conducted the experiment, they noticed small colonies of bacteria starting to grow and eventually combining to form one big layer that covered the whole chamber. At around the 100-minute mark, something exciting happened: there was a sudden burst of fluorescence or glowing in one area, and this glowing effect spread out to the left and right sides over time. Interestingly, a second burst of glowing happened near where the first one did, and it also spread to the left and right.
The scientists wanted to see how this glowing changed over time and across the chamber, so they plotted the intensity of the fluorescence against time and distance. Imagine this like a heatmap showing where and when the bacteria were glowing the most. Similarly, for the first 100 minutes, nothing really happened, and the plot was blue, indicating no fluorescence or glowing. But at the 100-minute mark, there was a burst of glowing in one area (around 1,350 micrometres along the chamber), shown as an orange spot on the plot.
The plot also showed the spread of this glowing effect. Waves of fluorescence spread out to the left and right of the original burst, appearing as a green-yellow line that was concave (bent inwards). Interestingly, the leftward wave was moving a bit slower than the rightward wave. There were also some really cool ‘annihilation events’ where the leftward and rightward waves would meet and cancel each other out, otherwise known as disruptive interference.
When the researchers looked at the movies they made of the experiment, they could see some interesting things happening. These events were a bit harder to see when they plotted the data on their charts. For example, as the glow started to spread from where it first burst out, it eventually formed a “packet” of glowing cells that moved to the left at a certain speed. This speed initially was 12.5 micrometres per minute but slowed down to 8.5 micrometres per minute when it got towards the end of the trap where there weren’t as many cells.
When they looked at how many cells were in different parts of the chamber over time, they saw that the centre of the colony was where the most cells were, and there were fewer cells towards the left edge. Because of this difference, the critical number of cells and AHL (the molecule that makes the cells glow) needed for the glow to spread reached different areas at different times.
The researchers also ran some other experiments in a larger chamber. In this chamber, the colony of cells started to grow outwards in all directions over the course of about 3 hours, but didn’t glow until it was about 100 millimetres across. At this size, a big burst of glowing started from the centre of the colony, and a particularly bright band of cells showed up near the centre. These cells, which weren’t at the very centre or on the outer edge but somewhere in between, had the biggest and longest-lasting glow.
As the colony of cells grew even bigger, another burst of glowing happened, again at this intermediate cell density. The edge of the growing colony kept glowing in this rhythmic way, but inside the colony, the glow was weak and didn’t last long. This suggests that this rhythmic glowing behaviour is stronger and lasts longer at the edge of the growing colony, but not as much inside the colony.
Quantitative Modelling
To understand the behaviour of the system, the researchers built a computational model based on ordinary differential equations (ODE) that describe how the protein and AHL concentrations change over time. The model takes into account the delay between when these substances are produced and when they become active, as well as the interaction between different cells through the shared environment of AHL molecules.
These four equations are a set of partial differential equations that describe the temporal evolution of different components of the system: the AHL (A), the protein LuxI (I), the intracellular AHL concentration (Hi), and the extracellular AHL concentration (He).
Equation 1 and 2 (∂A/∂t and ∂I/∂t) are for the change in AHL and LuxI protein levels over time, respectively. Both equations consist of two terms: a production term and a degradation term.
The production term, Ca[1 − (d/d0)⁴] P(α, τ), represents the production of AHL and LuxI which depends on the cell density (d) and a Hill function (P(α, τ)). The Hill function describes the delayed production of proteins, taking into account the past concentration of internal AHL (Hτ(t) = Hi(t − τ)).
The delay here refers to the time it takes for these proteins to be produced in response to a particular concentration of AHL within the cells. In this particular Hill function, the subscript τ is a time delay, indicating that the function describes the concentration of AHL at an earlier time (t — τ). This reflects the reality of biological processes, where there’s often a delay between a signal (like a certain concentration of a molecule) and the response (like the production of a protein). Here, it means that the production of LuxI and AHL proteins at a certain time (t) is affected by the concentration of AHL inside the cell at a previous time (t — τ). The exponent 2 in the function signifies the Hill coefficient, which represents the level of cooperativity in the system i.e. how effectively AHL promotes protein production.
The parameters δ, α, and k1 are constants that influence the sensitivity and dynamics of the system’s response to changes in AHL concentration. The term (δ + αH²_τ) in the numerator influences the maximum response level, while k1 in the denominator represents the AHL concentration needed to achieve half of this maximum response.
The [1 − (d/d0)⁴] factor is a damping term that accounts for the slowing down of protein synthesis at high cell density due to lower nutrient supply and high waste concentration.
The degradation term, (γ_A A)/(1 + f(A + I)) represents the degradation of AHL and LuxI proteins, modelled using Michaelis-Menten kinetics. This term describes the rate at which the AHL and LuxI proteins are broken down by enzymes within the cell. In Michaelis-Menten kinetics, the rate of an enzymatic reaction (in this case, protein degradation) depends on the concentration of the substance being broken down (here, AHL and LuxI). The γ_A term is the maximum rate of this degradation process, while the (A + I) in the denominator indicates that the rate of degradation depends on the total concentration of AHL and LuxI. The factor f modulates this dependence.
Equation 3 (∂Hi/∂t) describes the change in the internal AHL concentration over time. This equation contains three terms: a production term, a degradation term, and a diffusion term. The production term, bI/(1 + kI), accounts for the production of AHL in the presence of LuxI. The degradation term, (γ_H AH_i)/(1 + gA), represents the degradation of AHL. The diffusion term, D(He − Hi), describes the diffusion of AHL across the cell membrane.
Equation 4 (∂He/∂t) describes the change in the extracellular AHL concentration over time. This is crucial because AHL’s concentration outside the cells is what allows it to act as a signal for quorum sensing, coordinating behaviour among the bacterial population. The first term, − d /(1 − d )D(He − Hi), represents the diffusion of AHL across the cell membrane, with the cell density (d) affecting the decay rate. The second term, − µHe, models the dilution of external AHL by external fluid flow. The last term, D_1(∂² He)/(∂x²), describes the spatial diffusion of AHL in the external environment.
The researchers have made the simplifying assumption that LuxR is constantly produced at a constant level and hence, no equation is included for LuxR. This is based on previous work suggesting that LuxR levels are mainly controlled by the LuxR-AHL complex, but the researchers did not find this necessary to capture the essential behaviour of the synchronised oscillator.
The model predictions matched the experimental data quite well. It showed that the period (time between bursts) and amplitude (size of bursts) of the oscillations increase with increasing AHL flow rate, just like in the experiments. It also helped the researchers understand what happens in each oscillation cycle. At the beginning of each cycle, AiiA and LuxI proteins and AHL are produced but remain inactive for a while. After this delay, they all become active at once in a big burst. This burst then triggers the degradation (breakdown) of AiiA and LuxI proteins and AHL, bringing the system back down and setting the stage for the next cycle.
The researchers modelled the collective behaviour of these ‘biological clocks’ by using a mathematical model that could account for the interaction between these clocks via the extracellular AHL. Each of these cells were each represented by the set of mathematical equations described above.
This model took into account the spatially uneven field of extracellular AHL, which is influenced by diffusion (movement of AHL from an area of high concentration to low concentration) across the cell membrane and its dilution in the environment. They introduced a small disturbance in AHL levels in the middle of the model. This initiated waves of changes in LuxI protein concentrations, and the simulation results were in excellent agreement with the experimental data.
The speed at which these LuxI waves propagated was found to depend on the diffusion rate of AHL, and the simulated speed matched well with experimental data for the values used.They also found that cell density, the number of cells in a given space, significantly influenced wave propagation.
When modelling a three-dimensional colony, they observed that the high cell density at the centre of the colony suppressed oscillations, meaning the biological clocks were not ticking synchronously. Instead, the changes in LuxI only occurred at the periphery, the outer edge of the growing colony. This was also in line with their experimental observations.
Emergence
In this system, the synchronised oscillations of these biological clocks is a feature that arises due to the circuit design of this cell colony. Instead of being a freak occurrence, it can be explained by how the cells and molecules interact.
A molecule called AHL plays a key role in this. It has two jobs — it activates the genes required for the ticking inside each cell and also helps cells ‘talk’ to each other.
However, as the colony of cells unfettered, AHL over accumulates, leading to a situation where it’s everywhere and constantly activating the genes, making it difficult for the cells to establish a coordinated rhythm or ‘ticking’. So, the researchers used open-flow microfluidic devices that allowed AHL flow out of the colony.
At low cell densities, the ticking doesn’t occur because AHL diffuses across the cell membrane and flows out into the waste port. But at an ideal cell density, the AHL being produced by each cell compensates for the AHL loss, and so the genes can get activated to produce the colony-wide ticking seemingly out of nowhere.
To further verify their claims, the researchers also wanted to know how individual cells behave when they can’t communicate with each other. While they couldn’t perform this experiment in the lab, they used computer simulations to modify the AHL such that it was unable to move across the cell membrane.
What they found was that, in this situation, each cell ticks on its own, irrespective of cell density, because they’re not influenced by the environment or other cells. This shows that the movement of AHL between cells is what allows all these individual tickings to synchronise when cell concentrations are precisely balanced.
Usefulness
This discovery provides a mechanism to synchronise the biological clocks in a cell colony, much like Huygens did for pendulum clocks centuries ago, offering a way to manage the inherent randomness found in synthetic gene networks. By using this synchronisation approach, researchers can design more sensitive and robust cellular networks, opening new possibilities in creating distributed biological sensors or synthetic systems that can coordinate complex processes across a group of cells.
Sources:
1. https://www.nature.com/articles/nature08753
