Cells must make decisions in stochastic environments using stochastic biochemistry. The aim of our research is to uncover the information-processing strategies that allow cells to decide reliably.
Cells infer the current and potentially future state of the extracellular environment from local signals: those sensed at the cell membrane and intracellularly. Based on this inference, on the expected costs and benefits of each potential response, and on the possible presence of other organisms, be they either competitors or cooperators, a decision is made.
Our focus is nutrient-sensing by budding yeast. Extracellular nutrients in yeast can act analogously to hormones in mammalian cells, and we are interested in how cells determine how fast they should grow.
We use a combination of both experiment and theory: microfluidics to generate dynamically changing environments, fluorescence microscopy and machine learning to quantitatively monitor the responses of individual cells, and techniques from stochastic processes and non-linear dynamics to develop mathematical models of cellular information-processing.
Factors influencing cellular decision-making. A cell senses signals generated by a change in the environment and must decide an appropriate response (Perkins & Swain (2009)).
When things change, life responds. Yet for that response to be useful, an organism must recognise and remember, even if only briefly, the nature of the change. Moving from the sun into the shade, we detect the lower levels of light and convert this observation into neural signals and then into dilated irises. But how do single-celled organisms, which lack a nervous system, deal with change in their environment?
Using fluorescent proteins from jellyfish to follow molecules inside cells, we show that although from the outside single cells of baker's yeast appear to sit passively when their source of food disappears, there are dramatic intracellular changes. Transcription factors, the protein conductors of gene expression, zip into or out of the cell's nucleus, where the genome is stored. The detection of a change outside by proteins at the cell's surface becomes a sudden swirl of motion inside: some transcription factors exit the nucleus; others enter; others still pulse in and out.
It is this motion that allows the cells to remember an environmental shift. Rather than the pulses of electrical activity used by our brain to represent the external world, yeast, at least, use the movement of potentially hundreds of proteins. By adapting the mathematics developed to improve telecommunications, we can quantify how easy it is to figure out the nature of the new environment from these intracellular movements alone. We show that this task becomes less difficult if we observe how a protein moves rather than only where in the cell it ends up. In this sense, we demonstrate that yeast encode information about their external world in the movements of intracellular proteins.
The movement of the transcription factor, Sfp1, can encode that glucose is lost from the extracellular environment. Top: When the external concentration of glucose suddenly falls, Sfp1 moves out of the nucleus on average (black line), but individual cells behave quite differently from this mean response. Colours show the fraction of Spf1 in the nucleus for examples of single cells, and the gray shading is the interquartile range for all cells. Bottom: We estimate the mutual information, which here measures how different the typical movement of Sfp1 is before and after the shift in glucose concentration (the maximum mutual information is 1 bit).
We develop a novel modelling approach to predict how microbial communities might adapt in response to changing environments with the aim of understanding how microbial communities emerge, establish, and diversify.
Communities of microbes grow on mixtures of different foods, and there is often intense competition for each type. Microbes in natural communities, for example in our intestines, do not try to consume all the available nutrients but, instead, each species specializes to only a few.
This metabolic specialization is driven by cellular trade-offs, where importing and metabolizing one resource reduces a microbe's ability to import and metabolize another. Random genetic mutations can affect how these trade-offs are balanced, and communities evolve with a complex interdependence between species. Consequently, we do not understand how, and under what conditions, this evolutionary process leads to communities that are stable and long-lived.
Our mathematical model integrates aspects of intracellular constraints, ecological dynamics, and random mutational processes to describe the evolution of microbial communities. Using the model, we could re-construct all evolutionary histories that lead to the same stable community and discovered that properties of these evolutionary trajectories, but not properties of the environment, can be used to predict the type of stable community that ultimately forms. Using evolutionary trajectories, we can therefore forecast whether a community will, for example, eventually collapse or diversify.
The evolutionary dynamics of a microbial community shown as a network of evolutionary trajectories. Nodes represent different types of communities (squares show stable communities that are resistant to mutation; circles show transitory ones) and are coloured according to how that community exploits the environment. Arrows represent eco-evolutionary transitions, where a mutant population arises and out-competes a resident population. Two sample trajectories are indicated in red and blue.
In times of danger, popular culture tells us to rely on instinct. Evolutionarily honed reflexes will see us through. Heat burns, and we're all familiar with the automatic response of jerking our hand away from an object that is too hot. Yet this fast response is too quick for us to know if we can pick up, say, a cup of coffee. Speed undermines accuracy: we know that the cup is hot but not how hot. We must hold a finger against the cup to accurately judge its temperature.
Although picking up a cup of coffee is rarely a life-and-death situation, microbes can respond analogously when in peril. We consider single cells of baker's yeast suddenly plunged into a thick syrup (imagine falling into an overly ripe grape). In response water rushes out of the cells (the opposite of the wrinkling of skin caused by a long bath), and we can see individual cells collapse in seconds. To grow again, they must recover that lost volume.
This extracellular stress is detected by two cellular pathways or tripwires comprising chains of proteins, where the shrinking of the cell generates changes in shape of proteins at the cell surface which in turn generate changes in shape of intracellular proteins. These new conformations are further recognised by other proteins, which too alter their own shape to pass information down the chain. Why two sensing pathways have evolved rather than one is not understood.
By watching the responses of single cells and using genetic mutants, we showed that the two pathways allow the cells to be both fast and accurate. One pathway acts like a reflex-like response. It is quick, ready for emergencies, but, like a jerked back finger, does not report well on the severity of the stress. For cells, this inaccuracy is a problem. To thrive in syrupy environments energy that could be spent on growth is instead diverted to make glycerol, and so draw water back inside cells. Making too little glycerol compromises growth by preventing a full recovery of the volume, but making too much is wasteful with the excess glycerol leaking from the cell. Here the second pathway steps up. This pathway is slow but by forsaking speed it senses accurately, like the firmly held out finger, and allows the cell to match intracellular glycerol with levels of extracellular stress.
The two pathways allow a division of labour—one specialising in speed and the other specialising in accuracy—that enhances survival. We can compare the behaviour of cells with the behaviour of mutants that have just one of the sensing pathways. Cells with only the reflex-like pathway survive best in emergency-like situations where stress is sudden and severe. Cells with only the slow pathway survive best in gradually increasing, fluctuating stress where accurate responses eventually pay off. The natural cells by having both pathways have the benefits of both short-term speed and long-term accuracy and survive better than the mutants in any environment.
Following single cells of budding yeast during the application of high osmotic stress (the addition of a syrup of sorbitol), we can measure the accuracy of each cell's stress response. Top: Imaging using ALCATRAS with a fluorescently tagged Hog1 protein (the protein activated by both pathways that sense osmotic stress and shown in green), we can see Hog1 move into the nucleus when the stress is applied (become more confined) and then back into the cytoplasm as cells adapt to the stress. Bottom: We quantify accuracy by the correlation between the decrease in cellular volume (the actual stress) and the increase in nuclear localisation of Hog1 (the perceived stress). Time-series from single cells are shown as light lines; the mean is shown as a dark line.