Infant respiratory distress syndrome (IRDS) is a tragic health condition when premature babies cannot breathe by themselves at birth. The cause of the condition is that soap-like molecules that coat the surface of our lungs and allow us to breathe, called lung surfactant, have not had enough time to mature during pregnancy. The purpose of lung surfactant is to reduce the surface tension of the fluid in our lungs, which in turn reduces the energy we need to expend when we breathe. Without enough of the surfactant produced during pregnancy, babies who suffer from IRDS do not even have the strength they need to take their first breath. Lung surfactant is a complex mixture of biological molecules, and the key component missing in premature babies is a protein. It has a special function that allows the rest of the surfactant coating the lung fluid to gather in small pockets as the surface area is small when we breathe out, enabling them to reorganise very quickly and keep the fluid coated as the surface area increases when we breathe in. In the absence of the protein, the surfactant molecules struggle to keep the fluid coated throughout breathing cycles, the surface tension goes up, and the lungs collapse. Unfortunately, it is too expensive and difficult for drug companies to make this protein, and scientists have not yet managed to design replacement molecules that have the same function. Current medicines are crude extracts from animal lungs with no design efforts having been made to make them well suited for use in humans. These treatments are good in that survival rates are high, but a serious bowel condition can be a severe side effect, and the medicines have such poor shelf life they are not widely available in developing countries. Further efforts are clearly needed to develop new and improved treatments. This research project builds on two recent discoveries I have made whilst working as a scientist studying the behaviour of biological films on the surface of water. I reflect light off the films, and just like we can use our eyes to distinguish different objects when we see light that has reflected off them, the laser instruments in my lab work in the same way except that the information is about single layers of molecules. The first discovery was that when I squeezed certain films to reduce the surface area, like when we breathe out, I could generate these pockets of material if the films contained certain types of tiny particles called nanoparticles. The second discovery was that when I made films made of lung surfactant itself, I could use my laser reflection techniques to see the depth and diameter of these pockets formed at very low surface tension for the first time. These breakthroughs have created an exciting opportunity to use reflection techniques to work out the important properties of nanoparticles that can help form the vital pockets of material in lung surfactant. First, the project will consider effects of the size, charge, affinity (oil vs water) and degree of swelling of the nanoparticles in their ability to recreate the performance of healthy lung surfactant in the absence of the protein. Second, the most promising nanoparticles will be dressed up in a cloak of relatively cheap portions of the original protein to see if this could be an even better way to reach optimal performance. The overarching goal of the project is to establish knowledge on the ability of nanoparticles to help recreate the performance of healthy lungs with a view to the future design of new medicines to treat IRDS. The ambition of developing these new medicines is that they could result in fewer side effects and/or have an improvement in shelf-life, which in turn can lead to improvements in health here in the UK or in survival rates in developing countries. The work will also provide a platform to establish the UK as a scientific and medical leader in the treatment of IRDS on which it is currently missing presence.

Understanding the behaviour of materials on the atomic scale is fundamental to modern science and technology, because most properties and phenomena are ultimately controlled by the details of atomistic processes. During the past decades computer simulations on the atomistic level became a powerful tool in modern chemistry, augmenting experiments, by making initial predictions, aiding studies under extreme conditions or providing an atomistic insight into mechanisms. For example, predicting the state of matter in planetary interiors or in nuclear reactors where measurements are impossible or dangerous, or pinpointing stable structures and properties efficiently, such as for trial drugs or alloys, reduces the amount of expensive and time-consuming experiments. One of the major fields where computer simulations became widely used is material science, studying phase transitions and phase diagrams. A phase diagram shows the properties of a given material at specific conditions, for example, tells whether a substance is found as gas, liquid or solid at a particular temperature and pressure, or at a particular composition in case of a multicomponent system. It also shows when these phases transform into each other, corresponding to phase transitions. It is of great technological importance to have a complete picture of the phase diagram, and computational tools are widely employed to enable this. Nonetheless, the main difficulty in using computer simulations is that the number of possible ways atoms can be arranged in space is enormous, and no technique is capable of considering all of them, hence we need importance sampling. A plethora of computational techniques exist, however, these are usually problem specific and rely on prior knowledge of the atomic structure, limiting their predictive power. I have been developing a novel computational technique, nested sampling (NS), which addresses these challenges from a new perspective: it automatically generates all relevant atomic configurations (a small subset of all possible variations), and determines their relative stability, offering complete thermodynamic information without any advance knowledge of the material, except its composition. I have already shown how NS can be used to calculate the phase diagram of metals and alloys, in an automated way, and my aim is to extend its applicability to a broader range of problems: augment crystal structure prediction studies (highly relevant in developing pharmaceuticals), a novel application in calculating spectroscopic properties (for accurate measurements of composition in climate science and astrochemistry), and develop strategies to determine and improve the reliability of potential models (the mathematical formulation of atomic interactions) benefiting computational research in a wide context.

A group of ants in tropical America, known as the attines, evolved agriculture 50-60 million years ago. These ants collect plant material and take it back to their nests, where they chew it up and feed it to a special fungus that is only able to live in attine ant nests. The most highly evolved attines are known as leafcutters because they actively cut leaves from high up in the rainforest canopy and carry them back as food for their fungus. In return for housing and food, the fungus produces fat- and sugar-rich structures, called gongylidia that the ants harvest as food. Scientists call this co-dependence a mutualism because the ants and the fungus mutually benefit each other. The ants protect their valuable fungal gardens by weeding out unwanted microbes (fungi and bacteria), which, if not controlled, would eventually consume the garden. The ants also apply antibiotics to kill the foreign microbes. They get the antibiotics from another mutualist, a special set of filamentous bacteria, called actinomycetes, which are famous (amongst biologists) for making many kinds of antibiotics. The actinomycetes are mutualists with the ant and the fungus garden, because the bacteria fight disease, and in return, live on the ant bodies, where specialised glands appear to feed the bacteria. With previous NERC funding we have shown that different actinomycete bacteria live on the ants and provide a mixture of antibiotics, probably to slow down the evolution of antibiotic resistance in the diseases that invade the fungus gardens. Biologists call the bacterial communities that live on a host organism its microbiome. In the attine microbiome, one group of actinomycetes, known as Pseudonocardia, have been handed down over generations (vertically transmitted), and have adapted to their ant hosts. Other actinomycetes, mostly in a group called Streptomyces, appear to be acquired anew from the soil in each generation (horizontal transmission). This is surprising, because the soil is full of bacteria, most of which are not Streptomyces, but somehow the ant is able to selectively take up useful, antibiotic-producing bacteria from their environment, and not harmful or useless bacteria. How does the ant make the right Partner Choice? We have shown that to invade an ant covered in Pseudonocardia another bacterial strain must make antibiotics so it can fight the Pseudonocardia for some space and it must also be resistant to antibiotics made by the Pseudonocardia so it doesn't get killed. We call this SCREENING and it results in a microbiome dominated by antibiotic-producing and -resistant bacteria, which, of course, is the desired outcome for the ant because it gets a mixture of antibiotics to use. In this new project we want to understand this system at an even deeper level, taking apart both the Pseudonocardia mutualists to understand the antibiotics they produce and how they influence 'Partner Choice' and to test whether the ants really do provide food to the bacteria and whether this is private to Pseudonocardia or public, that is, available to all bacteria. We also plan experiments to find out exactly which bacteria are present on these leafcutter ant cuticles and exactly where they are on individual ants. In this way we will build the first 3D microbiome maps of an animal host and overlay it with maps of the most abundantly produced antibiotics. The advantage of using attine ants to study and model these microbiomes is that they are easy to keep and their microbiome is on the outside, which means we can do experiments with it. This gives us hope that we can work out general principles governing how to create and manage protective microbiomes in free-living marine and terrestrial systems, including all land plants.

Combinatorics is a branch of mathematics studying finite structures. The generality of these questions suggests wide applicability of combinatorics in other areas of pure mathematics (most notably in algebra, number theory, probability, and topology), as well as in real-world applications (discrete optimization, computer science).One of the oldest and most central parts of combinatorics are graph theory and enumerative combinatorics. Graph theory models networks (such as road connections, or internet users), and enumerative combinatorics concerns studying counting questions of various kinds.Extremal graph theory is a broad part of graph theory which investigates interplay between various graph parameters. One of the main tools in Extremal graph theory is the so-called Szemeredi Regularity Lemma. This tool (developed in the 70's) has become one of the corner-stones of modern mathematics. Recently, using the insights gained from the Regularity Lemma, Lovasz and Szegedy initiated study of graph limits.The proposed research project addresses major open questions in extremal graph theory and aims contribute to general theories the Regularity Lemma, graph limits, and by developing novel tools which will be used in enumerative combinatorics.

The main focus of this project is to experimentally investigate and mathematically describe emergent properties of a large cellular system. A large cellular population is a complex dynamical system far from equilibrium, where macro-dynamics are driven by interactions and heterogeneity at the systems micro- or cell-level. Understanding exactly how microstate properties instigate and perpetuate emergent macroscopic phenomena is one of the fundamental challenges facing contemporary biology today. Quantifying such symbiotic relationships is at the heart of many scientific research endeavours. This broad scientific area covers an equally matched myriad of length scales, ranging from spontaneous symmetry breaking at the sub-atomic level through to galactic cluster formation at the cosmic scale. For the most part, formations of emergent configurations in these systems are intrinsically linked to non-linear interactions between the individual components that together constitute the complex system. It has been established that many of the confounding features of such systems can be adequately described through the application of statistical mechanics. The mathematical methodology can encapsulate and link macroscopic descriptions of the system to that of the microstate, allowing emergent ensemble behaviours to be quantified. Large cellular populations fulfil all necessary criteria to be considered a complex system (i.e. the cell being the systems microstate); constituent cells are vast number; cells are heterogeneous in physical, biological function; cell-cell and cell-environment interactions are inherently nonlinear. Adherence of the microstates to these criteria promotes the formation of emergent behaviour at the cellular population level; significant examples include embryo development, tissue regeneration during wound healing and the proliferation of metastatic diseases. However, application of statistical mechanics to describe and predict large-scale cellular systems have been hampered due to the fact that (i) such systems are in a state of non-equilibrium exhibiting vast heterogeneity across constituent microstates, simply averaging over ensemble variability results in distorted macroscopic system view and (ii) the ability to identify, track and quantify significant numbers of individuals within a cellular population to assess and account for microstate variability has been hindered by the availability of high-throughput microscopy platforms. Together these issues have obstructed application of statistical mechanics methods to elucidate upon the formation, function and stability of ensemble behaviour of a complex cellular system. The work presented as part of this EPSRC first grant application will address this current shortfall in scientific application and understanding. Recent advances in high-throughput microscopy present an opportunity to collate detailed information of microstate behaviour and allow development of mathematical models to describe the system. This interdisciplinary proposal seeks to unify contemporary biology, advanced imaging and statistical mathematics in order to measure and track the evolving interactions, dynamics and fate of >100,000 individual cells over extended periods. This databank will provide invaluable information, detailing microstate quantities such as morphology, biological function and spatial correlation and will further allow realisation of stochastic and master equation descriptions of the large-scale cellular system in question. Furthermore, this will ensure system variability is incorporated within models at the outset, providing robust linkage between the systems micro- to macro-levels and allowing sources of emergent phenomena to be more accurately described and predicted.