Antibody-antigen complex modelling is an important step in computational workflows for therapeutic antibody design. While experimentally determined structures of both antibody and the cognate antigen are often not available, recent advances in machine learning-driven protein modelling have enabled accurate prediction of both antibody and antigen structures. Here, we analyse the ability of protein-protein docking tools to use machine learning generated input structures for information-driven docking. We find that HADDOCK can generate accurate models of antibodyantigen complexes using an ensemble of antibody structures generated by machine learning tools and AlphaFold2 predicted antigen structures. Targeted docking using knowledge of the complementary determining regions on the antibody and some information about the targeted epitope allows the generation of high quality models of the complex with reduced sampling, resulting in a computationally cheap protocol that outperforms the ZDOCK baseline. The data set used to benchmark the docking protocols in this study is available at github.com/haddocking/ai-antibodies. The docking models will be deposited at data.sbgrid.org/labs/32/ upon acceptance.

Developing therapeutic antibodies is a challenging endeavour, often requiring large-scale screening to produce initial binders, that still often require optimisation for developability. We present a computational pipeline for the discovery and design of therapeutic antibody candidates, which incorporates physics- and AI-based methods for the generation, assessment, and validation of developable candidate antibodies against diverse epitopes, via efficient few-shot experimental screens. We demonstrate that these orthogonal methods can lead to promising designs. We evaluated our approach by experimentally testing a small number of candidates against multiple SARS-CoV-2 variants in three different tasks: (i) traversing sequence landscapes of binders, we identify highly sequence dissimilar antibodies that retain binding to the Wuhan strain, (ii) rescuing binding from escape mutations, we show up to 54% of designs gain binding affinity to a new subvariant and (iii) improving developability characteristics of antibodies while retaining binding properties. These results together demonstrate an end-to-end antibody design pipeline with applicability across a wide range of antibody design tasks. We experimentally characterised binding against different antigen targets, developability profiles, and cryo-EM structures of designed antibodies. Our work demonstrates how combined AI and physics computational methods improve productivity and viability of antibody designs. ### Competing Interest Statement F.D., C.S., A.K., D.C., M.B., D.N., N.W., H.K., C.M., D.E., R.G., D.D., P.T., W.B., J.D., D.P., S.S. and C.D. are or have previously been employees of Exscientia. I.D. is an employee of Thermo Fisher Scientific.

We introduce IgDiff, an antibody variable domain diffusion model based on a general protein backbone diffusion framework, which was extended to handle multiple chains. Assessing the designability and novelty of the structures generated with our model, we find that IgDiff produces highly designable antibodies that can contain novel binding regions. The backbone dihedral angles of sampled structures show good agreement with a reference antibody distribution. We verify these designed antibodies experimentally and find that all express with high yield. Finally, we compare our model with a state-of-the-art generative backbone diffusion model on a range of antibody design tasks, such as the design of the complementarity determining regions or the pairing of a light chain to an existing heavy chain, and show improved properties and designability.

Accurate prediction of antibody structure is a central task in the design and development of monoclonal antibodies, notably to understand both their developability and their binding properties. In this article, we introduce ABodyBuilder3, an improved and scalable antibody structure prediction model based on ImmuneBuilder. We achieve a new state-of-the-art accuracy in the modelling of CDR loops by leveraging language model embeddings, and show how predicted structures can be further improved through careful relaxation strategies. Finally, we incorporate a predicted Local Distance Difference Test into the model output to allow for a more accurate estimation of uncertainties.

We consider the problem of antibody sequence design given 3D structural information. Building on previous work, we propose a fine-tuned inverse folding model that is specifically optimised for antibody structures and outperforms generic protein models on sequence recovery and structure robustness when applied on antibodies, with notable improvement on the hypervariable CDR-H3 loop. We study the canonical conformations of complementarity-determining regions and find improved encoding of these loops into known clusters. Finally, we consider the applications of our model to drug discovery and binder design and evaluate the quality of proposed sequences using physics-based methods.

We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under infinitesimal symmetry transformations on the input variables. As symmetry transformations are generated post-training, the methodology does not rely on sampling of the full representation space or binning of the dataset, and the possibility of false identification is minimised. We demonstrate our method in the SU(3)-symmetric (non-) linear $\Sigma$ model.

We simulate the decay of isolated, spherically symmetric droplets in a cosmological phase transition. It has long been posited that such heated droplets of the metastable state could form, and they have recently been observed in 3D multibubble simulations. In those simulations, the droplets were associated with a reduction in the wall velocity and a decrease in the kinetic energy of the fluid, with a consequent suppression in the gravitational wave power spectrum. In the present work, we track the wall speed and kinetic energy production in isolated droplets and compare them to those found in multibubble collisions. The late-time wall velocities that we observe match those of the 3D simulations, though we find that the spherical simulations are a poor predictor of the kinetic energy production. This implies that spherically symmetric simulations could be used to refine baryogenesis predictions due to the formation of droplets, but not to estimate any accompanying suppression of the gravitational wave signal.

We study the stochastic gravitational wave background (SGWB) produced by freely decaying vortical turbulence in the early Universe. We thoroughly investigate the time correlation of the velocity field, and hence of the anisotropic stresses producing the gravitational waves. With hydrodynamical simulations, we show that the unequal time correlation function (UETC) of the Fourier components of the velocity field is Gaussian in the time difference, as predicted by the “sweeping” decorrelation model. We introduce a decorrelation model that can be extended to wavelengths around the integral scale of the flow. Supplemented with the evolution laws of the kinetic energy and of the integral scale, this provides a new model UETC of the turbulent velocity field consistent with the simulations. We discuss the UETC as a positive definite kernel, and propose to use the Gibbs kernel for the velocity UETC as a natural way to ensure positive definiteness of the SGWB. The SGWB is given by a 4-dimensional integration of the resulting anisotropic stress UETC with the gravitational wave Green's function. We perform this integration using a Monte Carlo algorithm based on importance sampling, and find that the result matches that of the simulations. Furthermore, the SGWB obtained from the numerical integration and from the simulations show close agreement with a model in which the source is constant in time and abruptly turns off after a few eddy turnover times. Based on this assumption, we provide an approximate analytical form for the SGWB spectrum and its scaling with the initial kinetic energy and integral scale. Finally, we use our model and numerical integration algorithm to show that including an initial growth phase for the turbulent flow heavily influences the spectral shape of the SGWB. This highlights the importance of a complete understanding of the turbulence generation mechanism.

Upcoming space based gravitational wave observatories like the Laser Interferometer Space Antenna (LISA) will provide a new window into early universe physics. While the results from ground-based detectors have largely concerned astrophysical objects such as black holes and neutron stars, future space-based gravitational wave observatories will be able to observe far earlier times in the history of the universe than are directly accessible through the electromagnetic spectrum. LISA in particular will be sensitive to the detection of a stochastic gravitational wave background from a first-order cosmological phase transition around the electroweak scale. In cosmological phase transitions, an e↵ective scalar field passes from a false vacuum state to the true vacuum. If the transition is first-order, this occurs through the nucleation of bubbles of the true vacuum. These bubbles expand and, upon collision, produce gravitational waves. The focus of this thesis is to better characterise the gravitational wave signal from a first-order phase transition using numerical simulations. Within this thesis, I study both vacuum and thermal first-order phase transitions. In a vacuum phase transition, bubble walls accelerate to ultra-relativistic speeds. In this case, the gradients in the scalar field during bubble collisions form the dominant source of gravitational waves. I perform full 3D classical lattice field theory simulations, compute the gravitational wave signature and compare it to previously used techniques such as the envelope approximation. I further extend this work to investigate whether the shape of the e↵ective potential of the scalar field can a↵ect the final gravitational wave signal. In thermal phase transitions, the bubbles of the true vacuum nucleate in the presence of a relativistic plasma. As the bubbles expand, friction between the outward propagating bubble wall and the plasma causes shells of fluid to form around the bubble wall. The dominant source of gravitational waves from thermal transitions is shear-stress that remains in the fluid after the transition completes. While simulations of weak and intermediate strength phase transitions have been conducted, I perform the first 3D simulations of a strongly first-order phase transition and provide results for the generation of vorticity, formation of heated droplets, and the e↵ect that this has on the gravitational wave signal.

Astroparticle physics is undergoing a profound transformation, due to a series of extraordinary new results, such as the discovery of high-energy cosmic neutrinos with IceCube, the direct detection of gravitational waves with LIGO and Virgo, and many others. This white paper is the result of a collaborative effort that involved hundreds of theoretical astroparticle physicists and cosmologists, under the coordination of the European Consortium for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics community, it explores upcoming theoretical opportunities and challenges for our field of research, with particular emphasis on the possible synergies among different subfields, and the prospects for solving the most fundamental open questions with multi-messenger observations.

Building on previous work (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.97.123513), the authors study through extensive numerical simulations the possibility of observing the gravitational wave spectrum created in a first-order phase transition (in beyond the standard model theories) in upcoming space-based detectors like LISA. Different effective potentials are considered and it is shown that the potential could be determined by the form of the gravitational wave spectrum.

We have performed the first three-dimensional simulations of strong first-order thermal phase transitions in the early universe. For deflagrations, we find that the rotational component of the fluid velocity increases as the transition strength is increased. For detonations, however, the rotational velocity component remains constant and small. We also find that the efficiency with which kinetic energy is transferred to the fluid falls below theoretical expectations as we increase the transition strength. The probable origin of the kinetic energy deficit is the formation of reheated droplets of the metastable phase during the collision, slowing the bubble walls. The rate of increase in the gravitational wave energy density for deflagrations in strong transitions is suppressed compared to that predicted in earlier work. This is largely accounted for by the reduction in kinetic energy. Current modeling therefore substantially overestimates the gravitational wave signal for strong transitions with deflagrations, in the most extreme case by a factor of 10^{3}. Detonations are less affected.

We conduct large scale numerical simulations of gravitational wave production at a first-order vacuum phase transition. We find a power law for the gravitational wave power spectrum at high wave number which falls off as k(-1.5) rather than the k(-1) produced by the envelope approximation. The peak of the power spectrum is shifted to slightly lower wave numbers from that of the envelope approximation. The envelope approximation reproduces our results for the peak power less well, agreeing only to within an order of magnitude. After the bubbles finish colliding, the scalar field oscillates around the true vacuum. An additional feature is produced in the UV of the gravitational wave power spectrum, and this continues to grow linearly until the end of our simulation. The additional feature peaks at a length scale close to the bubble wall thickness and is shown to have a negligible contribution to the energy in gravitational waves, providing the scalar field mass is much smaller than the Planck mass.