Opening Lecture

David A Leigh FRS
University of Manchester, UK

Making the Tiniest Machines

"We are at the dawn of a new industrial revolution of the twenty-first century, and the future will show how molecular machinery can become an integral part of our lives. The advances made have also led to the first steps towards creating truly programmable machines, and it can be envisaged that molecular robotics will be one of the next major scientific areas." [1].
The 2016 Nobel Prize in Chemistry Committee, October 2016

Over the past few years some of the first examples of synthetic molecular level machines and motors - all be they primitive by biological standards - have been developed [2]. These molecules are often best designed to work through statistical mechanisms, rectifying random thermal motion through ratchet mechanisms [3, 4, 5, 6] in a manner reminiscent of Maxwell's Demon. Recently the first programmable systems have been developed [7, 8], the forerunners of a new technological era of molecular robotics.
Perhaps the best way to appreciate the technological potential of controlled molecular-level motion is to recognise that nanomotors and molecular-level machines lie at the heart of every significant biological process. Over billions of years of evolution Nature has not repeatedly chosen this solution for achieving complex task performance without good reason. In stark contrast to biology, none of mankind's fantastic myriad of present day technologies exploit controlled molecular-level motion in any way at all: every catalyst, every material, every plastic, every pharmaceutical, every chemical reagent, all function exclusively through their static or equilibrium dynamic properties. When we learn how to build artificial structures that can control and exploit molecular level motion, and interface their effects directly with other molecular-level substructures and the outside world, it will potentially impact on every aspect of functional molecule and materials design. An improved understanding of physics and biology will surely follow.

     

Adam Liwo "Theory and practice of coarse graining"

Coarse-grained approaches, in which several atoms are merged into extended interaction sites, are widely used in simulating large systems, including biological macromolecules. Such reduction of representation offers a tremendous benefit of extending the accessible time- and size-scales by orders of magnitude. However, designing the pertinent force fields poses problems and simple translation of all-atom energy terms to coarse-grained representation does not give satisfactory result. The fundamental physical principle behind the coarse-grained force field is Boltzmann averaging over the degrees of freedom that are lost when passing from the all-atom to the coarse-grained representation; consequently, an effective coarse-grained energy function is a potential of mean force (PMF). Approximation of the PMF is, however, necessary, for tractability and transferability. This can be done by (1) defining the components of the PMF as statistical potentials extracted from structural databases (e.g., the ROSETTA or CABS force fields), (2) fitting neo-classical expression from all-atom force fields to thermodynamic and structural quantities (e.g., the MARTINI force field), (3) iterative Boltzmann inversion, (3) force matching, and (iv) factor expansion of the PMF into Kubo's cluster cumulants (e.g., the UNRES force field). The factor expansion approach enables aggressive coarse graining with retaining the ability to models the structural features without knowledge-based restraints. In this talk, these approaches will be described and examples to illustrate the ability of coarse-grained models to treat large systems at long time scales will be presented.

Antti J Niemi "Time crystals and rotary molecular motors"

I develop a novel theoretical physics based approach to explain how a general class of autonomous rotating molecular motors function: molecular machines are not rigid bodies, they are deformable bodies, and I propose new paradigms that are appropriate for their description. For this I employ topological and geometrical methods that are already indispensable in numerous theoretical studies elsewhere, including particle physics, condensed matter physics and gravity. I exploit the geometry in the shape space of deformable bodies to explain how a cyclic motion in one set of variables, in my case the vibrations of individual atoms in a molecule, produces other kind of periodic motion in another set variables, that in my case describe the rotational motion of the entire molecule. This self-organization of fast individual atom oscillations into a slow rotational motion of the entire molecule can occur even with no angular momentum. It is due to the geometric concepts of holonomy, and a connection in the shape space. I also reveal an analogy between a rotating molecular machine and the concept of a driven time crystal, a material system that can sustain cyclic motion in response to an external cyclic drive, albeit with a different frequency. I use the analogy to develop an effective theory description that I combine with detailed all-atom molecular dynamics simulations, to investigate various ring-like and knotted molecular rotors. As a proof of concept, I describe how in the case of a single cyclopropane molecule, the individual atom vibrations can transduce into a uniform and sustainable rotational motion of the entire molecule.

Franco Ferrari "Modeling polymer systems in the presence of non-trivial topological relations: a combined analytical-numerical approach"

This lecture attempts to present a joint analytical-numerical point of view on the properties of knotted and topologically linked polymer rings with a perspective for future applications and experiments. Single knots and links formed by polymers are complex systems. Even in the case of knots consisting of a homopolymer in a bad solvent, a Monte Carlo Wang-Landau study has revealed that their energy landscape exhibits a funnel-like structure similar to that of proteins. Computer simulations show also that several different phases may be observed when a knot is stretched. A more complicated behaviour is obtained by changing the monomer compositions. The possibility of controlling the amplitudes and the temperatures of the reversible expansions of single knots and other properties by tuning topology, monomer composition and polymer length, paves the way for applications of polymers subjected to topological constraints as molecular motors and machines. Despite the fact that for a long time the problem of knotted and linked polymer rings has been considered as mathematically untractable, it is now possible to model links using analytical methods. These methods provide not only important hints about the way in which the monomers interact due to the presence of topological relations. They allow also to establish new correspondences with other systems in which the topological relations between quasi one-dimensional objects become relevant, such as for instance the lines of the solar magnetic fields. Some calculations in the case of two linked ideal polymer rings can be performed exactly or, in the case in which the excluded volume interactions are present, several approximations are possible. The results are in agreement with the observations on on linked DNA rings made in the ninties of the previous century by Nicholas Cozzarelli and his group. Finally, a way for checking experimentally some of the numerical and analytical findings using calorimetry will be outlined.

Marek Cieplak "Dynamics of intrinsically disordered proteins and their droplet-like aggregates"

The intrinsically disordered proteins (IDPs) may aggregate and form multiprotein droplets that act as membraneless organelles. Theoretical understanding of the formation and dynamics of such droplets requires using coarse-grained molecular dynamics models. We describe a novel model (constructed with Lukasz Mioduszewski) that is a generalization of the so-called Go-like model, originally designed for structured proteins, and based on the concept of contact interactions between amino acids. In the case of the IDPs, the contacts are derived primarily from an instantaneous shape of the backbone and not from the geometry of a single reference state (such as the native state). The metastable proteinaceous droplets may arise within the two-fluid coexistence region that is bounded by the binodal and spinodal lines. We present novel theoretical methods to derive these lines. As an illustration, we discuss phase diagrams for systems of elastins and polyglutamines.

Noam Kaplan "Deciphering 3D genome organization with probabilistic models"

The spatial organization of the genome is closely linked with its function. Recent genomic technologies allow interrogating 3D genome organization by measuring spatial interaction frequencies of all pairs of loci in the genome. Investigation and interpretation of the resulting interaction matrices, which represent an average representation of highly stochastic genomic structures across a cell population, poses a major challenge. In my talk I will show how probabilistic models provide an excellent framework to accomplish this goal. These models allow to capture explicit mechanistic hypotheses, while simultaneously utilizing the large amounts of available data to infer genome-wide biological meaningful parameters. Modelling specific patterns of genomic structure such as topologically associating domains and genomic compartments, I will show how these models can be used to methodically ask biological questions about 3D genome organization.

Pietro Faccioli "Pharmacological Protein Inactivation by Targeting Protein Folding Intermediates"

Enhanced path sampling methods developed by our group over the last decade have made it possible predict the folding process of biologically relevant proteins (consisting of several hundreds of amino acids), using realistic all-atom force fields. Based on this technological advancement, we proposed an entirely new paradigm for rational drug discovery named Pharmacological Protein Inactivation by Folding Intermediate Targeting (PPI-FIT). This scheme is based on the rationale of identifying small molecule that bind to theoretically predicted folding intermediates, thus blocking the protein folding process and targeting protein degradation. Using the PPI-FIT paradigm we have discovered molecules that can selectively and dose-dependently modulate the cellular expression of the human prion protein (PrPc), a protein considered undruggable with conventional method and is involved in many fatal neurodegenerative diseases. An experiment is planned for 2022 in in International Space Station, to exploit microgravity conditions to attempt the crystallization of partially folded PrP proteins in complex with one of the small molecules discovered using PPI-FIT. The PPI-FIT approach is now being exploited industrially and has been applied to a number of different targets.

Roumen Anguelov "Mathematical models and analysis of the impact of CTCE9908 and kynurenine metabolites on the proliferation and survival of tumour cells"

Melanoma cells express chemokine receptor 4 (CXCR-4). When bound to chemokine ligand 12 (CXCL12) it activates signalling pathways such as mitogen-activated protein kinase (MAPK) and phosphatidylinositol 3-kinase (PI3K) that promote tumour cell proliferation, migration and adhesion CTCE9908 binds to the receptor CXCR-4 and prevents CXCL12 to dock on this sensor thus inhibiting adhesion and proliferation ability of the cell. The kynurenine metabolites act in a similar way as indicated on the diagram. Further, sufficient level of blocking the CXCR-4 receptor and inhibition of the respective signalling pathways causes cell death.
A generic mathematical model is constructed using the principle of mass action-reaction kinetics. It is a competitive dynamical system capturing the interplay between the activation process, that is CXCL12 docks on a CXCR-4 sensor, and the inhibition process, that is, an inhibition agent (CTCE9908 or a kynurenine metabolite) attaches to CXCR-4 and blocks it. Theoretically the unique equilibrium is reached via two processes (i) fast: occupying available docking places and (ii) slow: replacement of CXCL12 by the inhibition agent. Therefore, while the equilibrium itself does not depend on the initial state, the time to get near it does. When the equilibrium is in the domain of sufficient inhibition for cell death, the equilibrium is only theoretical in the sense that it cannot be reached, this being a desirable outcome.

Sarah Harris "Understanding the structure and dynamics of the SARS-CoV2 helicase (nsp13) from molecular dynamics simulations"

The SARS-CoV-2 nsp13 is one of the non-structural proteins of the SARS-CoV-2 coronavirus. It is a helicase protein that has a number of functions in the host cell during viral replication: it is involved in the separation of double stranded nucleic acid helices, it plays a role in single stranded nucleic acid translocation and it has nucleotide triphosphatase activity as part of the RNA capping machinery of the virus.
The SARS-CoV2 helicase consortium is an international team of volunteers using atomistic molecular dynamics simulations to model this protein in the context of the broader replication/transcription and proof-reading machinery. We have collectively generated multiple microseconds of simulation data for analysis. We have observed that binding either RNA or ATP leads to substantial stiffening of the helicase, suggesting that the apo protein is a bad target for rational drug-design compared to the bound helicase complexes. We have also seen that the major mode of flexibility of the apo helicase is consistent with the large-scale structural changes observed in recent cryo-EM studies of the co-transcriptional capping machinery.