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Silk is a semidilute solution of randomly coiled associating polypeptide chains that crystallize following the stretch-induced disruption, in the strong extensional flow of extrusion, of the solvation shell around their amino acids. We propose that natural silk spinning exploits both the exponentially broad stretch distribution generated by associating polymers in extensional flow and the criterion of a critical concentration of sufficiently stretched chains to nucleate flow-induced crystallization. To investigate the specific-energy input needed to reach this criterion in start-up flow, we have coupled a model for the Brownian dynamics of a bead-spring-type chain, whose beads represent coarse-grained Gaussian chain segments, to the stochastic, strain-dependent binding and unbinding of their associations. We have interpreted the simulations with the aid of analytic calculations on simpler, tractable models with the same essential physical features. Our simulations indicate that the associations hamper chain alignment in the initial slow flow, but, on the other hand, facilitate chain stretching at low specific work at later, high rates. We identify a minimum in the critical specific work at a strain rate just above the stretch transition (i.e., where the mean stretch diverges), which we explain in terms of analytical solutions of a two-state master equation. We further discuss how the silkworm appears to exploit the chemical tunability of the associations to optimize chain alignment and stretching in different locations along the spinning duct: this delicate mechanism also highlights the potential biomimetic industrial benefits of chemically tunable processing of synthetic association polymers.

A personal recollection of gratitude reports on the way that the writings of John Polkinghorne inspired and guided the author’s own thinking in science and theology since meeting him as a graduate student. Themes of both agreement and disagreement are selected from the many to be found in Polkinghorne’s corpus. Closer attention is paid to two of his books, Science and Christian Belief and Faith, Science and Understanding. A running theme is the creative tension of a ‘bottom-up thinker’, one of whose salient and influential arguments was that of ‘top-down causation’. Although there is disagreement over Polkinghorne’s exegesis of divine character in Job, thinking the argument through did bear fruit.

In his treatise On the Rainbow (De iride), composed nearly four hundred years before the first known telescope, the English polymath Robert Grosseteste identified three striking optical effects: distant objects can be rendered close by; close-by large objects can be rendered small; and distant small objects can be rendered large. In the context of the history of optics, the first effect is especially striking. Grosseteste did not give details of the mechanisms underlying these effects but did mention the passage of rays through refraction in “diaphanous” or transparent bodies. While making no final claim that Grosseteste himself necessarily knew of or used lenses, this essay examines the coherence between the three optical effects described in Grosseteste’s treatise and two candidate proposals for the deployment of a single convex lens. A convex lens, deployed in different ways, is shown to produce all three of Grosseteste’s optical effects, in a manner strikingly aligned with the language that he uses to distinguish changes in the location and size of objects. The implications of this coherence for interpretations of On the Rainbow are discussed throughout the essay.

Changes in the structural dynamics of double stranded (ds)DNA upon ligand binding have been linked to the mechanism of allostery without conformational change, but direct experimental evidence remains elusive. To address this, a combination of steady state infrared (IR) absorption spectroscopy and ultrafast temperature jump IR absorption measurements has been used to quantify the extent of fast (∼100 ns) fluctuations in (ds)DNA·Hoechst 33258 complexes at a range of temperatures. Exploiting the direct link between vibrational band intensities and base stacking shows that the absolute magnitude of the change in absorbance caused by fast structural fluctuations following the temperature jump is only weakly dependent on the starting temperature of the sample. The observed fast dynamics are some two orders of magnitude faster than strand separation and associated with all points along the 10-base pair duplex d(GCATATATCC). Binding the Hoechst 33258 ligand causes a small but consistent reduction in the extent of these fast fluctuations of base pairs located outside of the ligand binding region. These observations point to a ligand-induced reduction in the flexibility of the dsDNA near the binding site, consistent with an estimated allosteric propagation length of 15 Å, about 5 base pairs, which agrees well with both molecular simulation and coarse-grained statistical mechanics models of allostery leading to cooperative ligand binding.

Description, Bacteria use subcellular proteinaceous liquid droplets to survive stress., Liquid-liquid phase separation is emerging as a crucial phenomenon in several fundamental cell processes. A range of eukaryotic systems exhibit liquid condensates. However, their function in bacteria, which, in general, lack membrane-bound compartments, remains less clear. Here, we used high-resolution optical microscopy to observe single bacterial aggresomes, nanostructured intracellular assemblies of proteins, to undercover their role in cell stress. We find that proteins inside aggresomes are mobile and undergo dynamic turnover, consistent with a liquid state. Our observations are in quantitative agreement with phase-separated liquid droplet formation driven by interacting proteins under thermal equilibrium that nucleate following diffusive collisions in the cytoplasm. We have found aggresomes in multiple species of bacteria and show that these emergent, metastable liquid-structured protein assemblies increase bacterial fitness by enabling cells to tolerate environmental stresses.

The flow-induced self-assembly of entangled Bombyx mori silk proteins is hypothesised to be aided by the ‘registration’ of aligned protein chains using intermolecularly interacting ‘sticky’ patches. This suggests that upon chain alignment, a hierarchical network forms that collectively stretches and induces nucleation in a precisely controlled way. Through the lens of polymer physics, we argue that if all chains would stretch to a similar extent, a clear correlation length of the stickers in the direction of the flow emerges, which may indeed favour such a registration effect. Through simulations in both extensional flow and shear, we show that there is, on the other hand, a very broad distribution of protein–chain stretch, which suggests the registration of proteins is not directly coupled to the applied strain, but may be a slow statistical process. This qualitative prediction seems to be consistent with the large strains (i.e., at long time scales) required to induce gelation in our rheological measurements under constant shear. We discuss our perspective of how the flow-induced self-assembly of silk may be addressed by new experiments and model development.

The COVID-19 pandemic caused by the novel coronavirus SARS-CoV-2 has no publicly available vaccine or antiviral drugs at the time of writing. An attractive coronavirus drug target is the main protease (M pro , also known as 3CL pro ) because of its vital role in the viral cycle. A significant body of work has been focused on finding inhibitors which bind and block the active site of the main protease, but little has been done to address potential non-competitive inhibition, targeting regions other than the active site, partly because the fundamental biophysics of such allosteric control is still poorly understood. In this work, we construct an elastic network model (ENM) of the SARS-CoV-2 M pro homodimer protein and analyse its dynamics and thermodynamics. We found a rich and heterogeneous dynamical structure, including allosterically correlated motions between the homodimeric protease's active sites. Exhaustive 1-point and 2-point mutation scans of the ENM and their effect on fluctuation free energies confirm previously experimentally identified bioactive residues, but also suggest several new candidate regions that are distant from the active site, yet control the protease function. Our results suggest new dynamically driven control regions as possible candidates for non-competitive inhibiting binding sites in the protease, which may assist the development of current fragment-based binding screens. The results also provide new insights into the active biophysical research field of protein fluctuation allostery and its underpinning dynamical structure.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which caused the COVID-19 pandemic, has no vaccine or antiviral drugs available to the public, at the time of writing. The virus’ non-structural proteins are promising drug targets because of their vital role in the viral cycle. A significant body of work has been focused on finding inhibitors which covalently and competitively bind the active site of the non-structural proteins, but little has been done to address regions other than the active site, i.e. for non-competitive inhibition. Here we extend previous work on the SARS-CoV-2 Mpro (nsp5) to three other SARS-CoV-2 proteins: host shutoff factor (nsp1), papain-like protease (nsp3, also known as PLpro) and RNA-dependent RNA-polymerase (nsp12, also known as RdRp) in complex with nsp7 and nsp8 cofactors. Using open-source software (DDPT) to construct Elastic Network Models (ENM) of the chosen proteins we analyse their fluctuation dynamics and thermodynamics, as well as using this protein family to study convergence and robustness of the ENM. Exhaustive 2-point mutational scans of the ENM and their effect on fluctuation free energies suggest several new candidate regions, distant from the active site, for control of the proteins’ function, which may assist the drug development based on the current small molecule binding screens. The results also provide new insights, including non-additive effects of double-mutation or inhibition, into the active biophysical research field of protein fluctuation allostery and its underpinning dynamical structure.

Soft Matter: A Very Short Introduction explores the field of soft matter, looking beneath the appearances of matter into its inner structure. Drawing on physics, chemistry, mathematics, and engineering, soft matter science links fundamental scientific ideas to everyday phenomena such as ‘inkiness’ and ‘stickiness’, with a rich history and philosophy. It studies materials such as polymers, colloids, liquid crystals, and foams. This VSI shows how Brownian Motion—the random molecular motion underlying ‘heat’—is an underpinning principle of soft matter. From hair conditioners to honey, it discusses how common characteristics of these materials shape their behaviour and applications.

‘Pearliness’ focuses on the soft matter class of ‘liquid crystals’ and considers a new ‘phase’ of matter: the ‘nematic’ state. The liquid crystal molecules are built of many atoms; they are mesoscopic objects. Their essential structure lies therefore in their overall rod-like shape, not in their specific atomistic constituents. In consequence, nematic behaviour is universal—there are many examples of molecules which form a nematic state. How do ideas from superconductivity and particle physics theory provide a conceptual framework for the theoretical physics of liquid crystals? There is another class of liquid crystals known as ‘smectic’ which are important to consider in this topic.

‘Milkiness, muddiness, and inkiness’ discusses the phenomena of ‘muddiness’ and ‘inkiness’, which are both examples of ‘colloids’—the fundamental class of soft matter constituted by dispersing very small particles of solid matter in a liquid environment. The colloidal state provided the final evidence that atoms existed. Michael Faraday gave a well-known lecture on the ‘Brownian Motion’ and he also researched gold colloids which show how small particles disperse. Albert Einstein came up with a theory of thermal noise, and Charles Perrin carried out a famous experiment in 1908 on this topic. Both Einstein and Perrin showed that colloidal particles can do everything that molecules do, but at a thousand times the size, and equally more slowly.

‘Liveliness’ studies the new biologically inspired field of active soft matter. Almost any type of soft matter possesses an active form. Using myosin corresponds to making the cross-links of a polymer gel active. However, polymerization itself can be actively driven, as well as the cross-linking between polymers. Bacteria are, within this perspective, an active form of colloid—nanoparticles that can swim. As their shape becomes highly anisotropic, they generate the notion of ‘active liquid crystals’.

‘Gelification and soapiness’ looks at the third class of soft matter: ‘self-assembly’. Like the colloids of inks and clays, and the polymers of plastics and rubbers, ‘self-assembled’ soft matter also emerges as a surprising consequence of Brownian motion combined with weak intermolecular forces. Like them, it also leads to explanations of a very rich world of materials and phenomena, such as gels, foams, soaps, and ultimately to many of the structures of biological life. There is an important distinction that needs to be made between one-dimensional and two-dimensional self-assembly.

‘Sliminess and stickiness’ examines the molecular origin of ‘stickiness’. It details Hermann Staudinger’s research on ‘double bonds’ and ‘macromolecules’. Understanding the unorthodox properties of the polymer liquid and gel state turned out to be one of the first successes of soft matter science. Staudinger faced a challenge: how much space would a polymer molecule occupy when in solution? Many of the mathematical techniques that had been developed to deal with the quantum mechanics of electrons, photons, and their interaction in solids could be translated into tools for solving polymer problems such as this one. The properties of rubber, and the sticky sliminess of rubbery liquids, are topics which relate to the notion of stickiness.

‘The science of softness’ provides a brief history and overview of soft matter science. The development of soft matter science was propelled by a combination of communication within the scientific community; intrinsic conceptual overlap and commonality; and visionary leadership from a small number of pioneering scientists. Chemistry proved as essential an ingredient to the new science of soft matter as ideas and techniques from physics. The characteristics of soft matter include motion; structure on intermediate length scales; slow dynamics; and universality. Microscopy is the most obvious and direct example of experimental tools applied across the gamut of soft materials.

The Conclusion looks at the topics that haven't been covered in this VSI. There is so much more to the topic to be learnt: recent developments in rheology at the single molecule level through atomic force microscopy, and the single polymer imaging of confocal microscopy to name but a few. It is an undisputed truth that, through evolution, life itself has recruited the structures of soft matter for its own purposes. Polymers, membranes, liquid crystallinity, self-assembly form its fundamental constituents, from the humblest bacterium to the most complex multicellular creature. The tree of life has taken these materials and combined them in vast complexities of such intricacy that the student of simple systems is easily bewildered by the questions of life.

We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by Leibler- Rubinstein-Colby theory. Although a single-mode DEMG approximation accurately describes the transient stretching of the polymers above a 'sticky' Weissenberg number (product of the strain rate with the sticky-Rouse time), the pre-averaged model fails to capture a remarkable development of a power-law distribution of stretch in steady-state extensional flow: while the mean stretch is finite, the fluctuations in stretch may diverge. We present an analytical model that shows how strong stochastic forcing drive the long tail of the distribution, gives rise to rare events of reaching a threshold stretch and constitutes a framework within which nucleation rates of flow-induced crystallization may understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations., 5 pages; 4 figures

We consider the polymer physics of a possible molecular mechanism for disentangled melt states observed recently. We find that the route from molten, but only marginally-overlapping single crystals to the equilibrium state must pass over a free-energy barrier that becomes large at high molecular weights. The penalty arises from elastic distortions of the entanglement network as the chains diffuse. A critical molecular weight arises naturally from the competition of elastic distortion and the free-energy of confinement. We calculate the barrier and critical molecular weight at both a simple single-chain level, and at a “one-loop” level of co-operative motion, finding that many-chain effects alter the physics quantitatively, but not qualitatively. Several new experiments are suggested.

The metaphor of nature as a book, and its reading, has arisen in many forms in theological discussions of natural philosophy from ancient to modern periods. It is far less fixed in form than often assumed, however, but reflects cultural contextual shape. It is also too often recruited without challenge, although the implied analogies of authorship, narrative shape, and hermeneutic contain many pitfalls. I explore four flaws in the ‘Book of Nature’ narrative, finding that they are connected with two related and troublesome tensions – that of ‘methodological naturalism’ within a theistic framework, and the redundancy of ‘natural theology’ in its nineteenth century form. Approaching a theology of science from the perspective of the Wisdom tradition offers a fresh conception of who does the writing, and reading, of nature’s living book.

Extending the approach to a ‘theology of science’ developed in Faith and Wisdom in Science (McLeish 2014), I expand its theme of the tension between chaos and emergent order, within the arc of the Biblical story of creation, towards a theol-ogy of evolutionary science. In addition to the material in Job, the book of Wisdomprovides a remarkable account of transmutation of species, within a recapitulation of the Exodus theme, that I reconsider as a background historical narrative to an inter-pretation of modern genotype-phenotype theory of evolutionary dynamics, exploiting analogies with statistical mechanics. The dual and connected structures of microscopic and macroscopic provide a contemporary locus for the Joban tensions of chaos and emergent order, and provide an interpretative narrative for the emergent directionality of evolution, and a theology that situates within a creation of freedom to explore the potential of the created order.

Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation takes place close to the critical point. Using kinetic Monte Carlo and molecular dynamics simulations of a binary surface fluid under these conditions, we show that the characteristic length scale of the emerging structure decreases, in 2D, with the 4/15 dynamic critical exponent of the quench rate rather than the mean-field 1/6th power. Hence, the dynamics of cluster formation governed by thermodynamically undriven Brownian motion is much more sensitive on the rate of destabilisation than expected from mean-field theory. We discuss the expected implications of this finding to 3D systems with ordering liquid crystals, as well as phase-separating passive or active particles., Comment: 8 pages, 9 figures

This historical paper examines a pioneering theory of speech production and perception from the thirteenth century. Robert Grosseteste (c.1175—1253) was a celebrated medieval thinker, who developed an impressive corpus of treatises on the natural world. This paper looks at his treatise on sound and phonetics, De generatione sonorum [On the Generation of Sounds]. Through interdisciplinary analysis of the text, this paper finds a theory of vowel production and perception that is notably mathematical, with a formulation of vowel space rooted in combinatorics. Specifically, Grosseteste constructs a categorical space comprising three fundamental types of movements pertaining to the vocal apparatus: linear, circular, and dilational-constrictional; these correspond to similarity transformations of translation, rotation, and uniform scaling, respectively. That Grosseteste's space is categorical, and low-dimensional, is remarkable vis-a-vis current theories of phoneme perception. As well as his description of vowel space, Grosseteste also sets out a hypothetical framework of multisensory integration, uniting the production, perception, and representation in writing of vowels with a set of geometric figures associated with “mental images.” This has clear resonances with contemporary studies of motor facilitation during speech perception and audiovisual speech. This paper additionally provides an experimental foray, illustrating the coherence of mathematical and scientific thinking underpinning this early theory.

Author summary Improvements in technology often drive scientific discovery. Therefore, research requires sustained investment in the latest equipment and training for the researchers who are going to use it. Prioritising and administering infrastructure investment is challenging because future needs are difficult to predict. In the past, highly computationally demanding research was associated primarily with particle physics and astronomy experiments. However, as biology becomes more quantitative and bioscientists generate more and more data, their computational requirements may ultimately exceed those of physical scientists. Computation has always been central to bioinformatics, but now imaging experiments have rapidly growing data processing and storage requirements. There is also an urgent need for new modelling and simulation tools to provide insight and understanding of these biophysical experiments. Bioscience communities must work together to provide the software and skills training needed in their areas. Research-active institutions need to recognise that computation is now vital in many more areas of discovery and create an environment where it can be embraced. The public must also become aware of both the power and limitations of computing, particularly with respect to their health and personal data.

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromo-lecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Personal accounts of the creative process in science tell us that there is no ‘method’ to the conception of a new scientific idea. Stories from physicist Richard Feynman, the author’s own scientific experience, an example of physics and biology working together, and a conversation of scientists assembled in Cambridge by The Imagination Institute, all give different accounts of the ways that imagination can play out in science. Themes emerge from these raw accounts that will shape the subsequent chapters: especially the experienced typology of imagination into visual, textual and abstract forms. The subtle interaction of conscious and non-conscious thought raises questions of the link between cognition and aesthetic response in mental creative acts.

The third mode of imagination is the abstract—the world shared by mathematics and music. Once held together in the ‘quadrivum’ of medieval liberal arts, they have now lost their obvious connection. This chapter explores their deeper commonalities, starting with Andrew Wiles’ proof of Fermat’s last theorem, and Shostakovich’s eighth string quartet, the shared role of number in rhythm, volume, and pitch leads to a deeper world of multi-layered structure and the unconscious imagination. The writing of, and writing about music of Robert Schumann, including a detailed examination of his Konzertstück for four horns and orchestra, is contrasted with writing about mathematical creativity by Hadamard. The collision of beauty, structure, and universality is illustrated by a close encounter with the Fluctuation–Dissipation Theorem. In both cases of mathematics and music, notation is explicitly displayed in an exploration of how it serves as an extension to imaginative thought.

This first chapter surveys the landscape of the book, and the questions it will seek to explore. By listening to the verbal associations we bring to arts and to science, we observe that one reason for the differences is that artists and scientists are private and public about different aspects of their work. Science only speaks of the creative, inspirational moments, more familiar in the arts, in hushed tones, while artists are less forthcoming about the arduous journey from concept to creation through experiment, trial, and error, an essential process closely shared with science. By listening to Einstein, Shakespeare, Wordsworth, Keats, and the biblical Book of Job, we conceive of the commonality of imagination within constraint that connects the work of art and science alike.

‘I could not see any place in science for my creativity or imagination’, was the explanation, of a bright school leaver to the author, of why she had abandoned all study of science. Yet as any scientist knows, the imagination is essential to the immense task of re-creating a shared model of nature from the scale of the cosmos, through biological complexity, to the smallest subatomic structures. Encounters like that one inspired this book, which takes a journey through the creative process in the arts as well as sciences. Visiting great creative people of the past, it also draws on personal accounts of scientists, artists, mathematicians, writers, and musicians today to explore the commonalities and differences in creation. Tom McLeish finds that the ‘Two Cultures’ division between the arts and the sciences is not after all, the best classification of creative processes, for all creation calls on the power of the imagination within the constraints of form. Instead, the three modes of visual, textual, and abstract imagination have woven the stories of the arts and sciences together, but using different tools. As well as panoramic assessments of creativity, calling on ideas from the ancient world, medieval thought, and twentieth-century philosophy and theology, The Poetry and Music of Science illustrates its emerging story by specific close-up explorations of musical (Schumann), literary (James, Woolf, Goethe) mathematical (Wiles), and scientific (Humboldt, Einstein) creation. The book concludes by asking how creativity contributes to what it means to be human.

The book finishes with an examination of the human purpose of creativity and creation. The evidence and narrative gathered so far is summarized in a ‘creation narrative’—a basic story of the emotional and cognitive trajectory of the creative process. Drawing on recent work in anthropology, narratology, and theology, and on phenomenological philosophy of the human condition, the chapter develops the thesis that creativity of all kinds contributes to a healing of a broken or incomplete human relationship with the world. The story of our growing understanding of the rainbow acts as an illustration of the extreme length, but great human depth, of this process.

The dual roles of cognition and emotion in creativity that have emerged at many points in the book so far are examined in their own right. Through the lens of medieval philosophy, especially the work of Robert Grosseteste, then Kant, Spinoza, Hume, and the recent study of Iain McGilchrist, this chapter examines the structure of how the affective works in the origination of ideas, not just in response to them. Contemporary scientific testimony to the creative function of emotion leads to a detailed case study of a Caltech project to develop a polymer additive to make jet fuel safe in crashes, and other stories of scientific creation, earth the philosophical discussion in experience.

The first mode of imagination—the visual—is shared by art and science. The chapter starts with an account of the history of visual perception, working though the ancient theory of ‘extramission’, because it sheds light on the role of the mind’s active projection of visual impressions on the world in the interpretation of incoming images. The commonality of scientific and artistic visual imagination is partially to be found in mappings between spaces of three to two dimensions, exemplified perfectly by astronomy, and the work of medieval painter Giotto. Comparisons of the creative process in a recent astrophysical discovery are made with a contemporary artist (Graeme Willson) and through a detailed study of a lesser-known work by Monet.