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We numerically investigate the competition between phase separation and dynamical arrest in a colloidal system interacting via a short-ranged attractive potential. Equilibrium fluid configurations are quenched at two different temperatures below the critical temperature and followed during their time evolution. At the lowest studied T, the phase-separation process is interrupted by the formation of an attractive glass in the dense phase. At the higher T, no arrest is observed and the phase-separation process proceeds endlessly in the simulated time window. The final structure of the glass retains memory of the interrupted phase-separation process in the form of a frozen spinodal decomposition peak, whose location and amplitude is controlled by the average packing fraction. We also discuss the time evolution of the nonergodicity parameter, providing evidence of a progressively decreasing localization length on increasing the packing fraction. Finally, we confirm that the reported results are independent of the microscopic dynamics. [ABSTRACT FROM AUTHOR]

We study the aging dynamics in a model for dense simple liquids, in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. In this system, at large packing fractions, kinetically arrested disordered states can be created both on cooling (attractive glass) and on heating (repulsive glass). The possibility of having two distinct glasses, at the same packing fraction, with two different dynamics offers the unique possibility of comparing—within the same model—the differences in aging dynamics. We find that, while the aging dynamics of the repulsive glass is similar to the one observed in atomic and molecular systems, the aging dynamics of the attractive glass shows novel unexpected features. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state in which the system becomes entrapped, along with a transition, either continuous or discontinuous, to an active state. Understanding which physical mechanisms determine the order of these transitions represents a challenging open problem in nonequilibrium statistical mechanics. Here, by numerical simulations and mean-field analysis, we show that a quasi-2D vibrofluidized granular system exhibits a novel form of APT. The absorbing phase is observed in the horizontal dynamics below a critical packing fraction, and can be continuous or discontinuous based on the emergent degree of synchronization in the vertical motion. Our results provide a direct representation of a feasible experimental scenario, showcasing a surprising interplay between dynamic phase transition and synchronization.

Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001k_{B}T per particle-an observation that could be related to the observation of only random tilings in soft-matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is an excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.

Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.

The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different sizes. We show that the elastic properties vary in a highly non-trivial way as a consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its mechanical alteration originating from the inclusions. To confirm our observations and their generality, we performed experiments on an emulsion that presents strong analogies with colloidal gels and confirms the trends observed in the simulations.

We investigate avalanches and clusters associated with plastic rearrangements and the nature of structural change in the prototypical strong glass, silica, computationally. We perform a detailed analysis of avalanches, and of spatially disconnected clusters that constitute them, for a wide range of system sizes. Although qualitative aspects of yielding in silica are similar to other glasses, the statistics of clusters exhibits significant differences, which we associate with differences in local structure. Across the yielding transition, anomalous structural change and densification, associated with a suppression of tetrahedral order, is observed to accompany strain localization.

The correlation between the local structure and the propensity for structural rearrangements has been widely investigated in glass forming liquids and glasses. In this paper, we use the excess two-body entropy S 2 and tetrahedrality n tet as the per-particle local structural order parameters to explore such correlations in a three-dimensional model glass subjected to cyclic shear deformation. We first show that for both liquid configurations and the corresponding inherent structures, local ordering increases upon lowering temperature, signaled by a decrease in the two-body entropy and an increase in tetrahedrality. When the inherent structures, or glasses, are periodically sheared athermally, they eventually reach absorbing states for small shear amplitudes, which do not change from one cycle to the next. Large strain amplitudes result in the formation of shear bands, within which particle motion is diffusive. We show that in the steady state, there is a clear difference in the local structural environment of particles that will be part of plastic rearrangements during the next shear cycle and that of particles that are immobile. In particular, particles with higher S 2 and lower n tet are more likely to go through rearrangements irrespective of the average energies of the configurations and strain amplitude. For high shear, we find very distinctive local order outside the mobile shear band region, where almost 30% of the particles are involved in icosahedral clusters, contrasting strongly with the fraction of <5% found inside the shear band.

We study numerically the yielding transition of a two dimensional model glass subjected to athermal quasi-static cyclic shear deformation, with the aim of investigating the effect on the yielding behavior of the degree of annealing, which in turn depends on the preparation protocol. We find two distinct regimes of annealing separated by a threshold energy. Poorly annealed glasses progressively evolve toward the threshold energy as the strain amplitude is increased toward the yielding value. Well annealed glasses with initial energies below the threshold energy exhibit stable behavior, with a negligible change in energy with increasing strain amplitude, until they yield. Discontinuities in energy and stress at yielding increase with the degree of annealing, consistent with recent results found in three dimensions. We observe a significant structural change with strain amplitude that closely mirrors the changes in energy and stresses. We investigate groups of particles that are involved in plastic rearrangements. We analyze the distributions of avalanche sizes, of clusters of connected rearranging particles, and related quantities, employing finite size scaling analysis. We verify previously investigated relations between exponents characterizing these distributions.

Glass formers are characterized by their ability to avoid crystallization. As monodisperse systems tend to rapidly crystallize, the most common glass formers in simulations are systems composed of mixtures of particles with different sizes. Here, we make use of the ability of patchy particles to change their local structure to propose them as monodisperse glass formers. We explore monodisperse systems with two patch geometries: a 12-patch geometry that enhances the formation of icosahedral clusters and an 8-patch geometry that does not appear to strongly favor any particular local structure. We show that both geometries avoid crystallization and present glassy features at low temperatures. However, the 8-patch geometry better preserves the structure of a simple liquid at a wide range of temperatures and packing fractions, making it a good candidate for a monodisperse glass former.

Yielding behavior in amorphous solids has been investigated in computer simulations using uniform and cyclic shear deformation. Recent results characterize yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively modest but clear discontinuous change at yielding. To understand better the role of annealing on yielding characteristics, we perform athermal quasistatic cyclic shear simulations of glasses prepared with a wide range of annealing in two qualitatively different systems-a model of silica (a network glass) and an atomic binary mixture glass. Two strikingly different regimes of behavior emerge. Energies of poorly annealed samples evolve toward a unique threshold energy as the strain amplitude increases, before yielding takes place. Well-annealed samples, in contrast, show no significant energy change with strain amplitude until they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems corresponds to dynamical cross-over temperatures associated with changes in the character of the energy landscape sampled by glass-forming liquids., Competing Interests: Competing interest statement: P.G.D. and S.S. coauthored a research article in 2019.

Few questions in condensed matter science have proven as difficult to unravel as the interplay between structure and dynamics in supercooled liquids. To explore this link, much research has been devoted to pinpointing local structures and order parameters that correlate strongly with dynamics. Here we use an unsupervised machine learning algorithm to identify structural heterogeneities in three archetypical glass formers-without using any dynamical information. In each system, the unsupervised machine learning approach autonomously designs a purely structural order parameter within a single snapshot. Comparing the structural order parameter with the dynamics, we find strong correlations with the dynamical heterogeneities. Moreover, the structural characteristics linked to slow particles disappear further away from the glass transition. Our results demonstrate the power of machine learning techniques to detect structural patterns even in disordered systems, and provide a new way forward for unraveling the structural origins of the slow dynamics of glassy materials.

One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the self-assembly of mixtures of spherical particles of two different sizes, which we map to (additive or non-additive) hard-disk mixtures. We map out the infinite-pressure phase diagram for these mixtures using Floppy Box Monte Carlo simulations to systematically sample candidate crystal structures with up to 12 disks in the unit cell. As a function of the size ratio and the number ratio of the two species of particles, we find a rich variety of periodic crystal structures. Additionally, we identify random tiling regions to predict random tiling quasicrystal stability ranges. Increasing non-additivity both gives rise to additional crystal phases and broadens the stability regime for crystal structures involving a large number of large-small contacts, including random tilings. Our results provide useful guidelines for controlling the self-assembly of colloidal particles at interfaces.

The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixtures-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the number of tetrahedral clusters in a hard sphere mixture is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.

We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of components leads to softer solids that can accommodate progressively larger strains before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work provides new insight into mechanisms at play for controlling the material properties and opens a road to new design principles for soft composite solids.

We explore the effect of directionality on rotational and translational relaxation in glassy systems of patchy particles. Using molecular dynamics simulations, we analyze the impact of two distinct patch geometries, one that enhances the local icosahedral structure and the other one that does not strongly affect the local order. We find that in nearly all investigated cases, rotational relaxation takes place on a much faster time scale than translational relaxation. By comparing to a simplified dynamical Monte Carlo model, we illustrate that rotational diffusion can be qualitatively explained as purely local motion within a fixed environment, which is not coupled strongly to the cage-breaking dynamics required for translational relaxation. Nonetheless, icosahedral patch placement has a profound effect on the local structure of the system, resulting in a dramatic slowdown at low temperatures, which is strongest at an intermediate "optimal" patch size.

Glasses remain an elusive and poorly understood state of matter. It is not clear how we can control the macroscopic dynamics of glassy systems by tuning the properties of their microscopic building blocks. In this paper, we propose a simple directional colloidal model that reinforces the optimal icosahedral local structure of binary hard-sphere glasses. We show that this specific symmetry results in a dramatic slowing down of the dynamics. Our results open the door to controlling the dynamics of dense glassy systems by selectively promoting specific local structural environments.

The dynamics of concentrated suspensions of the eye-lens protein alpha crystallin have been measured using x-ray photon correlation spectroscopy. Measurements were made at wave vectors corresponding to the first peak in the hard-sphere structure factor and volume fractions close to the critical volume fraction for the glass transition. Langevin dynamics simulations were also performed in parallel to the experiments. The intermediate scattering function f(q,τ) could be fit using a stretched exponential decay for both experiments and numerical simulations. The measured relaxation times show good agreement with simulations for polydisperse hard-sphere colloids.

In this paper we probe the structural response to oscillatory shear deformations of polycrystalline monolayers of soft repulsive colloids with varying area fraction over a broad range of frequencies and amplitudes. The particles are confined at a fluid interface, sheared using a magnetic microdisk, and imaged through optical microscopy. The structural and mechanical response of soft materials is highly dependent on their microstructure. If crystals are well understood and deform through the creation and mobilization of specific defects, the situation is much more complex for disordered jammed materials, where identifying structural motifs defining plastically rearranging regions remains an elusive task. Our materials fall between these two classes and allow the identification of clear pathways for structural evolution. In particular, we demonstrate that large enough strains are able to fluidize the system, identifying critical strains that fulfill a local Lindemann criterion. Conversely, smaller strains lead to localized and erratic irreversible particle rearrangements due to the motion of structural defects. In this regime, oscillatory shear promotes defect annealing and leads to the growth of large crystalline domains. Numerical simulations help identify the population of rearranging particles with those exhibiting the largest deviatoric stresses and indicate that structural evolution proceeds towards the minimization of the stress stored in the system. The particles showing high deviatoric stresses are localized around grain boundaries and defects, providing a simple criterion to spot regions likely to rearrange plastically under oscillatory shear.

In this paper we introduce a fully flexible coarse-grained model of immunoglobulin G (IgG) antibodies parametrized directly on cryo-EM data and simulate the binding dynamics of many IgGs to antigens adsorbed on a surface at increasing densities. Moreover, we work out a theoretical model that allows to explain all the features observed in the simulations. Our combined computational and theoretical framework is in excellent agreement with surface-plasmon resonance data and allows us to establish a number of important results. (i) Internal flexibility is key to maximize bivalent binding, flexible IgGs being able to explore the surface with their second arm in search for an available hapten. This is made clear by the strongly reduced ability to bind with both arms displayed by artificial IgGs designed to rigidly keep a prescribed shape. (ii) The large size of IgGs is instrumental to keep neighboring molecules at a certain distance (surface repulsion), which essentially makes antigens within reach of the second Fab always unoccupied on average. (iii) One needs to account independently for the thermodynamic and geometric factors that regulate the binding equilibrium. The key geometrical parameters, besides excluded-volume repulsion, describe the screening of free haptens by neighboring bound antibodies. We prove that the thermodynamic parameters govern the low-antigen-concentration regime, while the surface screening and repulsion only affect the binding at high hapten densities. Importantly, we prove that screening effects are concealed in relative measures, such as the fraction of bivalently bound antibodies. Overall, our model provides a valuable, accurate theoretical paradigm beyond existing frameworks to interpret experimental profiles of antibodies binding to multi-valent surfaces of different sorts in many contexts.

We show that, while the gelation of colloidal silica proceeds much faster in the presence of added KCl than NaCl, the final gels are very similar in structure and properties. We have studied the gelation process by visual inspection and by small angle X-ray scattering for a range of salt and silica particle concentrations. The characteristic times of the early aggregation process and the formation of a stress-bearing structure with both salts are shown to collapse onto master curves with single multiplicative constants, linked to the stability ratio of the colloidal suspensions. The influence of the salt type and concentration is confirmed to be mainly kinetic, as the static structure factors and viscoelastic moduli of the gels are shown to be equivalent at normalized times. While there is strong variation in the kinetics, the structure and properties of the gel at long-times are shown to be mainly controlled by the concentration of particles, and hardly influenced by the type or the concentration of salt. This suggests that the differences between gels generated by different salts are only transient in time., (Copyright © 2015 Elsevier Inc. All rights reserved.)

We consider two schematic models of glasses subjected to oscillatory shear deformation, motivated by the observations, in computer simulations of a model glass, of a nonequilibrium transition from a localized to a diffusive regime as the shear amplitude is increased, and of persistent memory effects in the localized regime. The first of these schematic models is the NK model, a spin model with disordered multi-spin interactions previously studied as a model for sheared amorphous solids. The second model, a transition matrix model, is an abstract formulation of the manner in which occupancy of local energy minima evolves under oscillatory deformation cycles. In both of these models, we find a behavior similar to that of an atomic model glass studied earlier. We discuss possible further extensions of the approaches outlined.

We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.

We show that memory can be encoded in a model amorphous solid subjected to athermal oscillatory shear deformations, and in an analogous spin model with disordered interactions, sharing the feature of a deformable energy landscape. When these systems are subjected to oscillatory shear deformation, they retain memory of the deformation amplitude imposed in the training phase, when the amplitude is below a "localization" threshold. Remarkably, multiple persistent memories can be stored using such an athermal, noise-free, protocol. The possibility of such memory is shown to be linked to the presence of plastic deformations and associated limit cycles traversed by the system, which exhibit avalanche statistics also seen in related contexts.

We report computer simulations of oscillatory athermal quasistatic shear deformation of dense amorphous samples of a three-dimensional model glass former. A dynamical transition is observed as the amplitude of the deformation is varied: For large values of the amplitude the system exhibits diffusive behavior and loss of memory of the initial conditions, whereas localization is observed for small amplitudes. Our results suggest that the same kind of transition found in driven colloidal systems is present in the case of amorphous solids (e.g., metallic glasses). The onset of the transition is shown to be related to the onset of energy dissipation. Shear banding is observed for large system sizes, without, however, affecting qualitative aspects of the transition.

More than 60 years of biochemical and biophysical studies have accustomed us to think of proteins as highly purified entities that act in isolation, more or less freely diffusing until they find their cognate partner to bind to. While in vitro experiments that reproduce these conditions largely remain the only way to investigate the intrinsic properties of molecules, this approach ignores an important factor: in their natural milieu , proteins are surrounded by several other molecules of different chemical nature, and this crowded environment can considerably modify their behaviour. About 40% of the cellular volume on average is occupied by all sorts of molecules. Furthermore, biological macromolecules live and operate in an extremely structured and complex environment within the cell (endoplasmic reticulum, Golgi apparatus, cytoskeletal structures, etc). Hence, to further complicate the picture, the interior of the cell is by no means a simply crowded medium, rather, a most crowded and confining one. In recent times, several approaches have been developed in the attempt to take into account important factors such as the ones mentioned above, at both theoretical and experimental levels, so that this field of research is now emerging as one of the most thriving in molecular and cell biology (see figure 1). [Formula: see text] Figure 1. Left: number of articles containing the word 'crowding' as a keyword limited to the biological and chemical science domains (source: ISI Web of Science). The arrow flags the 2003 'EMBO Workshop on Biological Implications of Macromolecular Crowding' (Embo, 2012). Right: number of citations to articles containing the word 'crowding' limited to the same domains (bars) and an exponential regression curve (source: Elsevier Scopus). To promote the importance of molecular crowding and confinement and provide researchers active in this field an interdisciplinary forum for meeting and exchanging ideas, we recently organized an international conference held in Ascona from 10 to 14 June 2012. In the unique scenario of the Maggiore lake and absorbed in the magic atmosphere of the Centro Stefano Franscini (CSF) at Monte Verità, we enjoyed three-and-a-half days of intense and inspiring activity, where not only many of the most prominent scientists working on macromolecular crowding, but also experts in closely related fields such as colloids and soft matter presented their work. The meeting was intended and has been organized to bring theoreticians and experimentalists together in the attempt to promote an active dialogue. Moreover, we wanted different disciplines to be represented, notably physics and chemistry, besides biology, as cross-fertilization is proving an increasingly fundamental source of inspiration and advancement. This issue of Physical Biology (PB) features a selection of the oral contributions presented at the conference, expanded in the form of research or review articles. PB, one of the scientific journals of the Institute of Physics (IOP), is one of the most dynamic and lively forums active at the interface between biology on one side, and physics and mathematics on the other. As its mission is stated by IOP, PB 'focuses on research in which physics-based approaches lead to new insights into biological systems at all scales of space and time, and all levels of complexity'. For these reasons, and also in view of its high reputation and broad readership, PB appears to be the ideal place for disseminating the thriving pieces of research presented at the conference. We are extremely grateful to PB and its kind and efficient editorial staff who helped make this issue a great scientific follow-up to the conference. The opening lecture of the conference, the first of four day-opening keynote lectures, was given by Allen P Minton from NIH (USA), possibly the most influential among the pioneers in the field. He provided a lucid and well-thought-out overview of the concept of macromolecular crowding through an exhaustive chronological account of the major milestones. It is clear that the concept of excluded volume as a key factor remains central to the concept of molecular crowding. As a consequence, simple descriptive paradigms borrowed essentially from colloid physics may still provide useful tools to understand the subtle effects of crowding and confinement in living matter. The contiguity between crowding, colloids and soft matter further emerged as an important concept in the course of the conference in several theoretical lectures and a few experimental ones. Dave Thirumalai, from the University of Maryland (USA), one of the most active theoreticians in the field of theoretical biophysics, outlined scaling theories, concepts from colloid literature and different simulation techniques to describe scenarios for crowding-induced changes in the structure and dynamics of proteins and RNA. In particular, he showed the importance of the shape of crowding particles in affecting folding oligomerization of amyloidogenic peptides. Johannes Schöneberg, from IMPRS, Mathematics Institute (Germany), illustrated ReaDDy , a newly developed particle-based simulation software tool for reaction-diffusion dynamics, developed in the group of Frank Noe at EMPRS. He showed that ReaDDy makes it possible to bridge the gap between soft matter and molecular dynamics (MD) simulations on the one hand and particle-based stochastic reaction-diffusion simulations on the other. We asked Johannes to organize a tutorial session to lead interested participants into the package and 'get their hands wet' under the guidance of the developers. The tutorial session was indeed successful and the broad possibilities offered by the simulation toolkit appeared to be clear to the participants. Paolo De Los Rios, from the Ecole Polytechnique Fédérale de Lausanne (EPFL, Switzerland), examined the complexity of the effects caused by crowding conditions from the point of view of statistical physics. Starting from a modification of the well-known Smoluchowski approach to calculate the encounter rate of diffusion-limited reactions, he showed how more realistic situations accounting for crowding effects could be treated equally well on the same theoretical grounds. This talk marked an important point in the conference as it reinforced the idea that simple models of theoretical physics still have the power to provide inspiring results in spite of the intrinsic simplifications of such theoretical approaches. Along the same lines, Nicolas Dorsaz, from the University of Cambridge (UK), proposed an extension of the Smoluchowski framework that incorporates repulsive and attracting interactions between the reactants. This approach was illustrated by reaction rates obtained from event-driven Brownian dynamics and dynamical Monte Carlo simulations. Another striking example of the physical subtleties associated with modelling crowding effects was provided by Jeffrey Skolnick, from the Georgia Institute of Technology (USA). He examined the role of hydrodynamic interactions in the self-organization of biological assemblies in the presence of crowding. His results strongly suggest that hydrodynamic interactions greatly affect the kinetics of self-assembly reactions, so that including them in the picture appears crucial for understanding the dynamics of biological systems in vivo . Margareth Cheung, from the University of Houston (USA), emphasized that how the crowded environment inside a cell affects the structural conformation of a protein with a spherical shape is a vital question because the geometry of proteins and protein-protein complexes are far from globules in vivo . Her work demonstrates the malleability of 'native' proteins and implies that crowding-induced shape changes may be important for protein function and malfunction in vivo . Huan-Xiang Zhou, from the Florida State University (USA), focused on atomistic simulations of protein folding and binding under crowding conditions. His lab has developed a post-processing method that allows the atomistic representation of proteins in folding and binding processes under crowding. A comparison with experimental results was also presented. Other lecturers pointed out that there are still aspects not entirely explored in the effects of both crowding and confinement. As suggested in the talk by Gary Pielak, from the University of North Carolina (USA), the currently used synthetic crowding agents are far from being satisfactory in replicating naturally occurring effects associated with crowded environments. For example, non-specific binding seems to play a subtle role in the cell, as natural macromolecules can induce both stabilization and destabilization when used as crowders. It is indeed possible to fine-tune the effect of proteins, as crowders, on the stability of other proteins. Another aspect that became clear is that new, more powerful methods need to be developed to study the effect of crowding, but even more to compare crowding and confinement. Indeed, it appeared clear from the lecture by Pierandrea Temussi, from the University of Naples (Italy), that a reliable comparison of the effects of crowding and confinement on the stability of proteins can only be based on the measurement of the whole stability curve of the same protein. Controversial aspects do not pertain only to the influence of crowding on protein stability, but also to aggregation phenomena in natural fluids. Domenico Sanfelice, from NIMR (London, UK), reported an interesting case of the apparent influence of crowding on aggregation. Hen egg white, a possible natural medium to study macromolecules in crowded conditions can dramatically increase the aggregation kinetics of proteins with an inbuilt tendency to associate. By carefully dissecting the phenomenology, it was shown that only part of this effect is due to crowding, while another factor playing an important role is the interaction with proteins from the milieu . In other words, high-molecular-weight glycoproteins can act as efficient molecular seeds for aggregation. A special topic of great relevance in the conference appeared to be the direct study of crowding in living systems. Alan Verkman, from the University of California, San Francisco (USA), one of the world's leading scientific personalities in the field of experimental investigation of crowding and confinement, was invited to give the second plenary lecture devoted to the experimental study of crowding effects in vivo . In his keynote lecture, Dr Verkman led us on a wide and compelling tour, exploring the main experimental approaches to study molecular crowding in and around cells. After a thorough examination of methods such as fluorescence recovery after photo-bleaching, fluorescence correlation spectroscopy, photo-activation localization microscopy and stochastic reconstruction microscopy, he concluded that the general consensus emerging from experimental studies is that the notion of universally anomalous diffusion in and around cells as a consequence of molecular crowding may not be correct, and that the slowing of diffusion in cells is less marked than has been widely assumed and can be simply described through a five- to sixfold reduction of the normal diffusion coefficient. A Soranno, from the University of Zürich (Switzerland), described how, by employing FRET measurements, it is possible to quantify the effect of molecular crowding on the dimensions of the highly charged, intrinsically disordered protein human prothymosin alpha. For a large variety of polymeric crowders (PEG, PVP, Ficoll, Dextran, PVA, PAA), a collapse of the polypeptide chain is observed with increasing polymer size and polymer concentration. The largest extent of collapse is observed for polymer radii comparable to the dimensions of the protein, in agreement with theoretical considerations. For his contribution, A Soranno was awarded the CSF Award for the best contributed talk. In his most inspiring talk, Clifford Brangwynne, from Princeton University (USA), drew attention to very important objects, namely Ribonucleoprotein (RNP) bodies. These are non-membrane-bound macromolecular assemblies that form from the dynamic interactions of RNA and proteins. The assembly of RNP bodies may sensitively depend on the biophysical features of the surrounding cytoplasm, including the degree of crowding, transport coefficients and mechanical properties. This dependency may have important implications for the RNA processing reactions involved in fundamental biological processes such as developmental cell growth. Remarkably, Brangwynne showed how RNPs behave in the cell as liquid droplets, pointing to a possible entirely new means that the cell could use to control and fine-tune its internal processes, in fact, more than that, a completely unexplored, new state of organization of living matter, and a functional one. Giuseppe Zaccai, from Institut Laue Langevin, Grenoble (France), showed that protein dynamics is more sensitive than structure to environmental factors such as crowding, solvent, temperature or pressure. Furthermore, he convincingly explained how neutron scattering provides unique experimental data to underpin MD calculations in this context. Following up on environment-induced modulations of protein functional dynamics, Ruth Nussinov, from Tel Aviv University (Israel), addressed the important problem of whether cellular signals can travel long distances in a crowded environment. She proposed a model based on the evolution of at least three properties: a modular functional organization of the cellular network, sequences in some key regions of proteins, such as linkers or loops, and compact interactions between proteins, possibly favoured by a crowded environment. The workshop ended on a keynote lecture by Jean-Marie Lehn, from the Université de Strasbourg (France). Lehn, 1987 Nobel Laureate in chemistry, offered a 'supramolecular view' of the field of molecular interactions. Supramolecular chemistry explores the design of systems undergoing self-organization , i.e. systems capable of generating well-defined functional supramolecular architectures by self-assembling from their components, thus behaving as programmed chemical systems . Chemistry may therefore be considered an information science , the science of informed matter. Supramolecular chemistry is intrinsically a dynamic chemistry in view of the ability of the interactions connecting the molecular components of a supramolecular entity and the resulting ability of supramolecular species to exchange their constituents. The same holds for molecular chemistry when the molecular entity contains covalent bonds that may form and break reversibly, so as to allow a continuous change in constitution by the reorganization and exchange of building blocks. These features define a constitutional dynamic chemistry (CDC) on both the molecular and supramolecular levels. CDC takes advantage of dynamic constitutional diversity to allow variation and selection in response to either internal or external factors to achieve adaptation . The merging of the features-information and programmability, dynamics and reversibility, constitution and structural diversity-points towards the emergence of adaptive and evolutive chemistry . The whole workshop could have not taken place without the help of the Centro Stefano Franscini. The CSF is the congress centre of the Swiss Federal Institute of Technology of Zurich (ETH Zurich) and has been situated at Monte Verità since 1989. It is an ideal meeting point for all members of the international scientific community who wish to discuss the state-of-the-art and new challenges of any field of research. The CSF supports 20-25 international conferences every year and, since 2010, up to ten winter doctoral schools 1 . The competence and professionalism of the staff were at the same level of beauty and inspiring character as that of Monte Verità. A meeting of this sort, if successful, leaves the audience with more open questions than settled answers, and this was definitely the case for Crowding 2012. Excluded volume is clearly a fundamental concept that has allowed crowding, a very familiar concept in soft matter, to enter into the domain of biological sciences. However, the complexity of the biological milieu calls for more refined descriptions. What is the role of electrostatic and electrodynamic interactions? What is the role of hydrodynamics interactions? To what extent does the strong spatial inhomogeneity (clustering of molecules, cellular compartmentalization, etc) have to be taken into account? Or, more generally, what are the minimal elements that prove crucial to describe reactions within a cell? How does the diffusion proceed (diffusion, slow diffusion, sub-diffusion) given that the experimental evidences are still controversial? In conclusion, we knew that allowing scientists with very different backgrounds and ideas to mingle was a hazardous attempt. Despite that, the workshop turned out to be a very successful experiment, which was highly enjoyed both by the participants and the organizers. Discussions sparked regularly among ever-changing groups, comprising senior scientists and students, despite the rather tight schedule, adding to the sense of fulfilment ignited by the outstanding level of the presentations. Given the success of the meeting Crowding 2012, a new event has been organized and will take place on the same themes during fall 2013, this time in the beautiful scenery of the Loire valley in France. The workshop 'Macromolecular crowding effects in cell biology: models and experiments' will be held on the CNRS campus in Orléans, France, on 24-25 October 2013. More information can be found on the workshop website: http://dirac.cnrs-orleans.fr/∼piazza/. 1 Source: www.csf.ethz.ch/

We investigate numerically pseudo-first-order irreversible bimolecular reactions of the type A + B → B between hard spheres undergoing event-driven Brownian dynamics. We study the encounter rate and the survival probability of A particles as functions of the packing fraction ϕ in the trapping (a single particle diffusing among static non-overlapping traps) and target (many traps diffusing in the presence of a single static target particle) settings, as well as in the case of diffusing traps and particles (full mobility). We show that, since inertial effects are accounted for in our simulation protocol, the standard Smoluchowski theory of coagulation of non-interacting colloids is recovered only at times greater than a characteristic time Δt, marking the transition from the under-damped to the over-damped regime. We show that the survival probability S(t) decays exponentially during this first stage, with a rate 1/τ0 is proportional to φ. Furthermore, we work out a simple analytical expression that is able to capture to an excellent extent the numerical results for t < Δt at low and intermediate densities. Moreover, we demonstrate that the time constant of the asymptotic exponential decay of S(t) for diffusing traps and particles is k(S)(-1), where kS = 4π(DA + DB)Rρ is the Smoluchowski rate. Detailed analyses of the effective decay exponent β = d [log(-logS(t))]/d (logt) and of the steady-state encounter rate reveal that the full mobility and trapping problem are characterized by very similar kinetics, rather different from the target problem. Our results do not allow one to ascertain whether the prediction S(t) is proportional to exp(-at(3/2)) (a = const.) as t → ∞ for the trapping problem in 3D is indeed recovered. In fact, at high density, S(t) is dominated by short encounter times, which makes it exceedingly hard to record the events corresponding to the exploration of large, trap-free regions. As a consequence, at high densities the steady-state rate simply tends to 1/τ0. Finally, we work out an analytical formula for the rate that shows a remarkable agreement with the numerics up φ = 0.4.