Sozza A., Piazza F., Cencini M., De Lillo F. and Boffetta G. (

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate themethod, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of themethod by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

Sozza A., Piazza F., Cencini M., De Lillo F. and Boffetta G. (

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study the configurations of multiple absorbers of increasing complexity to examine the performance of the method by comparing our simulations with available exact analytical or numerical results. We demonstrate the potential of the method to resolve the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudospectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry, and related sciences.

Galanti M., Fanelli D. and Piazza F. (

Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level. In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.

Correction for ’Theory of diffusion-influenced reactions in complex geometries’ by Marta Galanti et al., Phys. Chem. Chem. Phys., 2016, DOI : 10.1039/c6cp01147k.

Chemical transformations involving the diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced reactions" (DIR). Virtually all biochemical processes in living media can be counted among them, together with those occurring in an ever-growing number of emerging nano-technologies. The role of the environment’s geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) is key in modulating the rate constants of DIRs, and is therefore a prime design parameter. Yet, it is a formidable challenge to build a comprehensive theory that is able to describe the environment’s "reactive geometry". Here we show that such a theory can be built by unfolding this many-body problem through addition theorems for special functions. Our method is powerful and general and allows one to study a given DIR reaction occurring in arbitrary "reactive landscapes", made of multiple spherical boundaries of given size and reactivity. Importantly, ready-to-use analytical formulas can be derived easily in most cases.

We present a detailed theory for the total reaction rate constant of a composite core-shell nanoreactor, consisting of a central solid core surrounded by a hydrogel layer of variable thickness, where a given number of small catalytic nanoparticles are embedded at prescribed positions and are endowed with a prescribed surface reaction rate constant. Besides the precise geometry of the assembly, our theory accounts explicitly for the diffusion coefficients of the reactants in the hydrogel and in the bulk as well as for their transfer free energy jump upon entering the hydrogel shell. Moreover, we work out an approximate analytical formula for the overall rate constant, which is valid in the physically relevant range of geometrical and chemical parameters. We discuss in depth how the diffusion-controlled part of the rate depends on the essential variables, including the size of the central core. In particular, we derive some simple rules for estimating the number of nanocatalysts per nanoreactor for an efficient catalytic performance in the case of small to intermediate core sizes. Our theoretical treatment promises to provide a very useful and flexible tool for the design of superior performing nanoreactor geometries with optimized nanoparticle load.

Antibodies are large, extremely flexible molecules, whose internal dynamics is certainly key to their astounding ability to bind antigens of all sizes, from small hormones to giant viruses. In this paper, we build a shape-based coarse-grained model of IgG molecules and show that it can be used to generate 3D conformations in agreement with single-molecule Cryo-Electron Tomography data. Furthermore, we elaborate a theoretical model that can be solved exactly to compute the binding rate constant of a small antigen to an IgG in a prescribed 3D conformation. Our model shows that the antigen binding process is tightly related to the internal dynamics of the IgG. Our findings pave the way for further investigation of the subtle connection between the dynamics and the function of large, flexible multi-valent molecular machines.

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.

Piazza F. and Traytak S. D. (

Hollow nanostructures are paid increasing attention in many nanotechnology-related communities in view of their numerous applications in chemistry and biotechnology, e.g. as smart nanoreactors or drug-delivery systems. In this paper we consider irreversible, diffusion-influenced reactions occurring within a hollow spherical cavity endowed with a circular hole on its surface. Importantly, our model is not limited to small sizes of the aperture. In our scheme, reactants can freely diffuse inside and outside the cavity through the hole, and react at a spherical boundary of given size encapsulated in the chamber and endowed with a given intrinsic rate constant. We work out the solution of the above problem, enabling one to compute the reaction rate constant to any desired accuracy. Remarkably, we show that, in the case of narrow holes, the rate constant is extremely well-approximated by a simple formula that can be derived on the basis of simple physical arguments and that can be readily employed to analyze experimental data.

The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.

In this paper we consider the problem of optimal search strategies on multi-linked networks, i.e. graphs whose nodes are endowed with several independent sets of links. We focus preliminarily on agents randomly hopping along the links of a graph, with the additional possibility of performing non-local hops to randomly chosen nodes with a given probability. We show that an optimal combination of the two jump rules exists that maximises the efficiency of target search, the optimum reflecting the topology of the network. We then generalize our results to multi-linked networks with an arbitrary number of mutually interfering link sets.

The competition for access to space that arises between macromolecules is the basis of the macromolecular crowding phenomenon, known to modulate biochemical reactions in subtle ways. Crowding is a highly conserved physiological condition in and around cells in metazoans, and originates from a mixture of heterogeneous biomolecules. Here, using collagen fibrillogenesis as an experimental test platform and ideas from the theory of nonideal solutions, we show that an entropy-based synergy is created by a mixture of two different populations of artificial crowders, providing small crowders with extra volume occupancy when in the vicinity of bigger crowders. We present the physiological mechanism by which synergistic effects maximize volume exclusion with the minimum amount of heterogeneous crowders, demonstrating how the evolutionarily optimized crowded conditions found in vivo can be reproduced effectively in vitro.

Predicting function-related amino acids in proteins with unknown function or unknown allosteric binding sites in drug-targeted proteins is a task of paramount importance in molecular biomedicine. In this paper we introduce a simple, light and computationally inexpensive structure-based method to identify catalytic sites in enzymes. Our method, termed cutoff lensing, is a general procedure consisting in letting the cutoff used to build an elastic network model increase to large values. A validation of our method against a large database of annotated enzymes shows that optimal values of the cutoff exist such that three different structure-based indicators allow one to recover a maximum of the known catalytic sites. Interestingly, we find that the larger the structures the greater the predictive power afforded by our method. Possible ways to combine the three indicators into a single figure of merit and into a specific sequential analysis are suggested and discussed with reference to the classic case of HIV-protease. Our method could be used as a complement to other sequence- and/or structure-based methods to narrow the results of large-scale screenings.

Piazza F. (

In this paper we propose a novel theoretical framework for interpreting long-range dynamical correlations unveiled in proteins through NMR measurements. The theoretical rationale relies on the hypothesis that correlated motions in proteins may be reconstructed as large-scale, collective modes sustained by long-lived nonlinear vibrations known as discrete breathers (DB) localized at key, hot-spot sites. DBs are spatially localized modes, whose nonlinear nature hinders resonant coupling with the normal modes, thus conferring them long lifetimes as compared to normal modes. DBs have been predicted to exist in proteins, localized at few hot-spot residues typically within the stiffest portions of the structure. We compute DB modes analytically in the framework of the nonlinear network model, showing that the displacement patterns of many DBs localized at key sites match to a remarkable extent the experimentally uncovered correlation blueprint. The computed dispersion relations prove that it is physically possible for some of these DBs to be excited out of thermal fluctuations at room temperature. Based on our calculations, we speculate that transient energy redistribution among the vibrational modes in a protein might favor the emergence of DB-like bursts of long-lived energy at hot-spot sites with lifetimes in the ns range, able to sustain critical, function-encoding correlated motions. More generally, our calculations provide a novel quantitative tool to predict fold-spanning dynamical pathways of correlated residues that may be central to allosteric cross-talk in proteins.

The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability distribution function of the tagged particles obeys to a nonlinear Smoluchowski equation, where the force and diffusion terms are determined self-consistently by the concentration of crowders in the medium. Transient sub-diffusive or super-diffusive behaviors are observed, depending on the selected initial conditions, that bridge normal diffusion regimes characterized by different diffusion coefficients. These anomalous crossovers originate from the microscopic competition for space and reflect the peculiar form of the non-homogeneous force term in the governing equation. Our results strongly warn against the overly simplistic identification of crowding with anomalous transport tout court .

A new mechanism of catalysis is discussed, which is based on the rate-promoting effect of large-amplitude anharmonic

lattice vibrations, a.k.a. intrinsic localized modes or ‘discrete breathers’ (DBs), which can excite atoms at specific ‘active sites’

rather strongly, giving them energy far exceeding the energy of thermal vibrations for hundreds of oscillation periods. The

DB-induced modulation of activation energies (free energy barriers between reactants and products) results in a drastic

amplification of the reaction rates, which can be described by a simple analytical expression in the adiabatic limit. The striking

site selectiveness of DB excitation dynamics in the presence of spatial (quenched) disorder makes these nonlinear vibrations

viable candidates to play the role of ‘active modes’ in the catalytic process in various physical, chemical and biological systems.

We present herein a thorough description of the effects of high glucose concentrations on the diffusion, hydration and internal dynamics of ubiquitin, as predicted from extensive molecular dynamics simulations on several systems described at fully atomistic level. We observe that the protein acts as a seed that speeds up the natural propensity of glucose to cluster at high concentration ; the sugar molecules thus aggregate around the protein trapping it inside a dynamic cage. This process extensively dehydrates the protein surface, restricts the motions of the remaining water molecules, and drags the large-scale, collective motions of protein atoms slowing down the rate of exploration of the conformational space despite only a slight dampening of fast, local dynamics. We discuss how these effects could be relevant to the function of sugars as preservation agents in biological materials, and how crowding by small sticky molecules could modulate proteins across different reaction coordinates inside the cellular cytosol.

Piazza F., Foffi G. and De Michele C. (

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 varphi 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 Deltat, 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/tau0 is proportional to phi. Furthermore, we work out a simple analytical expression that is able to capture to an excellent extent the numerical results for t < Deltat 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 = 4pi(DA + DB)Rrho is the Smoluchowski rate. Detailed analyses of the effective decay exponent beta = 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 —> infinity 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/tau0. Finally, we work out an analytical formula for the rate that shows a remarkable agreement with the numerics up phi = 0.4.

In the real world, diffusion-limited reactions in chemistry and biology mostly occur in crowded environments, such as macromolecular complex formation in the cell. Despite the paramount importance of such phenomena, theoretical approaches still mainly rely on the Smoluchowski theory, only valid in the infinite dilution limit. In this paper we introduce a novel theoretical framework to describe the encounter rate and the stationary density profiles for encounters between an immobilized target and a fluid of interacting spherical particles, valid in the local density approximation. A comparison with numerical simulations performed for a fluid of hard spheres and square well attractive hard spheres confirms the accuracy of our treatment.

Here we report high-precision measurements of structural relaxation dynamics in the glass transition range at the intermediate and short length scale for a strong sodium silicate glass during long annealing times. We evidence for the first time the heterogeneous dynamics at the intermediate range order by probing the acoustic longitudinal frequency in the GHz region by Brillouin light scattering spectroscopy. Or, from in ?situ Raman measurements, we show that relaxation is indeed homogeneous at the interatomic length scale. Our results show that the dynamics at the intermediate range order contains two distinct relaxation time scales, a fast and a slow component, differing by about a 10-fold factor below Tg and approaching to one another past the glass transition. The slow relaxation time agrees with the shear relaxation time, proving that Si ?O bond breaking constitutes the primary control of structural relaxation at the intermediate range order.

Modelling the propagation of a pulse in a dense milieu poses fundamental challenges at the theoretical and applied levels. To this aim, in this paper we generalize the telegraph equation to non-ideal conditions by extending the concept of persistent random walk to account for spatial exclusion effects. This is achieved by introducing an explicit constraint in the hopping rates, that weights the occupancy of the target sites. We derive the mean-field equations, which display nonlinear terms that are important at high density. We compute the evolution of the mean square displacement (MSD) for pulses belonging to a specific class of spatially symmetric initial conditions. The MSD still displays a transition from ballistic to diffusive behaviour. We derive an analytical formula for the effective velocity of the ballistic stage, which is shown to depend in a nontrivial fashion upon both the density (area) and the shape of the initial pulse. After a density-dependent crossover time, nonlinear terms become negligible and normal diffusive behaviour is recovered at long times.

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 Verita, 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 Schoneberg, 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 Federale 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 Zurich (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 Universite 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 Verita 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 schools1. The competence and professionalism of the staff were at the same level of beauty and inspiring character as that of Monte Verita. 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 Orleans, France, on 24-25 October 2013. More information can be found on the workshop website : http://dirac.cnrs-orleans.fr/ approximately piazza/. Source : www.csf.ethz.ch/

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics.

Maffi, C., Baiesi, M., Casetti, L., Piazza, F. and De Los Rios, P. (

By shifting the balance between conformational entropy and internal energy, polymers modify their shape under external stimuli, such as changes in temperature. Prominent among such transformations is the coil-globule transition, whereby a polymer can switch from an entropy-dominated coil conformation to a globular one, governed by energy. The nature of the coil-globule transition has remained elusive, with evidence for both continuous and discontinuous transitions, with the two-state behaviour of proteins as an instance of the latter. Theoretical models mostly predict second-order transitions. Here we introduce a model that takes into consideration hitherto neglected features common to any polymer. We show that a first-order phase transition smoothly appears as a function of the model parameters. Our results can relieve part of the conflicts between theory and experiments in the field of protein folding, in the wake of recent studies tracing back the remarkable properties of proteins to basic polymer physics.

Piazza, F. and Sanejouand, Y. H. (

In this paper we investigate how energy is redistributed across protein structures, following localized kicks, within the framework of a nonlinear network model. We show that energy is directed most of the times to a few specific sites, systematically within the stiffest regions. This effect is sharpened as the energy of the kicks is increased, with fractions of transferred energy as high as 70% already for kicks above [20] kcal/mol. Remarkably, we show that such site-selective, high-yield transfers mark the spontaneous formation of spatially localized, time-periodic vibrations at the target sites, acting as efficient energy-collecting centers. A comparison of our simulations with a previously developed theory reveals that such energy-pinning modes are discrete breathers, able to carry energy across the structure in an quasi-coherent fashion by jumping from site to site.

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin, discrete breathers (DBs), emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. DBs are time-periodic, space-localized vibrational modes that exist generically in nonlinear discrete systems and are known for their resilience and ability to concentrate energy for long times. In the case of the small beta-barrel structure that we consider, DB-mediated localization occurs on the turns connecting the strands. At high energies, DBs stabilize the structure by concentrating energy on a few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of these two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.

In the diffusion model of chemical reactions, the encounter (reaction) rate between reactant particles is governed by the Smoluchowski equation, which is a diffusion equation in a field of forces. We consider crowded environments where the particles diffuse through a "liquid" of like particles. Assuming that the liquid-like short-range structure around the reactant gives rise to an effective (osmotic) barrier leads us to map a complicated many-body problem to a one-dimensional problem. This allows us to describe theoretically such complex systems that are encountered in many applications where crowding, intermolecular interactions, and simultaneously present. A particularly important effect is discovered which is due to the interplay between shear and crowding. This effect is responsible for unexpected peaks in the reactivity at low flow intensity which may explain, among other things, the bizarre colloidal stability behavior of concentrated protein suspensions.

Professeur , Biophysique théorique, simulation moléculaire et calcul scientifique