Duality in single-file diffusion

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems have been considered, such as the simple exclusion process (SEP), which has reached the status of a paradigmatic model. Several different models of single-file diffusion have been shown to be related by a duality relation, which holds either microscopically or only in the hydrodynamic limit of large time and large distances. Here we show that these relations are not specific to these models and that, in the hydrodynamic limit, every single-file system can be mapped onto a dual single-file system. This general duality relation allows to obtain new results for different models, by exploiting the solutions that are available for their dual

Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond

Tracer dynamics in the Symmetric Exclusion Process, where hardcore particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by an external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference, and higher-order moments but only in the high-density limit. Here, we provide a general hydrodynamic framework that allows us to determine the first cumulants of the bath-tracer correlations and of the tracer's position in function of the driving force, up to quadratic order (beyond linear response). This result constitutes the first determination of the bias-dependence of the variance of a driven tracer in the SEP for an arbitrary density. The framework presented here can be applied, beyond the SEP, to more general configurations of a driven tracer in interaction with obstacles in one dimension.Comment: 6 pages + 11 pages of supplementary material; update: minor typos correcte

Absolute negative mobility of an active tracer in a crowded environment

Absolute negative mobility (ANM) refers to the situation where the average velocity of a driven tracer is opposite to the direction of the driving force. This effect was evidenced in different models of nonequilibrium transport in complex environments, whose description remains effective. Here, we provide a microscopic theory for this phenomenon. We show that it emerges in the model of an active tracer particle submitted to an external force, and evolving on a discrete lattice populated with mobile passive crowders. Resorting to a decoupling approximation, we compute analytically the velocity of the tracer particle as a function of the different parameters of the system, and confront our results to numerical simulations. We determine the range of parameters where ANM can be observed, characterize the response of the environment to the displacement of the tracer, and clarify the mechanism underlying ANM and its relationship with negative differential mobility (another hallmark of driven systems far from the linear response)

Joint distribution of currents in the symmetric exclusion process

The symmetric simple exclusion process (SEP) is a paradigmatic model of diffusion in a single-file geometry, in which the particles cannot cross. In this model, the study of currents have attracted a lot of attention. In particular, the distribution of the integrated current through the origin, and more recently, of the integrated current through a moving reference point, have been obtained in the long time limit. This latter observable is particularly interesting, as it allows to obtain the distribution of the position of a tracer particle. However, up to now, these different observables have been considered independently. Here, we characterise the joint statistical properties of these currents, and their correlations with the density of particles. We show that the correlations satisfy closed integral equations, which generalise the ones obtained recently for a single observable. We also obtain boundary conditions verified by these correlations, which take a simple physical form for any single-file system. As a consequence of our results, we quantify the correlations between the displacement of a tracer, and the integrated current of particles through the origin.Comment: 29 pages, 3 figur

Exact spatial correlations in single-file diffusion

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behaviour results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles. Despite their importance, these bath-tracer correlations have long remained elusive, because their determination is a complex many-body problem. Recently, we have shown that, for several paradigmatic models of single-file diffusion such as the Simple Exclusion Process, these bath-tracer correlations obey a simple exact closed equation. In this paper, we provide the full derivation of this equation, as well as an extension to another model of single-file transport: the double exclusion process. We also make the connection between our results and the ones obtained very recently by several other groups, and which rely on the exact solution of different models obtained by the inverse scattering method.Comment: 32 pages, 9 figure

Universal Correlation Profiles in Single-File Systems

Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which have recently been shown to play a central role in single-file systems. Up to now, these correlations have only been determined for diffusive systems in the hydrodynamic limit. Here, we consider a model of reflecting point particles on the infinite line, with a general individual stochastic dynamics. We show that the correlation profiles take a simple universal form, at arbitrary time. We illustrate our approach by the study the integrated current of particles through the origin, and apply our results to representative models such as Brownian particles, run-and-tumble particles and L\'evy flights. We further emphasise the generality of our results by showing that they also apply beyond the 1d case, and to other observables.Comment: 6 pages, 7 figures + 14 pages of supplementary materia

Synthetic Peptides with Inadvertent Chemical Modifications Can Activate Potentially Autoreactive T Cells

The human CD8+ T cell clone 6C5 has previously been shown to recognize the tert-butyl-modified Bax161–170 peptide LLSY(3-tBu)FGTPT presented by HLA-A*02:01. This nonnatural epitope was likely created as a by-product of fluorenylmethoxycarbonyl protecting group peptide synthesis and bound poorly to HLA-A*02:01. In this study, we used a systematic approach to identify and characterize natural ligands for the 6C5 TCR. Functional analyses revealed that 6C5 T cells only recognized the LLSYFGTPT peptide when tBu was added to the tyrosine residue and did not recognize the LLSYFGTPT peptide modified with larger (di-tBu) or smaller chemical groups (Me). Combinatorial peptide library screening further showed that 6C5 T cells recognized a series of self-derived peptides with dissimilar amino acid sequences to LLSY(3-tBu)FGTPT. Structural studies of LLSY(3-tBu)FGTPT and two other activating nonamers (IIGWMWIPV and LLGWVFAQV) in complex with HLA-A*02:01 demonstrated similar overall peptide conformations and highlighted the importance of the position (P) 4 residue for T cell recognition, particularly the capacity of the bulky amino acid tryptophan to substitute for the tBu-modified tyrosine residue in conjunction with other changes at P5 and P6. Collectively, these results indicated that chemical modifications directly altered the immunogenicity of a synthetic peptide via molecular mimicry, leading to the inadvertent activation of a T cell clone with unexpected and potentially autoreactive specificities

Crystal structure of enhanced green fluorescent protein to 1.35 Å resolution reveals alternative conformations for Glu222

Enhanced Green Fluorescent Protein (EGFP) is one of the most widely used engineered variants of the original wild-type Green Fluorescent Protein. Here, we report the high resolution (1.35 Å) structure of EGFP crystallised in its untagged sequence form that reveals the combined impact of the F64L and S65T, that give rise to improved folding and spectral characteristics. The overall structure of EGFP is very similar to wt GFP, forming the classical β-barrel fold with the chromophore containing helix running through the core of the structure. Replacement of Phe64 with Leu in EGFP results in subtle rearrangement of hydrophobic core packing close to the chromophore including the reduction in surface exposure of two hydrophobic residues. Replacement of Ser65 with Thr has a significant impact on the local hydrogen bond network in the vicinity of the chromophore. Detailed analysis of electron density reveals that several residues close to the chromophore occupy at least two distinct conformations. This includes Glu222 that defines the charged state on the chromophore, with the two conformations having slightly different effects on the hydrogen bond network surrounding the chromophore. Hence, the reported high-resolution structure of EGFP has provided a long overdue molecular description of one of the most important fluorescent protein variants currently in general use

Molecular basis for functional switching of GFP by two disparate non-native post-translational modifications of a phenyl azide reaction handle

Through the genetic incorporation of a single phenyl azide group into superfolder GFP (sfGFP) at residue 148 we provide a molecular description of how this highly versatile chemical handle can be used to positively switch protein function in vitro and in vivo via either photochemistry or bioconjugation. Replacement of H148 with p-azido-L-phenylalanine (azF) blue shifts the major excitation peak ∼90 nm by disrupting the H-bond and proton transfer network that defines the chromophore charged state. Bioorthogonal click modification with a simple dibenzylcyclooctyne or UV irradiation shifts the neutral-anionic chromophore equilibrium, switching fluorescence to the optimal ∼490 nm excitation. Click modification also improved quantum yield over both the unmodified and original protein. Crystal structures of both the click modified and photochemically converted forms show that functional switching is due to local conformational changes that optimise the interaction networks surrounding the chromophore. Crystal structure and mass spectrometry studies of the irradiated protein suggest that the phenyl azide converts to a dehydroazepine and/or an azepinone. Thus, protein embedded phenyl azides can be used beyond simple photocrosslinkers and passive conjugation handles, and mimic many natural post-translational modifications: modulation though changes in interaction networks

Conformationally restricted calpain inhibitors

The cysteine protease calpain-I is linked to several diseases and is therefore a valuable target for inhibition. Selective inhibition of calpain-I has proved difficult as most compounds target the active site and inhibit a broad spectrum of cysteine proteases as well as other calpain isoforms. Selective inhibitors might not only be potential drugs but should act as tools to explore the physiological and pathophysiological roles of calpain-I. α-Mercaptoacrylic acid based calpain inhibitors are potent, cell permeable and selective inhibitors of calpain-I and calpain-II. These inhibitors target the calcium binding domain PEF(S) of calpain-I and -II. Here X-ray diffraction analysis of co-crystals of PEF(S) revealed that the disulfide form of an α-mercaptoacrylic acid bound within a hydrophobic groove that is also targeted by a calpastatin inhibitory region and made a greater number of favourable interactions with the protein than the reduced sulfhydryl form. Measurement of the inhibitory potency of the α-mercaptoacrylic acids and X-ray crystallography revealed that the IC50 values decreased significantly on oxidation as a consequence of the stereo-electronic properties of disulfide bonds that restrict rotation around the S–S bond. Consequently, thioether analogues inhibited calpain-I with potencies similar to those of the free sulfhydryl forms of α-mercaptoacrylic acids