The macroscopic effects of microscopic heterogeneity

Over the past decade, advances in super-resolution microscopy and particle-based modeling have driven an intense interest in investigating spatial heterogeneity at the level of single molecules in cells. Remarkably, it is becoming clear that spatiotemporal correlations between just a few molecules can have profound effects on the signaling behavior of the entire cell. While such correlations are often explicitly imposed by molecular structures such as rafts, clusters, or scaffolds, they also arise intrinsically, due strictly to the small numbers of molecules involved, the finite speed of diffusion, and the effects of macromolecular crowding. In this chapter we review examples of both explicitly imposed and intrinsic correlations, focusing on the mechanisms by which microscopic heterogeneity is amplified to macroscopic effect.Comment: 20 pages, 5 figures. To appear in Advances in Chemical Physic

A two-domain elevator mechanism for sodium/proton antiport

Sodium/proton (Na+/H+) antiporters, located at the plasma membrane in every cell, are vital for cell homeostasis1. In humans, their dysfunction has been linked to diseases, such as hypertension, heart failure and epilepsy, and they are well-established drug targets2. The best understood model system for Na+/H+ antiport is NhaA from Escherichia coli1, 3, for which both electron microscopy and crystal structures are available4, 5, 6. NhaA is made up of two distinct domains: a core domain and a dimerization domain. In the NhaA crystal structure a cavity is located between the two domains, providing access to the ion-binding site from the inward-facing surface of the protein1, 4. Like many Na+/H+ antiporters, the activity of NhaA is regulated by pH, only becoming active above pH 6.5, at which point a conformational change is thought to occur7. The only reported NhaA crystal structure so far is of the low pH inactivated form4. Here we describe the active-state structure of a Na+/H+ antiporter, NapA from Thermus thermophilus, at 3 Å resolution, solved from crystals grown at pH 7.8. In the NapA structure, the core and dimerization domains are in different positions to those seen in NhaA, and a negatively charged cavity has now opened to the outside. The extracellular cavity allows access to a strictly conserved aspartate residue thought to coordinate ion binding1, 8, 9 directly, a role supported here by molecular dynamics simulations. To alternate access to this ion-binding site, however, requires a surprisingly large rotation of the core domain, some 20° against the dimerization interface. We conclude that despite their fast transport rates of up to 1,500 ions per second3, Na+/H+ antiporters operate by a two-domain rocking bundle model, revealing themes relevant to secondary-active transporters in general

Experimental and numerical signatures of dynamical crossover in orientationally disordered crystals

By means of NMR experiment and MD computer simulation we investigate the dynamical properties of a chloroadamantane orientationally disordered crystal. We find a plastic-plastic dynamical transition at T_x ~ 330 K in the pico-nanosecond regime. It is interpreted as the rotational analogue of the Goldstein crossing temperature between quasi-free diffusion and activated regime predicted in liquids. Below T_x, NMR experimental data are well described by a Frenkel model corresponding to a strongly anisotropic motion. At higher temperatures, a drastic deviation is observed toward quasi-isotropic rotational diffusion. Close to T_x, we observe that two-step relaxations emerge. An interpretation which is based on the present study of a specific heat anomaly detected by a recent calorimetric experiment is proposed.Comment: 4 pages, 4 figures; changed abstract and references; corrected figure

The conduction pathway of potassium channels is water free under physiological conditions.

Ion conduction through potassium channels is a fundamental process of life. On the basis of crystallographic data, it was originally proposed that potassium ions and water molecules are transported through the selectivity filter in an alternating arrangement, suggesting a "water-mediated" knock-on mechanism. Later on, this view was challenged by results from molecular dynamics simulations that revealed a "direct" knock-on mechanism where ions are in direct contact. Using solid-state nuclear magnetic resonance techniques tailored to characterize the interaction between water molecules and the ion channel, we show here that the selectivity filter of a potassium channel is free of water under physiological conditions. Our results are fully consistent with the direct knock-on mechanism of ion conduction but contradict the previously proposed water-mediated knock-on mechanism

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a power-law increase of the MSD, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations, non-gaussian distributions of the displacements, heterogeneous diffusion, and immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like FBM and Langevin equations for visco-elastic media, the CTRW model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Emphasis is put on the spatio-temporal properties of the transport in terms of 2-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even for identical MSDs. Then, we review the theory underlying common experimental techniques in the presence of anomalous transport: single-particle tracking, FCS, and FRAP. We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where model systems mimic physiological crowding conditions. Finally, computer simulations play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.Comment: review article, to appear in Rep. Prog. Phy

Salient Frame Detection for Molecular Dynamics Simulations

Recent advances in sophisticated computational techniques have facilitated simulation of incrediblydetailed time-varying trajectories and in the process have generated vast quantities of simulation data. The current tools to analyze and comprehend large-scale time-varying data, however, lag far behind our ability to produce such simulation data. Saliency-based analysis can be applied to time-varying 3D datasets for the purpose of summarization, abstraction, and motion analysis. As the sizes of time-varying datasets continue to grow, it becomes more and more difficult to comprehend vast amounts of data and information in a short period of time. In this paper, we use eigenanalysis to generate orthogonal basis functions over sliding windows to characterize regions of unusual deviations and significant trends. Our results show that motion subspaces provide an effective technique for summarization of large molecular dynamics trajectories

Crystal structure of Hop2-Mnd1 and mechanistic insights into its role in meiotic recombination

In meiotic DNA recombination, the Hop2-Mnd1 complex promotes Dmc1-mediated single-stranded DNA (ssDNA) invasion into homologous chromosomes to form a synaptic complex by a yet-unclear mechanism. Here, the crystal structure of Hop2-Mnd1 reveals that it forms a curved rod-like structure consisting of three leucine zippers and two kinked junctions. One end of the rod is linked to two juxtaposed winged-helix domains, and the other end is capped by extra ?-helices to form a helical bundle-like structure. Deletion analysis shows that the helical bundle-like structure is sufficient for interacting with the Dmc1-ssDNA nucleofilament, and molecular modeling suggests that the curved rod could be accommodated into the helical groove of the nucleofilament. Remarkably, the winged-helix domains are juxtaposed at fixed relative orientation, and their binding to DNA is likely to perturb the base pairing according to molecular simulations. These findings allow us to propose a model explaining how Hop2-Mnd1 juxtaposes Dmc1-bound ssDNA with distorted recipient double-stranded DNA and thus facilitates strand invasion