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In school districts where assignments are exclusively determined by a clearinghouse students can only appeal their assignment with a valid reason. An assignment is incontestable if it is appeal-proof. We study incontestability when students do not observe the other students' preferences and assignments. Incontestability is shown to be equivalent to individual rationality, non-wastefulness, and respect for top-priority sets (a weakening of justified envy). Stable mechanisms and those Pareto dominating them are incontestable, as well as the Top-Trading Cycle mechanism (but Boston is not). Under a mild consistency property, incontestable mechanisms are i-indinstiguishable (Li, 2017), and share similar incentive properties.

We compare two jury selection procedures meant to safeguard against the inclusion of biased jurors that are perceived as causing minorities to be under-represented. The Strike and Replace procedure presents potential jurors one-by-one to the parties, while the Struck procedure presents all potential jurors before the parties exercise their challenges. Struck more effectively excludes extreme jurors but leads to a worse representation of minorities. The advantage of Struck in terms of excluding extremes is sizable in a wide range of cases. In contrast, Strike and Replace better represents minorities only if the minority and majority are polarized. Results are robust to assuming the parties statistically discriminate against jurors based on group identity.

Progress in hardware, algorithms, and force fields are pushing the scope of molecular dynamics (MD) simulations towards the length- and time scales of complex biochemical processes. This creates a need for developing advanced analysis methods tailored to the specific questions at hand. We present mxdrfile, a set of fast routines for manipulating the binary xtc and trr trajectory files formats of Gromacs, one of the most commonly used MD codes, with Matlab, a powerful and versatile language for scientific computing. The unique ability to both read and write binary trajectory files makes it possible to leverage the broad capabilities of Matlab to speed up and simplify the development of complex analysis and visualization methods. We illustrate these possibilities by implementing an alignment method for buckled surfaces, and use it to briefly dissect the curvature-dependent composition of a buckled lipid bilayer. The mxdrfile package, including the buckling example, is available as open source at http://kaplajon.github.io/mxdrfile/ ., Comment: 3 pages, 1 figure. Code: http://kaplajon.github.io/mxdrfile/ . SI movie: https://github.com/bmelinden/bucklemovie_magainin/

Symmetry is closely intertwined with the function, genetics, and chemical properties of multiprotein complexes. Here, we explore the relation between structural symmetry and the ability of membrane proteins to sense and induce membrane curvature, which is a key factor for modulating the shape and organization of cell membranes. Using coarse-grained simulations and elasticity theory, we show that the potential for direction-dependent membrane curvature sensing is limited to asymmetric proteins, dimers, and tetramers, and argue that one should expect this anisotropy to be strongest for dimers. Odd and higher-order symmetries strongly suppress directional curvature sensing. This classification gives a new perspective on the structure-function relation for membrane proteins, and simplifies the task of translating between molecular sensing mechanisms and their large-scale cellular consequences., Comment: 6 pages, 4 figures

Point-wise localization of individual fluorophores is a critical step in super-resolution microscopy and single particle tracking. Although the methods are limited by the accuracy in localizing individual flourophores, this point-wise accuracy has so far only been estimated by theoretical best case approximations, disregarding for example motional blur, out of focus broadening of the point spread function and time varying changes in the fluorescence background. Here, we show that pointwise localization uncertainty can be accurately estimated directly from imaging data using a Laplace approximation constrained by simple mircoscope properties. We further demonstrate that the estimated localization uncertainty can be used to improve downstream quantitative analysis, such as estimation of diffusion constants and detection of changes in molecular motion patterns. Most importantly, the accuracy of actual point localizations in live cell super-resolution microscopy can be improved beyond the information theoretic lower bound for localization errors in individual images, by modeling the fluorophores' movement and accounting for their point-wise localization uncertainty., Comment: Accompanying software available at https://github.com/bmelinden/uncertainSPT

Despite much scientific evidence, a large fraction of the American public doubts that greenhouse gases are causing global warming. We present a simulation model as a computational test-bed for climate prediction markets. Traders adapt their beliefs about future temperatures based on the profits of other traders in their social network. We simulate two alternative climate futures, in which global temperatures are primarily driven either by carbon dioxide or by solar irradiance. These represent, respectively, the scientific consensus and a hypothesis advanced by prominent skeptics. We conduct sensitivity analyses to determine how a variety of factors describing both the market and the physical climate may affect traders' beliefs about the cause of global climate change. Market participation causes most traders to converge quickly toward believing the "true" climate model, suggesting that a climate market could be useful for building public consensus., Comment: All code and data for the model is available at http://johnjnay.com/predMarket/. Forthcoming in Proceedings of the 2016 Winter Simulation Conference. IEEE Press

SMeagol is a software tool to simulate highly realistic microscopy data based on spatial systems biology models, in order to facilitate development, validation, and optimization of advanced analysis methods for live cell single molecule microscopy data. Availability and Implementation: SMeagol runs on Matlab R2014 and later, and uses compiled binaries in C for reaction-diffusion simulations. Documentation, source code, and binaries for recent versions of Mac OS, Windows, and Ubuntu Linux can be downloaded from http://smeagol.sourceforge.net., Comment: v2: 14 pages including supplementary text. Pre-copyedited, author-produced version of an application note published in Bioinformatics following peer review. The version of record, and additional supplementary material is available online at: https://academic.oup.com/bioinformatics/article-lookup/doi/10.1093/bioinformatics/btw109

Many proteins and peptides have an intrinsic capacity to sense and induce membrane curvature, and play crucial roles for organizing and remodelling cell membranes. However, the molecular driving forces behind these processes are not well understood. Here, we describe a new approach to study curvature sensing, by simulating the direction-dependent interactions of single molecules with a buckled lipid bilayer. We analyse three amphipathic antimicrobial peptides, a class of membrane-associated molecules that specifically target and destabilize bacterial membranes, and find qualitatively different sensing characteristics that would be difficult to resolve with other methods. These findings provide new insights into the curvature sensing mechanisms of amphipathic peptides and challenge existing theories of hydrophobic insertion. Our approach is generally applicable to a wide range of curvature sensing molecules, and our results provide strong motivation to develop new experimental methods to track position and orientation of membrane proteins., Comment: 14 pages. Supplementary movies available on request. Accepted version, with corrected description lipid bilayer composition

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple co-existing loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly-used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e., DNA-protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein-nucleic acid interactions., Comment: 34 pages, 25 figures, including Supporting information. To appear in Nucleic Acids Research. Accompanying open-source software: http://sourceforge.net/projects/vbtpm/

DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes, and DNA looping in transcriptional regulation in both prokaryotes and eukaryotes. These kinds of regulatory problems are now becoming amenable to systematic quantitative dissection with a powerful dialogue between theory and experiment. Here we use a single-molecule experiment in conjunction with a statistical mechanical model to test quantitative predictions for the behavior of DNA looping at short length scales, and to determine how DNA sequence affects looping at these lengths. We calculate and measure how such looping depends upon four key biological parameters: the strength of the transcription factor binding sites, the concentration of the transcription factor, and the length and sequence of the DNA loop. Our studies lead to the surprising insight that sequences that are thought to be especially favorable for nucleosome formation because of high flexibility lead to no systematically detectable effect of sequence on looping, and begin to provide a picture of the distinctions between the short length scale mechanics of nucleosome formation and looping., Comment: Nucleic Acids Research (2012); Published version available at http://nar.oxfordjournals.org/cgi/content/abstract/gks473? ijkey=6m5pPVJgsmNmbof&keytype=ref

Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function \emph{in vivo}. Despite their obvious importance, crowding phenomena in membranes are much less well studied than in the cytoplasm. Using statistical mechanics results for hard disk liquids, we show that crowding induces an entropic tension in the membrane, which influences transitions that alter the projected area and circumference of a membrane protein. As a specific case study in this effect, we consider the impact of crowding on the gating properties of bacterial mechanosensitive membrane channels, which are thought to confer osmoprotection when these cells are subjected to osmotic shock. We find that crowding can alter the gating energies by more than $2\;k_BT$ in physiological conditions, a substantial fraction of the total gating energies in some cases. Given the ubiquity of membrane crowding, the nonspecific nature of excluded volume interactions, and the fact that the function of many membrane proteins involve significant conformational changes, this specific case study highlights a general aspect in the function of membrane proteins., Comment: 20 pages (inclduing supporting information), 4 figures, to appear in PLoS Comp. Biol

The first passage times for enzymatic turnovers in non-equilibrium steady state display a statistical symmetry property related to non-equilibrium fluctuation theorems, that makes it possible to extract the chemical driving force from single molecule trajectories in non-equilibrium steady state. Below, we show that this system violates the general expectation that the number of decay constants needed to fit a first passage time distribution reflects the number of states in the escape problem. In fact, the structure of the kinetic mechanism makes half of the decay times vanish identically from the turnover time distribution. The terms that cancel out correspond to the eigenvalues of a certain sub-matrix of the master equation matrix for the first exit time problem. We discuss how these results make modeling and data analysis easier for such systems, and how the turnovers can be measured., Comment: 4 pages, 1 figure v2: Published version, minor corrections in response to referee comments

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this paper, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits. Key words: motor proteins; single molecule kinetics; enzyme kinetics; flagellar motor; Markov process; non-equilibrium fluctuations., Comment: revtex, 15 pages, 8 figures, 2 tables. v2: Minor revision, corrected typos, added references, and moved mathematical parts to new appendices

Processive molecular motors take more-or-less uniformly sized steps, along spatially periodic tracks, mostly forwards but increasingly backwards under loads. Experimentally, the major steps can be resolved clearly within the noise but one knows biochemically that one or more mechanochemical substeps remain hidden in each enzymatic cycle. In order to properly interpret experimental data for back/forward step ratios, mean conditional step-to-step dwell times, etc., a first-passage analysis has been developed that takes account of hidden substeps in $N$-state sequential models. The explicit, general results differ significantly from previous treatments that identify the observed steps with complete mechanochemical cycles; e.g., the mean dwell times $\tau_+$ and $\tau_-$ prior to forward and back steps, respectively, are normally {\it unequal} although the dwell times $\tau_{++}$ and $\tau_{--}$ between {\it successive} forward and back steps are equal. Illustrative (N=2)-state examples display a wide range of behavior. The formulation extends to the case of two or more detectable transitions in a multistate cycle with hidden substeps.

The type IV pilus retraction motor is found in many important bacterial pathogens. It is the strongest known linear motor protein and is required for bacterial infectivity. We characterize the dynamics of type IV pilus retraction in terms of a stochastic chemical reaction model. We find that a two state model can describe the experimental force velocity relation and qualitative dependence of ATP concentration. The results indicate that the dynamics is limited by an ATP-dependent step at low load and a force-dependent step at high load, and that at least one step is effectively irreversible in the measured range of forces. The irreversible nature of the sub-step(s) lead to interesting predictions for future experiments: We find different parameterizations with mathematically identical force velocity relations but different fluctuations (diffusion constant). We also find a longer elementary step compared to an earlier analysis, which agrees better with known facts about the structure of the pilus filament and energetic considerations. We conclude that more experimental data is needed, and that further retraction experiments are likely to resolve interesting details and give valuable insights into the PilT machinery. In light of our findings, the fluctuations of the retraction dynamics emerge as a key property to be studied in future experiments., Comment: 10 pages, 2 figures, 1 table

The motility of certain gram-negative bacteria is mediated by retraction of type IV pili surface filaments, which are essential for infectivity. The retraction is powered by a strong molecular motor protein, PilT, producing very high forces that can exceed 150 pN. The molecular details of the motor mechanism are still largely unknown, while other features have been identified, such as the ring-shaped protein structure of the PilT motor. The surprisingly high forces generated by the PilT system motivate a model investigation of the generation of large forces in molecular motors. We propose a simple model, involving a small ensemble of motor subunits interacting through the deformations on a circular backbone with finite stiffness. The model describes the motor subunits in terms of diffusing particles in an asymmetric, time-dependent binding potential (flashing ratchet potential), roughly corresponding to the ATP hydrolysis cycle. We compute force-velocity relations in a subset of the parameter space and explore how the maximum force (stall force) is determined by stiffness, binding strength, ensemble size, and degree of asymmetry. We identify two qualitatively different regimes of operation depending on the relation between ensemble size and asymmetry. In the transition between these two regimes, the stall force depends nonlinearly on the number of motor subunits. Compared to its constituents without interactions, we find higher efficiency and qualitatively different force-velocity relations. The model captures several of the qualitative features obtained in experiments on pilus retraction forces, such as roughly constant velocity at low applied forces and insensitivity in the stall force to changes in the ATP concentration., Comment: RevTex 9 pages, 4 figures. Revised version, new subsections in Sec. III, removed typos