Optical approaches for tracking neural dynamics are of widespread interest, but a theoretical framework quantifying the physical limits of these techniques has been lacking. We formulate such a framework by using signal detection and estimation theory to obtain physical bounds on the detection of neural spikes and the estimation of their occurrence times as set by photon counting statistics (shot noise). These bounds are succinctly expressed via a discriminability index that depends on the kinetics of the optical indicator and the relative fluxes of signal and background photons. This approach facilitates quantitative evaluations of different indicators, detector technologies, and data analyses. Our treatment also provides optimal filtering techniques for optical detection of spikes. We compare various types of Ca(2+) indicators and show that background photons are a chief impediment to voltage sensing. Thus, voltage indicators that change color in response to membrane depolarization may offer a key advantage over those that change intensity. We also examine fluorescence resonance energy transfer indicators and identify the regimes in which the widely used ratiometric analysis of signals is substantially suboptimal. Overall, by showing how different optical factors interact to affect signal quality, our treatment offers a valuable guide to experimental design and provides measures of confidence to assess optically extracted traces of neural activity.

One approach to super-resolution fluorescence microscopy, termed stochastic localization microscopy, relies on the nanometer scale spatial localization of individual fluorescent emitters that stochastically label specific features of the specimen. The precision of emitter localization is an important determinant of the resulting image resolution but is insufficient to specify how well the derived images capture the structure of the specimen. We address this deficiency by considering the inference of specimen structure based on the estimated emitter locations. By using estimation theory, we develop a measure of spatial resolution that jointly depends on the density of the emitter labels, the precision of emitter localization, and prior information regarding the spatial frequency content of the labeled object. The Nyquist criterion does not set the scaling of this measure with emitter number. Given prior information and a fixed emitter labeling density, our resolution measure asymptotes to a finite value as the precision of emitter localization improves. By considering the present experimental capabilities, this asymptotic behavior implies that further resolution improvements require increases in labeling density above typical current values. Our treatment also yields algorithms to enhance reliable image features. Overall, our formalism facilitates the rigorous statistical interpretation of the data produced by stochastic localization imaging techniques.

The estimation of visual motion has long been studied as a paradigmatic neural computation, and multiple models have been advanced to explain behavioral and neural responses to motion signals. A broad class of models, originating with the Reichardt correlator model, proposes that animals estimate motion by computing a temporal cross-correlation of light intensities from two neighboring points in visual space. These models provide a good description of experimental data in specific contexts but cannot explain motion percepts in stimuli lacking pairwise correlations. Here, we develop a theoretical formalism that can accommodate diverse stimuli and behavioral goals. To achieve this, we treat motion estimation as a problem of Bayesian inference. Pairwise models emerge as one component of the generalized strategy for motion estimation. However, correlation functions beyond second order enable more accurate motion estimation. Prior expectations that are asymmetric with respect to bright and dark contrast use correlations of both even and odd orders, and we show that psychophysical experiments using visual stimuli with symmetric probability distributions for contrast cannot reveal whether the subject uses odd-order correlators for motion estimation. This result highlights a gap in previous experiments, which have largely relied on symmetric contrast distributions. Our theoretical treatment provides a natural interpretation of many visual motion percepts, indicates that motion estimation should be revisited using a broader class of stimuli, demonstrates how correlation-based motion estimation is related to stimulus statistics, and provides multiple experimentally testable predictions.

Since the demonstration that the sequence of a protein encodes its structure, the prediction of structure from sequence remains an outstanding problem that impacts numerous scientific disciplines, including many genome projects. By iteratively fixing secondary structure assignments of residues during Monte Carlo simulations of folding, our coarse-grained model without information concerning homology or explicit side chains can outperform current homology-based secondary structure prediction methods for many proteins. The computationally rapid algorithm using only single (phi,psi) dihedral angle moves also generates tertiary structures of accuracy comparable with existing all-atom methods for many small proteins, particularly those with low homology. Hence, given appropriate search strategies and scoring functions, reduced representations can be used for accurately predicting secondary structure and providing 3D structures, thereby increasing the size of proteins approachable by homology-free methods and the accuracy of template methods that depend on a high-quality input secondary structure.

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.

To identify basic local backbone motions in unfolded chains, simulations are performed for a variety of peptide systems using three popular force fields and for implicit and explicit solvent models. A dominant "crankshaft-like" motion is found that involves only a localized oscillation of the plane of the peptide group. This motion results in a strong anticorrelated motion of the phi angle of the ith residue (phi(i)) and the psi angle of the residue i - 1 (psi(i-1)) on the 0.1 ps time scale. Only a slight correlation is found between the motions of the two backbone dihedral angles of the same residue. Aside from the special cases of glycine and proline, no correlations are found between backbone dihedral angles that are separated by more than one torsion angle. These short time, correlated motions are found both in equilibrium fluctuations and during the transit process between Ramachandran basins, e.g., from the beta to the alpha region. A residue's complete transit from one Ramachandran basin to another, however, occurs in a manner independent of its neighbors' conformational transitions. These properties appear to be intrinsic because they are robust across different force fields, solvent models, nonbonded interaction routines, and most amino acids.