Biomedical subjects

Veit Elser

Publications and source records attributed to Veit Elser.

6 recordsLinked to original sources

PubMed2006

Sloppy-model universality class and the Vandermonde matrix.

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Algorithms↗

PubMed2006

Reconstruction of a yeast cell from X-ray diffraction data.

Details are provided of the algorithm used for the reconstruction of yeast cell images in the recent demonstration of diffraction microscopy by Shapiro, Thibault, Beetz, Elser, Howells, Jacobsen, Kirz, Lima, Miao, Nieman & Sayre [Proc. Natl Acad. Sci. USA (2005), 102, 15343-15346]. Two refinements of the iterative constraint-based scheme are developed to address the current experimental realities of this imaging technique, which include missing central data and noise. A constrained power operator is defined whose eigenmodes allow the identification of a small number of degrees of freedom in the reconstruction that are negligibly constrained as a result of the missing data. To achieve reproducibility in the algorithm's output, a special intervention is required for these modes. Weak incompatibility of the constraints caused by noise in both direct and Fourier space leads to residual phase fluctuations. This problem is addressed by supplementing the algorithm with an averaging method. The effect of averaging may be interpreted in terms of an effective modulation transfer function, as used in optics, to quantify the resolution. The reconstruction details are prefaced with simulations of wave propagation through a model yeast cell. These show that the yeast cell is a strong-phase-contrast object for the conditions in the experiment.

Algorithms↗

PubMed2006

Deconstructing the energy landscape: constraint-based algorithms for folding heteropolymers.

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a geometrical chain constraint and a threshold constraint on the contact energy. A dynamical system is then defined in terms of the projections to these constraint sets, such that its fixed points solve the set intersection problem. We present results for two off-lattice hydrophobic-polar models: one with only rotameric degrees of freedom, and one proposed by Stillinger [Phys. Rev. E 48, 1469 (1993)] with flexible bond angles. Our phase retrieval inspired algorithm is competitive with more established algorithms and even finds lower-energy folds for one of the longer polymer chains.

Journal Article↗

PubMed2005

Biological imaging by soft x-ray diffraction microscopy.

We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cell's major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.

Freeze Drying↗

PubMed2003

Solution of the crystallographic phase problem by iterated projections.

An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual reciprocal-space formulations of atomicity. The new algorithm implements atomicity constraints in real space, as well as intensity constraints in reciprocal space, by projections that restore each constraint with the minimal modification of the scattering density. To recover the true density, the two projections are combined into a single operation, the difference map, which is iterated until the magnitude of the density modification becomes acceptably small. The resulting density, when acted upon by a single additional operation, is by construction a density that satisfies both intensity and atomicity constraints. Numerical experiments have yielded solutions for atomic resolution X-ray data sets with over 400 non-hydrogen atoms, as well as for neutron data, where positivity of the density cannot be invoked.

Algorithms↗

PubMed2003

Phase retrieval by iterated projections.

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input-output map when a particular choice is made for two of the parameters. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby the form of stagnation encountered by alternating projection schemes is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved.

Journal Article↗