J. M. Deutsch

Evolutionary algorithms for finding optimal gene sets in microarray prediction

MOTIVATION Microarray data has been shown recently to be efficacious in distinguishing closely related cell types that often appear in different forms of cancer, but is not yet practical clinically. However, the data might be used to construct a minimal set of marker genes that could then be used clinically by making antibody assays to diagnose a specific type of cancer. Here a replication algorithm is used for this purpose. It evolves an ensemble of predictors, all using different combinations of genes to generate a set of optimal predictors. RESULTS We apply this method to the leukemia data of the Whitehead/MIT group that attempts to differentially diagnose two kinds of leukemia, and also to data of Khan et al. to distinguish four different kinds of childhood cancers. In the latter case we were able to reduce the number of genes needed from 96 to less than 15, while at the same time being able to classify all of their test data perfectly. We also apply this method to two other cases, Diffuse large B-cell lymphoma data (Shipp et al., 2002), and data of Ramaswamy et al. on multiclass diagnosis of 14 common tumor types. AVAILABILITY http://stravinsky.ucsc.edu/josh/gesses/.

NEW ALGORITHM FOR PROTEIN DESIGN

We apply a new approach to the reverse protein folding problem. Our method uses a minimization function in the design process which is different from the energy function used for folding. For a lattice model, we show that this new approach produces sequences that are likely to fold into desired structures. Our method is a significant improvement over previous attempts which used the energy function for designing sequences.

Explanation of anomalous mobility and birefringence measurements found in pulsed field electrophoresis

The study of DNA in a gel under the application of a time‐dependent field has revealed some unexpected experimental features. These features are recovered by means of a detailed numerical simulation incorporating the many internal degrees of freedom of the DNA chain. These results can in turn be understood qualitatively by means of a model containing only four degrees of freedom.

Disorder-induced microscopic magnetic memory

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories.

Equilibrium size of large ring molecules

The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had been previously conjectured. However this scaling was only seen for chains greater than 500 monomers.

Disorder-induced magnetic memory: Experiments and theories

Beautiful theories of magnetic hysteresis based on random microscopic disorder have been developed over the past ten years. Our goal was to directly compare these theories with precise experiments. To do so, we first developed and then applied coherent x-ray speckle metrology to a series of thin multilayer perpendicular magnetic materials. To directly observe the effects of disorder, we deliberately introduced increasing degrees of disorder into our films. We used coherent x rays, produced at the Advanced Light Source at Lawrence Berkeley National Laboratory, to generate highly speckled magnetic scattering patterns. The apparently “random” arrangement of the speckles is due to the exact configuration of the magnetic domains in the sample. In effect, each speckle pattern acts as a unique fingerprint for the magnetic domain configuration. Small changes in the domain structure change the speckles, and comparison of the different speckle patterns provides a quantitative determination of how much the domain structure has changed. Our experiments quickly answered one longstanding question: How is the magnetic domain configuration at one point on the major hysteresis loop related to the configurations at the same point on the loop during subsequent cycles? This is called microscopic return-point memory RPM. We found that the RPM is partial and imperfect in the disordered samples, and completely absent when the disorder is below a threshold level. We also introduced and answered a second important question: How are the magnetic domains at one point on the major loop related to the domains at the complementary point, the inversion symmetric point on the loop, during the same and during subsequent cycles? This is called microscopic complementary-point memory CPM. We found that the CPM is also partial and imperfect in the disordered samples and completely absent when the disorder is not present. In addition, we found that the RPM is always a little larger than the CPM. We also studied the correlations between the domains within a single ascending or descending loop. This is called microscopic half-loop memory and enabled us to measure the degree of change in the domain structure due to changes in the applied field. No existing theory was capable of reproducing our experimental results. So we developed theoretical models that do fit our experiments. Our experimental and theoretical results set benchmarks for future work.

Long range moves for high density polymer simulations

Monte Carlo simulations of proteins are hindered by the system’s high density which often makes local moves ineffective. Here we devise and test a set of long range moves that work well even when all sites in a lattice simulation are filled. We demonstrate that for a 27-mer cube, the ground state of random heteropolymers can quickly be reached. We discuss results for 48-mer systems where the ground state is known exactly. For ten sequences that were examined, the introduction of long range moves speeds up the search for the ground state by about one order of magnitude. The method is compared to a fast folding chain growth algorithm that had previously been used with much success. The new algorithm here appears to be more efficient. The point is illustrated by the folding of an 80-mer four-helix bundle considered previously.

Theoretical studies of DNA during orthogonal field alternating gel electrophoresis

We perform numerical simulations on a model of DNA molecules during gel electrophoresis in which the effect of periodically changing the applied field by 90° is examined. A random gel is used in this simulation. We find a scaling relationship between mobility and the ratio of the chain length to pulse time for 100 and 200 link chains. Also presented are results for the orientation, with respect to the new field direction, of chains being subjected to periodically varying orthogonal fields. We find no overshoot in this orientation. Results supporting the existence of persistence in the orientation of a chain over several field changes is presented for 400 link chains.

The diffusion coefficient of a reptating polymer

The dynamics of a polymer in a network of entanglements is studied. The viscosity has been examined for chains up to 50 links and is found to scale with chain length L as L3.41±0.14 in agreement with previous theoretical work, that attributes this anomalous exponent as a finite size effect because of the finite tube length. Numerical results for chains up to 100 links give that the diffusion coefficient D, scales as L−2.50±0.04. This result differs from theoretical predictions based on tube fluctuations which claim finite length effects are unimportant for diffusion and therefore imply a −2 power law dependence for D. The reason for this discrepancy is examined. Previous work used a one‐dimensional rather than a three‐dimensional diffusion coefficient as the starting point of analysis. By deriving the correct procedure for calculating the three‐dimensional D, one sees that it has corrections to its asymptotic behavior which are quite large, of order L−1/2, rather than L−1 as was thought previously. This s...

Microscopic origin of thermodynamic entropy in isolated systems.

The quantum entropy is usually defined using von Neumanns formula, which measures lack of information and vanishes for pure states. In contrast, we obtain a formula for the entropy of a pure state as it is measured from thermodynamic experiments, solely from the self-entanglement of the wave function, and find strong numerical evidence that the two are in agreement for nonintegrable systems, both for energy eigenstates and for states that are obtained at long times under the evolution of more general initial conditions. This is an extension of Boltzmanns hypothesis for classical systems, relating microscopic motion to thermodynamics.