A first-principles model of early evolution: Emergence of gene families, species and preferred protein folds

In this work we develop a microscopic physical model of early evolution, where phenotype,organism life expectancy, is directly related to genotype, the stability of its proteins in their native conformations which can be determined exactly in the model. Simulating the model on a computer, we consistently observe the Big Bang scenario whereby exponential population growth ensues as soon as favorable sequence-structure combinations (precursors of stable proteins) are discovered. Upon that, random diversity of the structural space abruptly collapses into a small set of preferred proteins. We observe that protein folds remain stable and abundant in the population at time scales much greater than mutation or organism lifetime, and the distribution of the lifetimes of dominant folds in a population approximately follows a power law. The separation of evolutionary time scales between discovery of new folds and generation of new sequences gives rise to emergence of protein families and superfamilies whose sizes are power-law distributed, closely matching the same distributions for real proteins. On the population level we observe emergence of species, subpopulations which carry similar genomes. Further we present a simple theory that relates stability of evolving proteins to the sizes of emerging genomes. Together, these results provide a microscopic first principles picture of how first gene families developed in the course of early evolutionComment: In press, PLoS Computational Biolog

Moire volume Bragg grating filter with tunable bandwidth

We propose a monolithic large-aperture narrowband optical filter based on a moire volume Bragg grating formed by two sequentially recorded gratings with slightly different resonant wavelengths. Such recording creates a spatial modulation of refractive index with a slowly varying sinusoidal envelope. By cutting a specimen at a small angle, to a thickness of one-period of this envelope, the longitudinal envelope profile will shift from a sine profile to a cosine profile across the face of the device. The transmission peak of the filter has a tunable bandwidth while remaining at a fixed resonant wavelength by a transversal shift of incidence position. Analytical expressions for the tunable bandwidth of such a filter are calculated and experimental data from a filter operating at 1064 nm with bandwidth range 30-90 pm is demonstrated

Beam combining using Orientational Stimulated Scattering in Liquid Crystals

Possibility of beam combining and clean-up using Orientational Stimulated Scattering in a Nematic Liquid Crystal is considered. We numerically study the dynamics of the process and find that back-conversion process tends to limit the effective interaction strength. Instability of the steady state of cross-phase modulation is demonstrated, when both waves have the same frequency. We show that high conversion efficiency can be achieved, and that the shape and wave-front of the amplified output signal are robust with respect to amplitude and phase distortions of the input pump.Comment: 24 pages, 6 figures, will be published in JOSA

Laser Pulse Temporal, Spectral And Spatial Shaping Devices Based On Volume Diffractive Gratings With Variable Parameters

Recent invention of longitudinally chirped volume Bragg gratings has dramatically changed a design of high power femtosecond lasers. Replacing of bulky pairs of conventional surface gratings with compact and robust chirped volume Bragg gratings for stretching and compression of laser pulses in chirped-pulse-amplification systems enabled decrease of size and weight of those systems by several times. This patent application enables substantial increase of stretching time and compression to shorter pulses along with more complex shaping of laser pulses in both temporal and spectral domains

Device and Method for Image Acquisition Through Multi-Mode Fiber

An endoscope for image acquisition via illumination of an objects image, such as but not limited to a bar code, by a set of spatially resolved patterns, with subsequent reconstruction of the image without detailed spatial resolution. A device to stabilize the prescribed set of illuminating patterns against bending of the fiber is also disclosed, which consists of the auxiliary pre-bent part of the fiber and the work part of the fiber, subject to the inevitable bends with or without additional compensation. The distorting influence of the bending of the work part is compensated by the controllable loosening of the pre-bent part of the fiber. Encoding of the pixels of the image or of the illumination patterns encodes the intensity of each pixel to the excitation intensity of the corresponding mode. Such encoding is stable to the bending of the guide. Special transverse profiles of the properties of the waveguide include a rectangular, triangular and hexagonal cross-sectional shaped wave

Strength Of Electromagnetic, Acoustic And Schrödinger Reflections

The notion of reflection strength S of a plane wave by an arbitrary non-absorbing layer is introduced, so that the intensity of reflection is R=tanh2S. We have shown that the total strength of reflection by a sequence of elements is expressed through particular element strengths and mutual phases between them by a simple addition rule; in particular, its possible maximum is the sum of the absolute strengths of constituents. We show that the standard Fresnel reflection may be understood in terms of variable S as a sum or difference of two separate contributions, due to an impedance step and a speed step. Strength of reflection for propagating acoustic and quantum mechanical waves is also discussed. © 2008 The Royal Society

Reflection Of Various Types Of Waves By Layered Media

The one-dimensional wave equation describing propagation and reflection of waves in a layered medium is transformed into an exact first-order system for the amplitudes of coupled counter-propagating waves. Any choice of such amplitudes, out of continuous multitude of them, allows one to get an accurate numerical solution of the reflection problem. We discuss relative advantages of particular choices of amplitude. We also introduce the notion of reflection strength S of a plane wave by a nonabsorbing layer, which is related to the reflection intensity R by R = tanh2 S. We show that the total reflection strength by a sequence of elements is bounded above by the sum of the constituent strengths, and bounded below by their difference. Reflection strength is discussed for propagating acoustic waves and quantum mechanical waves. We show that the standard Fresnel reflection may be understood in terms of the variable S as a sum or difference of two contributions, one due to a discontinuity in impedance and the other due to a speed discontinuity

Quality Deterioration Of Self-Phase Modulated Gaussian Beams

The beam quality parameter Mx2 for self-phase modulated Gaussian and super-Gaussian beams has been calculated analytically. These results can be used for experimental measurements of nonlinearities in optical materials. A super-Gaussian beam with a size comparable to a Gaussian one demonstrates much more stable behavior with propagation through Kerr media. The deteriorated beam quality parameter has also been calculated analytically in the case of higher order localized radial phase modes. The presented analysis of beam quality degradation due to localized phase aberrations is more efficient than the standard one based on polynomial aperture aberrations

High-Efficiency 1.5 Μm Thick Optical Axis Grating And Its Use For Laser Beam Combining

We demonstrate an optical axis grating (OAG) recorded in a nematic liquid crystal that yields a higher than 80% diffraction efficiency and over 800:1 switching contrast between diffraction orders for a laser beam of a red wavelength in a material layer only 1.5 μm thick. The grating was used for combining two laser beams with high efficiency. These observations prove the feasibility of new generation high-efficiency diffractive optical components, which are most promising for infrared and high-power applications owing to their enhanced transparency and reduced thermal effects in thin material layers. © 2006 Optical Society of America