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Modeling the Activity of Single Genes

The central dogma of molecular biology states that information is stored in DNA, transcribed to messenger RNA (mRNA) and then translated into proteins. This picture is significantly augmentated when we consider the action of certain proteins in regulating transcription. These transcription factors provide a feedback pathway by which genes can regulate one another's expression as mRNA and then as protein. To review: DNA, RNA and proteins have different functions. DNA is the molecular storehouse of genetic information. When cells divide, the DNA is replicated, so that each daughter cell maintains the same genetic information as the mother cell. RNA acts as a go-between from DNA to proteins. Only a single copy of DNA is present, but multiple copies of the same piece of RNA may be present, allowing cells to make huge amounts of protein. In eukaryotes (organisms with a nucleus), DNA is found in the nucleus only. RNA is copied in the nucleus then translocates(moves) outside the nucleus, where it is transcribed into proteins. Along the way, the RNA may be spliced, i.e., may have pieces cut out. RNA then attaches to ribosomes and is translated to proteins. Proteins are the machinery of the cell other than DNA and RNA, all the complex molecules of the cell are proteins. Proteins are specialized machines, each of which fulfills its own task, which may be transporting oxygen, catalyzing reactions, or responding to extracellular signals, just to name a few. One of the more interesting functions a protein may have is binding directly or indirectly to DNA to perform transcriptional regulation, thus forming a closed feedback loop of gene regulation. The structure of DNA and the central dogma were understood in the 50s; in the early 80s it became possible to make arbitrary modifications to DNA and use cellular machinery to transcribe and translate the resulting genes; more recently, genomes (i.e., the complete DNA sequence) of many organisms have been sequenced. This large-scale sequencing began with simple organisms, viruses and bacteria, progressed to eukaryotes such as yeast, and more recently (1998) progressed to a multi-cellular animal, the nematode Caenorhabditis elegans. Sequencers have now moved on to the fruit fly Drosophila melanogaster, whose sequence is slated for completion by the end of 1999. The human genome project is expected to determine the complete sequence of all 3 billion bases of human DNA within the next five years. In the wake of genome-scale sequencing, further instrumentation is being developed to assay gene expression and function on a comparably large scale. Much of the work in computational biology focuses on computational tools used in sequencing, finding genes that are related to a particular gene, finding which parts of the DNA code for proteins and which do not, understanding what proteins will be formed from a given length of DNA, predicting how the proteins will fold from a one-dimensional structure into a three dimensional structure, and so on. Much less computational work has been done regarding the function of proteins. One reason for this is that different proteins function very differently, and so work on protein function is very specific to certain classes of proteins. There are, for example, proteins such enzymes that catalyze various intracellular reactions, receptors that respond to extracellular signals and ion channels that regulate the flow of charged particles into and out of the cell. In this chapter, we will consider a particular class of proteins called transcription factors(TFs), which are responsible for regulating when a certain gene is expressed in a certain cell, which cells it is express in, and how much is expressed. Understanding these processes will involve developing a deeper understanding of transcription, translation, and the cellular processes that control those processes. All of these elements fall under the aegis of gene regulation or more narrowly transcriptional regulation. Some of the key questions in gene regulation are: What genes are expressed in a certain cell at a certain time? How does gene expression differ from cell to cell in a multicellular organism? Which proteins act as transcription factors, i.e., are important in regulating gene expression? From questions like these, we hope to understand which genes are important for various macroscopic processes. Nearly all of the cells of a multicellular organism contain the same DNA. Yet this same genetic information yields a large number of different cell types. The fundamental difference between a neuron and a liver cell, for example, is which genes are expressed. Thus understanding gene regulation is an important step in understanding development. Furthermore, understanding the usual genes that are expressed in cells may give important clues about various diseases. Some diseases, such as sickle cell anemia and cystic fibrosis, are caused by defects in single, non-regulatory genes; others, such as certain cancers, are caused when the cellular control circuitry malfunctions - an understanding of these diseases will involve pathways of multiple interacting gene products. There are numerous challenges in the area of understanding and modeling gene regulation. First and foremost, biologists would like to develop a deeper understanding of the processes involved, including which genes and families of genes are important, how they interact, etc. From a computation point of view, there has been embarrassingly little work done. In this chapter there are many areas in which we can phrase meaningful, non-trivial computational questions, but questions that have not been addressed. Some of these are purely computational (what is a good algorithm for dealing with a model of type X) and others are more mathematical (given a system with certain characteristics, what sort of model can one use? How does one find biochemical parameters from system-level behavior using as few experiments as possible?). In addition to biological and algorithmic problems, there is also the ever-present issue of theoretical biology - what general principles can be derived from these systems, what can one do with models other than just simulate time-courses, what can be deduced about a class of systems without knowing all the details? The fundamental challenge to computationalists and theorists is to add value to the biology - to use models, modeling techniques and algorithms to understand the biology in new ways.

Mjolsness, Eric↗

Statistical mechanics of light elements at high pressure. VII - A perturbative free energy for arbitrary mixtures of H and He

A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars.

Hubbard, W. B.↗

The equations of motion of an artificial satellite in nonsingular variables

The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r prime; r prime being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.

Giacaglia, G. E. O.↗

A general and computationally fast formulation for radiative transfer with scattering

A general formulation of monocromatic radiative transfer with scattering has been developed for plane-parallel geometry. The inhomogeneous and nonisothermal medium absorbs, emits, and anisotropically scatters radiation. Surfaces can emit and scatter radiation in any specified manner. The solution procedure uses the fact that phase incoherent scattering is linear in radiative sources. Certain basic scattering functions are then defined and calculated by an adding computer code using matrix algebra. These scattering functions are weighted by the temperature field and summed (superimposed) to obtain the solution for any specific problem. Numerical results for exiting intensities and one-sided heat fluxes from general media bound by one arbitrary surface are presented. These parametric studies demonstrate the effects of scattering particles and surfaces on radiative transfer from inhomogeneous and nonisothermal media. Application of the formulation to radiative equilibrium is also discussed. The conclusion is that all problems in plane-parallel radiative transfer with scattering can be solved by a common and computationally fast algorithm based on this formulation.

Cogley, A. C.↗

Generation of three-dimensional boundary-fitted curvilinear coordinate systems for wing/wing-tip geometries using the elliptic solver method

A three-dimensional elliptic solver technique is utilized to generate surface-fitted coordinates about wing/wing-tip configurations. The method is applicable to wings of arbitrary section profile and camber, leading-edge sweep, taper ratio, and spanwise thickness variation. The basic theory of three-dimensional elliptic mappings is developed along with a method to compute interior coordinate control functions. Examples of grids generated about several wing/wing-tip geometries are given. A 49 x 33 x 17 grid requires about 3 minutes of CPU time on a CYBER 203 computer.

Thames, F. C.↗

Investigation of fast initialization of spacecraft bubble memory systems

Bubble domain technology offers significant improvement in reliability and functionality for spacecraft onboard memory applications. In considering potential memory systems organizations, minimization of power in high capacity bubble memory systems necessitates the activation of only the desired portions of the memory. In power strobing arbitrary memory segments, a capability of fast turn on is required. Bubble device architectures, which provide redundant loop coding in the bubble devices, limit the initialization speed. Alternate initialization techniques are investigated to overcome this design limitation. An initialization technique using a small amount of external storage is demonstrated.

Looney, K. T.↗

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

Sorenson, R. L.↗

Solution of multi-center molecular integrals of Slater-type orbitals

The troublesome multi-center molecular integrals of Slater-type orbitals (STO) in molecular physics calculations can be evaluated by using the Fourier transform and proper coupling of the two center exchange integrals. A numerical integration procedure is then readily rendered to the final expression in which the integrand consists of well known special functions of arguments containing the geometrical arrangement of the nuclear centers and the exponents of the atomic orbitals. A practical procedure was devised for the calculation of a general multi-center molecular integrals coupling arbitrary Slater-type orbitals. Symmetry relations and asymptotic conditions are discussed. Explicit expressions of three-center one-electron nuclear-attraction integrals and four-center two-electron repulsion integrals for STO of principal quantum number n=2 are listed. A few numerical results are given for the purpose of comparison.

Tai, H.↗

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. The equation of motion and associated boundary conditions are derived for the free vibration of a composite beam with a delamination of arbitrary size and location. A generalized variational principle is used to formulate the equation of motion, taking into account the interlaminar stress concentration at the crack-tips. This is accomplished by introducing a 'crack function' into the beam's compatibility relations. This function has its maximum value at the crack tip and decays exponentially in the longitudinal direction. The rate of exponential decay is determined by a least-square fit with the experimental results. The effect of coupling between longitudinal vibration and bending vibration is considered in the present study. This coupling effect is found to significantly affect the natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

User's manual for CBS3DS, version 1.0

CBS3DS is a computer code written in FORTRAN 77 to compute the backscattering radar cross section of cavity backed apertures in infinite ground plane and slots in thick infinite ground plane. CBS3DS implements the hybrid Finite Element Method (FEM) and Method of Moments (MoM) techniques. This code uses the tetrahedral elements, with vector edge basis functions for FEM in the volume of the cavity/slot and the triangular elements with the basis functions for MoM at the apertures. By virtue of FEM, this code can handle any arbitrarily shaped three-dimensional cavities filled with inhomogeneous lossy materials; due to MoM, the apertures can be of any arbitrary shape. The User's Manual is written to make the user acquainted with the operation of the code. The user is assumed to be familiar with the FORTRAN 77 language and the operating environment of the computer the code is intended to run.

Reddy, C. J.↗

A Trilateration Scheme for Relative Positioning

We introduce a trilateration scheme that evaluates the 3-dimensional (3-D) relative position between a reference spacecraft and a target spacecraft using raw-range measurements from a distance baseline of known locations, which we call “anchors”. The anchors can be antennas of a ground-based network (e.g., Deep Space Network (DSN) or Near Earth Network (NEN) stations), or satellites of a spacebased network (e.g., global positioning system (GPS) or tracking and data relay satellite (TDRS)). We define raw-range as the range that includes all the systematic errors that occur during range measurements. A unique feature of this approach is that accurate relative position is derived from a “differencing function” of raw-range measurements of the reference spacecraft and target spacecraft, thereby eliminating most of the systematic errors, such as media effects, ephemeris errors, instrument delays, clock bias, etc. There can be an arbitrary number of target spacecraft, and relative positioning of target spacecraft with respect to the reference spacecraft can be done simultaneously. In this paper, we first assume an idealized system in which clocks on the reference and target spacecraft are synchronized, with clocks of the anchors synchronized as well. We develop a novel iterative algorithm that computes the relative position of the target spacecraft with respect to the reference spacecraft. We illustrate the relative positioning method using the scenario of a network of three ground stations (i.e., the anchors) at Goldstone, California, USA, Madrid, Spain, and Marlargue, Argentina tracking two spacecraft at geosynchronous orbit distance. We demonstrate that the algorithm converges to submeter accuracy in estimating the relative position, in the presence of random errors and systematic errors in raw-range measurements, and in the presence of angular errors in estimating the pointing vectors between the anchors and the reference spacecraft. Next, we relax the requirement of perfect time synchronization between spacecraft, and show that by using an additional anchor, one can estimate and remove the clock biases between the reference and target spacecraft. We add a ground station at Kourou to the above example of three ground stations of Goldstone, Madrid, and Marlargue, and demonstrate that the updated algorithm also converges to meter-level accuracy (submeter in some cases) in the presence of clock biases in addition to the random errors, systematic errors, and angular errors as shown in the above case. We compare this scheme with a similar trilateration scheme for relative positioning scheme first proposed by Montenbruck in 2002.

Cheung, Kar-Ming↗

A defect stream function, law of the wall/wake method for compressible turbulent boundary layers

The application of the defect stream function to the solution of the two-dimensional, compressible boundary layer is examined. A law of the wall/law of the wake formulation for the inner part of the boundary layer is presented which greatly simplifies the computational task near the wall and eliminates the need for an eddy viscosity model in this region. The eddy viscosity model in the outer region is arbitrary. The modified Crocco temperature-velocity relationship is used as a simplification of the differential energy equation. Formulations for both equilibrium and nonequilibrium boundary layers are presented including a constrained zero-order form which significantly reduces the computational workload while retaining the significant physics of the flow. A formulation for primitive variables is also presented. Results are given for the constrained zero-order and second-order equilibrium formulations and are compared with experimental data. A compressible wake function valid near the wall has been developed from the present results.

Barnwell, Richard W.↗

Electrostatic camera system functional design study

A functional design study for an electrostatic camera system for application to planetary missions is presented. The electrostatic camera can produce and store a large number of pictures and provide for transmission of the stored information at arbitrary times after exposure. Preliminary configuration drawings and circuit diagrams for the system are illustrated. The camera system's size, weight, power consumption, and performance are characterized. Tradeoffs between system weight, power, and storage capacity are identified.

Botticelli, R. A.↗

Alfven waves in spiral interplanetary field

A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.

Whang, Y. C.↗

Experimental examination of similarity measures and preprocessing methods used for image registration

The criterion used to measure the similarity between images and thus find the position where the images are registered is examined. The three similarity measures considered are the correlation coefficient, the sum of the absolute differences, and the correlation function. Three basic types of preprocessing are then discussed: taking the magnitude of the gradient of the images, thresholding the images at their medians, and thresholding the magnitude of the gradient of the images at an arbitrary level to be determined experimentally. These multitemporal registration techniques are applied to remote imagery of agricultural areas.

Svedlow, M.↗

Numerical solution of the Navier-Stokes equations for blunt nosed bodies in supersonic flows

A time dependent, two dimensional Navier-Stokes code employing the method of body fitted coordinate technique was developed for supersonic flows past blunt bodies of arbitrary shapes. The bow shock ahead of the body is obtained as part of the solution, viz., by shock capturing. A first attempt at mesh refinement in the shock region was made by using the forcing function in the coordinate generating equations as a linear function of the density gradients. The technique displaces a few lines from the neighboring region into the shock region. Numerical calculations for Mach numbers 2 and 4.6 and Reynolds numbers from 320 to 10,000 were performed for a circular cylinder with and without a fairing. Results of Mach number 4.6 and Reynolds number 10,000 for an isothermal wall temperature of 556 K are presented in detail.

Warsi, Z. U. A.↗