CHLOROPHYLL-PROTEINS AND REACTION CENTER PREPARATIONS FROM PHOTOSYNTHETIC BACTERIA,ALGAE AND HIGHER PLANTS*,‡

Abstract— The use of sodium dodecyl sulfate to dissociate photosynthetic membranes followed by standard fractionation techniques yields chlorophyll-proteins and reaction center complexes with molecular weights of 500,000 or less. Much about the structure and function of photo-synthetic units in vivo can be deduced from the properties of the isolated complexes. The Bchl-protein from green bacteria is approximated by an incompletely filled sphere ? 80 Â in diameter consisting of four identical subunits. The five Bchl molecules in each subunit are 14 to 20Â apart. The related Chl a-proteins from a blue-green alga and various eukaryotic plants may have similar structural characteristics. The Chl a-protein from a blue-green alga contains one molecule of P700 per 60–90 Chl a molecules. The quantum requirement for P700 oxidation is 2.6 or less. The midpoint potential in various preparations ranges from 0.38 V to 0.42 V. Green algae and higher plants yield a Chl a-protein similar to that from the blue-green alga; in addition they yield another Chl-protein (mol. wt. = 2–3×10⁴) which contains an equal amount of Chl a and Chl b. These two Chl-proteins account for most of the chlorophyll in these organisms. Two photosynthetic bacteria (Rhodopseudomonas viridis and Chromatium) yield protein complexes containing Bchl, carotenoid, and bound cytochromes. The reaction center complex from R. viridis contains P960 (E_m, ₈= 0.39 to 0.42 V), cytochrome 558 (E_m,8= 0.33 V) and cytochrome 553 (E_m,7=— 0.02 V). Quantum requirements for P960 and C558 oxidation are ?2.2 and 3.0, respectively. Complex A from Chromatium contains Bchl 890, P883, cytochrome 556 (E_m,8= 0.34 V) and cytochrome 552 (E_m,7=?0.04 V). The quantum requirement for C556 oxidation is about 15. Both high- and low-potential cytochromes can donate electrons to the reaction center chlorophyll present in either complex. This fact supports the idea that only one kind of photochemical reaction center functions in photosynthetic bacteria. An hypothesis about the nature of the photosynthetic unit in purple bacteria is outlined.     

The Solution of Large Sparse Unsymmetric Systems of Linear Equations

We describe in moderate detail an algorithm for the solutionof a general sparse set of linear equations. It aims to maintainboth stability and sparseness, and allows further systems withthe same matrix, or another matrix having the same sparsitypattern, to be solved economically. It is compared, in testson several non-trivial problems, with two earlier algorithmsfrom which it was derived, and appears to combine the best featuresof both.     

On the Automatic Scaling of Matrices for Gaussian Elimination

The usual pivotal strategies for Gaussian elimination are basedon the assumption that all the matrix elements are of comparablesize. We propose an algorithm for scaling based on the assumptionthat the given matrix can be scaled to this required form. Somenumerical experiments are presented to show that it producesmuch better results than straightforward row and column normequilibration, particularly in the sparse case, and that thecomputing cost is moderate.     

On the Estimation of Sparse Jacobian Matrices

We show how to use known constant elements in a Jacobian matrixto reduce the work required to estimate the remaining elementsby finite differences.     

Jacobian Matrix Properties and Their Impact on Choice of Software for Stiff ODE Systems

Information is presented about the spectral and other propertiesof Jacobian matrices occurring in the numerical solution ofa number of large, very stiff ODE problems, arising from massaction kinetics. These properties demonstrate that the conceptof a few "stiff" eigenvalues, the rest being "non-stiff", isnot valid for such problems; consequently, it is argued thatpartitioning and exponential-fitting methods are inappropriatefor use in general-purpose software for stiff systems. Moreover,second-derivative methods and all but a very few formulationsof implicit Runge-Kutta methods would be at a grave disadvantagewhen applied to large, very stiff problems.     

Spectroscopic, Chromatographic and Visual Investigation of Organic Dyes

An introductory level laboratory experiment is presented in which students learn about color using spectroscopy and chromatography. The pedagogical approach is discovery-based; students are given only enough background information to enable them to take good data. Commercially available dyes are dissolved in water to make concentrated stock solutions, which students then dilute to prepare solutions of primary, secondary and tertiary colors. The class works as a team to study colored solutions representing a range of concentrations and combinations of the three primary colors: cyan, yellow, and magenta. Students record transmission and absorption spectra and compare the results with human perception. They show the number of components in each solution by paper chromatography. They explore the filter nature of dyes, the effects of concentration, and the cumulative effects of mixing dyes. From this information they deduce the principles of color printing.The experiment is best performed with a photodiode array spectrophotometer; alternative approaches include spectrometers and simple spectroscopes which the students make from cereal boxes. The experiment can be performed in either a single three-hour laboratory period, or alternatively, three one-hour sessions.     

Continuous Data Assimilation with Blurred-in-Time Measurements of the Surface Quasi-Geostrophic Equation

An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. The authors consider a nudging-based \linebreak approach for data assimilation that constructs an approximate solution based on a feedback control mechanism that is designed to account for observations that have been blurred by a moving time average. Analysis of this nudging model in the context of the subcritical surface quasi-geostrophic equation shows, provided the time-averaging window is sufficiently small and the resolution of the observations sufficiently fine, that the approximating solution converges exponentially fast to the observed solution over time. In particular, the authors demonstrate that observational data with a small blur in time possess no significant obstructions to data assimilation provided that the nudging properly takes the time averaging into account. Two key ingredients in our analysis are additional boundedness properties for the relevant interpolant observation operators and a non-local Gronwall inequality.     

A Study of College Student Attrition Via Probabilistic Approach

This exploratory paper proposes a probabilistic approach to investigating college student attrition. Through the use of attributable risk, the top risk factors for attrition are identified and ranked. Then the issue of confounding risk between two risk factors is addressed by the means of relative attributable risk. Though it is only illustrated by the eight-year attrition data collected at a private institution, the proposed technique is comparatively simple for institutional researchers to test on their own data.     

The Choice of Step Lengths When Using Differences to Approximate Jacobian Matrices

We propose an algorithm for automatic choice of step lengthsfor use when approximating derivatives by differences. We envisagethat its principal application will be the approximation ofJacobian matrices and discuss this case explicitly.