The Flocculation of E. coli with Polyethyleneimine

A comprehensive study was made of the flocculation of dispersed E. coli bacterial cells by the cationic polymer polyethyleneimine (PEI). The three objectives of this study were to determine the primary mechanism involved in the flocculation of a colloid with an oppositely charged polymer, to determine quantitative correlations between four commonly-used measurements of the extent of flocculation, and to record the effect of varying selected system parameters on the degree of flocculation. The quantitative relationships derived for the four measurements of the extent of flocculation should be of direct assistance to the sanitary engineer in evaluating the effectiveness of specific coagulation processes.

A review of prior statistical mechanical treatments of absorbed polymer configuration revealed that at low degrees of surface site coverage, an oppositely- charged polymer molecule is strongly adsorbed to the colloidal surface, with only short loops or end sequences extending into the solution phase. Even for high molecular weight PEI species, these extensions from the surface are theorized to be less than 50 Å in length. Although the radii of gyration of the five PEI species investigated were found to be large enough to form interparticle bridges, the low surface site coverage at optimum flocculation doses indicates that the predominant mechanism of flocculation is adsorption coagulation.

The effectiveness of the high-molecular weight PEI species 1n producing rapid flocculation at small doses is attributed to the formation of a charge mosaic on the oppositely-charged E. coli surfaces. The large adsorbed PEI molecules not only neutralize the surface charge at the adsorption sites, but also cause charge reversal with excess cationic segments. The alignment of these positive surface patches with negative patches on approaching cells results in strong electrostatic attraction in addition to a reduction of the double-layer interaction energies. The comparative ineffectiveness of low-molecular weight PEI species in producing E. coli flocculation is caused by the size of the individual molecules, which is insufficient to both neutralize and reverse the negative E.coli surface charge. Consequently, coagulation produced by low molecular weight species is attributed solely to the reduction of double-layer interaction energies via adsorption.

Electrophoretic mobility experiments supported the above conclusions, since only the high-molecular weight species were able to reverse the mobility of the E. coli cells. In addition, electron microscope examination of the seam of agglutination between E. coli cells flocculation by PEI revealed tightly- bound cells, with intercellular separation distances of less than 100-200 Å in most instances. This intercellular separation is partially due to cell shrinkage in preparation of the electron micrographs.

The extent of flocculation was measured as a function of PEl molecular weight, PEl dose, and the intensity of reactor chamber mixing. Neither the intensity of mixing, within the common treatment practice limits, nor the time of mixing for up to four hours appeared to play any significant role in either the size or number of E.coli aggregates formed. The extent of flocculation was highly molecular weight dependent: the high-molecular-weight PEl species produce the larger aggregates, the greater turbidity reductions, and the higher filtration flow rates. The PEl dose required for optimum flocculation decreased as the species molecular weight increased. At large doses of high-molecular-weight species, redispersion of the macroflocs occurred, caused by excess adsorption of cationic molecules. The excess adsorption reversed the surface charge on the E.coli cells, as recorded by electrophoretic mobility measurements.

Successful quantitative comparisons were made between changes in suspension turbidity with flocculation and corresponding changes in aggregate size distribution. E. coli aggregates were treated as coalesced spheres, with Mie scattering coefficients determined for spheres in the anomalous diffraction regime. Good quantitative comparisons were also found to exist between the reduction in refiltration time and the reduction of the total colloid surface area caused by flocculation. As with turbidity measurements, a coalesced sphere model was used since the equivalent spherical volume is the only information available from the Coulter particle counter. However, the coalesced sphere model was not applicable to electrophoretic mobility measurements. The aggregates produced at each PEl dose moved at approximately the same vlocity, almost independently of particle size.

PEl was found to be an effective flocculant of E. coli cells at weight ratios of 1 mg PEl: 100 mg E. coli. While PEl itself is toxic to E.coli at these levels, similar cationic polymers could be effectively applied to water and wastewater treatment facilities to enhance sedimentation and filtration characteristics.

Kinetics and mechanisms of adsorption of Escherichia coli bacteriophage T_4 to activated carbon

A study was conducted on the adsorption of Escherichia coli bacteriophage T₄ to activated carbon. Preliminary adsorption experiments were also made with poliovirus Type III. The effectiveness of such adsorbents as diatomaceous earth, Ottawa sand, and coconut charcoal was also tested for virus adsorption.

The kinetics of adsorption were studied in an agitated solution containing virus and carbon. The mechanism of attachment and site characteristics were investigated by varying pH and ionic strength and using site-blocking reagents.

Plaque assay procedures were developed for bacteriophage T₄ on Escherichia coli cells and poliovirus Type III on monkey kidney cells. Factors influencing the efficiency of plaque formation were investigated.

The kinetics of bacteriophage T₄ adsorption to activated carbon can be described by a reversible second-order equation. The reaction order was first order with respect to both virus and carbon concentration. This kinetic representation, however, is probably incorrect at optimum adsorption conditions, which occurred at a pH of 7.0 and ionic strength of 0.08. At optimum conditions the adsorption rate was satisfactorily described by a diffusion-limited process. Interpretation of adsorption data by a development of the diffusion equation for Langmuir adsorption yielded a diffusion coefficient of 12 X 10^-8 cm²/sec for bacteriophage T₄. This diffusion coefficient is in excellent agreement with the accepted value of 8 X 10^-8 cm²/sec. A diffusion-limited theory may also represent adsorption at conditions other than the maximal. A clear conclusion on the limiting process cannot be made.

Adsorption of bacteriophage T₄ to activated carbon obeys the Langmuir isotherm and is thermodynamically reversible. Thus virus is not inactivated by adsorption. Adsorption is unimolecular with very inefficient use of the available carbon surface area. The virus is probably completely excluded from pores due to its size.

Adsorption is of a physical nature and independent of temperature. Attraction is due to electrostatic forces between the virus and carbon. Effects of pH and ionic strength indicated that carboxyl groups, amino groups, and the virus's tail fibers are involved in the attachment of virus to carbon. The active sites on activated carbon for adsorption of bacteriophage T₄ are carboxyl groups. Adsorption can be completely blocked by esterifying these groups.

I. Studies on bacteriophage DNA's and minicircular DNA's in M. lysodeikticus and E. coli 15. II. Flow dichroism of DNA solutions

Part I

Chapter 1.....A physicochemical study of the DNA molecules from the three bacteriophages, N1, N5, and N6, which infect the bacterium, M. lysodeikticus, has been made. The molecular weights, as measured by both electron microscopy and sedimentation velocity, are 23 x 10⁶ for N5 DNA and 31 x 10⁶ for N1 and N6 DNA's. All three DNA's are capable of thermally reversible cyclization. N1 and N6 DNA's have identical or very similar base sequences as judged by membrane filter hybridization and by electron microscope heteroduplex studies. They have identical or similar cohesive ends. These results are in accord with the close biological relation between N1 and N6 phages. N5 DNA is not closely related to N1 or N6 DNA. The denaturation T_m of all three DNA's is the same and corresponds to a (GC) content of 70%. However, the buoyant densities in CsCl of Nl and N6 DNA's are lower than expected, corresponding to predicted GC contents of 64 and 67%. The buoyant densities in Cs₂SO₄ are also somewhat anomalous. The buoyant density anomalies are probably due to the presence of odd bases. However, direct base composition analysis of N1 DNA by anion exchange chromatography confirms a GC content of 70%, and, in the elution system used, no peaks due to odd bases are present.

Chapter 2.....A covalently closed circular DNA form has been observed as an intracellular form during both productive and abortive infection processes in M. lysodeikticus. This species has been isolated by the method of CsC1-ethidium bromide centrifugation and examined with an electron microscope.

Chapter 3.....A minute circular DNA has been discovered as a homogeneous population in M. lysodeikticus. Its length and molecular weight as determined by electron microscopy are 0.445 μ and 0.88 x 10⁶ daltons respectively. There is about one minicircle per bacterium.

Chapter 4.....Several strains of E. coli 15 harbor a prophage. Viral growth can be induced by exposing the host to mitomycin C or to uv irradiation. The coliphage 15 particles from E. coli 15 and E, coli 15 T^- appear as normal phage with head and tail structure; the particles from E. coli 15 TAU are tailless. The complete particles exert a colicinogenic activity on E.coli 15 and 15 T^-, the tailless particles do not. No host for a productive viral infection has been found and the phage may be defective. The properties of the DNA of the virus have been studied, mainly by electron microscopy. After induction but before lysis, a closed circular DNA with a contour length of about 11.9 μ is found in the bacterium; the mature phage DNA is a linear duplex and 7.5% longer than the intracellular circular form. This suggests the hypothesis that the mature phage DNA is terminally repetitious and circularly permuted. The hypothesis was confirmed by observing that denaturation and renaturation of the mature phage DNA produce circular duplexes with two single-stranded branches corresponding to the terminal repetition. The contour length of the mature phage DNA was measured relative to φX RFII DNA and λ DNA; the calculated molecular weight is 27 x 10⁶. The length of the single-stranded terminal repetition was compared to the length of φX 174 DNA under conditions where single-stranded DNA is seen in an extended form in electron micrographs. The length of the terminal repetition is found to be 7.4% of the length of the nonrepetitious part of the coliphage 15 DNA. The number of base pairs in the terminal repetition is variable in different molecules, with a fractional standard deviation of 0.18 of the average number in the terminal repetition. A new phenomenon termed "branch migration" has been discovered in renatured circular molecules; it results in forked branches, with two emerging single strands, at the position of the terminal repetition. The distribution of branch separations between the two terminal repetitions in the population of renatured circular molecules was studied. The observed distribution suggests that there is an excluded volume effect in the renaturation of a population of circularly permuted molecules such that strands with close beginning points preferentially renature with each other. This selective renaturation and the phenomenon of branch migration both affect the distribution of branch separations; the observed distribution does not contradict the hypothesis of a random distribution of beginning points around the chromosome.

Chapter 5....Some physicochemical studies on the minicircular DNA species in E. coli 15 (0.670 μ, 1.47 x 10⁶ daltons) have been made. Electron microscopic observations showed multimeric forms of the minicircle which amount to 5% of total DNA species and also showed presumably replicating forms of the minicircle. A renaturation kinetic study showed that the minicircle is a unique DNA species in its size and base sequence. A study on the minicircle replication has been made under condition in which host DNA synthesis is synchronized. Despite experimental uncertainties involved, it seems that the minicircle replication is random and the number of the minicircles increases continuously throughout a generation of the host, regardless of host DNA synchronization.

Part II

The flow dichroism of dilute DNA solutions (A₂₆₀≈0.1) has been studied in a Couette-type apparatus with the outer cylinder rotating and with the light path parallel to the cylinder axis. Shear gradients in the range of 5-160 sec.^-1 were studied. The DNA samples were whole, "half," and "quarter" molecules of T4 bacteriophage DNA, and linear and circular λb₂b₅c DNA. For the linear molecules, the fractional flow dichroism is a linear function of molecular weight. The dichroism for linear A DNA is about 1.8 that of the circular molecule. For a given DNA, the dichroism is an approximately linear function of shear gradient, but with a slight upward curvature at low values of G, and some trend toward saturation at larger values of G. The fractional dichroism increases as the supporting electrolyte concentration decreases.

Effects of particle size ratio on single particle motion in colloidal dispersions

The motion of a single Brownian particle of arbitrary size through a dilute colloidal dispersion of neutrally buoyant bath spheres of another characteristic size in a Newtonian solvent is examined in two contexts. First, the particle in question, the probe particle, is subject to a constant applied external force drawing it through the suspension as a simple model for active and nonlinear microrheology. The strength of the applied external force, normalized by the restoring forces of Brownian motion, is the Péclet number, Pe. This dimensionless quantity describes how strongly the probe is upsetting the equilibrium distribution of the bath particles. The mean motion and fluctuations in the probe position are related to interpreted quantities of an effective viscosity of the suspension. These interpreted quantities are calculated to first order in the volume fraction of bath particles and are intimately tied to the spatial distribution, or microstructure, of bath particles relative to the probe. For weak Pe, the disturbance to the equilibrium microstructure is dipolar in nature, with accumulation and depletion regions on the front and rear faces of the probe, respectively. With increasing applied force, the accumulation region compresses to form a thin boundary layer whose thickness scales with the inverse of Pe. The depletion region lengthens to form a trailing wake. The magnitude of the microstructural disturbance is found to grow with increasing bath particle size -- small bath particles in the solvent resemble a continuum with effective microviscosity given by Einstein's viscosity correction for a dilute dispersion of spheres. Large bath particles readily advect toward the minimum approach distance possible between the probe and bath particle, and the probe and bath particle pair rotating as a doublet is the primary mechanism by which the probe particle is able to move past; this is a process that slows the motion of the probe by a factor of the size ratio. The intrinsic microviscosity is found to force thin at low Péclet number due to decreasing contributions from Brownian motion, and force thicken at high Péclet number due to the increasing influence of the configuration-averaged reduction in the probe's hydrodynamic self mobility. Nonmonotonicity at finite sizes is evident in the limiting high-Pe intrinsic microviscosity plateau as a function of bath-to-probe particle size ratio. The intrinsic microviscosity is found to grow with the size ratio for very small probes even at large-but-finite Péclet numbers. However, even a small repulsive interparticle potential, that excludes lubrication interactions, can reduce this intrinsic microviscosity back to an order one quantity. The results of this active microrheology study are compared to previous theoretical studies of falling-ball and towed-ball rheometry and sedimentation and diffusion in polydisperse suspensions, and the singular limit of full hydrodynamic interactions is noted.

Second, the probe particle in question is no longer subject to a constant applied external force. Rather, the particle is considered to be a catalytically-active motor, consuming the bath reactant particles on its reactive face while passively colliding with reactant particles on its inert face. By creating an asymmetric distribution of reactant about its surface, the motor is able to diffusiophoretically propel itself with some mean velocity. The effects of finite size of the solute are examined on the leading order diffusive microstructure of reactant about the motor. Brownian and interparticle contributions to the motor velocity are computed for several interparticle interaction potential lengths and finite reactant-to-motor particle size ratios, with the dimensionless motor velocity increasing with decreasing motor size. A discussion on Brownian rotation frames the context in which these results could be applicable, and future directions are proposed which properly incorporate reactant advection at high motor velocities.

Developing and characterizing bulk metallic glasses for extreme applications

Metallic glasses have typically been treated as a “one size fits all” type of material. Every alloy is considered to have high strength, high hardness, large elastic limits, corrosion resistance, etc. However, similar to traditional crystalline materials, properties are strongly dependent upon the constituent elements, how it was processed, and the conditions under which it will be used. An important distinction which can be made is between metallic glasses and their composites. Charpy impact toughness measurements are performed to determine the effect processing and microstructure have on bulk metallic glass matrix composites (BMGMCs). Samples are suction cast, machined from commercial plates, and semi-solidly forged (SSF). The SSF specimens have been found to have the highest impact toughness due to the coarsening of the dendrites, which occurs during the semi-solid processing stages. Ductile to brittle transition (DTBT) temperatures are measured for a BMGMC. While at room temperature the BMGMC is highly toughened compared to a fully glassy alloy, it undergoes a DTBT by 250 K. At this point, its impact toughness mirrors that of the constituent glassy matrix. In the following chapter, BMGMCs are shown to have the capability of being capacitively welded to form single, monolithic structures. Shear measurements are performed across welded samples, and, at sufficient weld energies, are found to retain the strength of the parent alloy. Cross-sections are inspected via SEM and no visible crystallization of the matrix occurs.

Next, metallic glasses and BMGMCs are formed into sheets and eggbox structures are tested in hypervelocity impacts. Metallic glasses are ideal candidates for protection against micrometeorite orbital debris due to their high hardness and relatively low density. A flat single layer, flat BMG is compared to a BMGMC eggbox and the latter creates a more diffuse projectile cloud after penetration. A three tiered eggbox structure is also tested by firing a 3.17 mm aluminum sphere at 2.7 km/s at it. The projectile penetrates the first two layers, but is successfully contained by the third.

A large series of metallic glass alloys are created and their wear loss is measured in a pin on disk test. Wear is found to vary dramatically among different metallic glasses, with some considerably outperforming the current state-of-the-art crystalline material (most notably Cu₄₃Zr₄₃Al₇Be₇). Others, on the other hand, suffered extensive wear loss. Commercially available Vitreloy 1 lost nearly three times as much mass in wear as alloy prepared in a laboratory setting. No conclusive correlations can be found between any set of mechanical properties (hardness, density, elastic, bulk, or shear modulus, Poisson’s ratio, frictional force, and run in time) and wear loss. Heat treatments are performed on Vitreloy 1 and Cu₄₃Zr₄₃Al₇Be₇. Anneals near the glass transition temperature are found to increase hardness slightly, but decrease wear loss significantly. Crystallization of both alloys leads to dramatic increases in wear resistance. Finally, wear tests under vacuum are performed on the two alloys above. Vitreloy 1 experiences a dramatic decrease in wear loss, while Cu₄₃Zr₄₃Al₇Be₇ has a moderate increase. Meanwhile, gears are fabricated through three techniques: electrical discharge machining of 1 cm by 3 mm cylinders, semisolid forging, and copper mold suction casting. Initial testing finds the pin on disk test to be an accurate predictor of wear performance in gears.

The final chapter explores an exciting technique in the field of additive manufacturing. Laser engineered net shaping (LENS) is a method whereby small amounts of metallic powders are melted by a laser such that shapes and designs can be built layer by layer into a final part. The technique is extended to mixing different powders during melting, so that compositional gradients can be created across a manufactured part. Two compositional gradients are fabricated and characterized. Ti 6Al¬ 4V to pure vanadium was chosen for its combination of high strength and light weight on one end, and high melting point on the other. It was inspected by cross-sectional x-ray diffraction, and only the anticipated phases were present. 304L stainless steel to Invar 36 was created in both pillar and as a radial gradient. It combines strength and weldability along with a zero coefficient of thermal expansion material. Only the austenite phase is found to be present via x-ray diffraction. Coefficient of thermal expansion is measured for four compositions, and it is found to be tunable depending on composition.

Binding site size limitations of imidazole-pyrrole polyamides for recognition in the minor groove of DNA

The discovery that the three ring polyamide Im-Py-Py-Dp containing imidazole (Im) and pyrrole (Py) carboxamides binds the DNA sequence 5'-(A,T)G(A,T)C(A,T)-3' as an antiparallel dimer offers a new model for the design of ligands for specific recognition of sequences in the minor groove containing both G,C and A,T base pairs. In Chapter 2, experiments are described in which the sequential addition of five N- methylpyrrolecarboxamides to the imidazole-pyrrole polyamide Im-Py-Py-Dp affords a series of six homologous polyamides, Im-(Py)_2-7-Dp, that differ in the size of their binding site, apparent first order binding affinity, and sequence specificity. These results demonstrate that DNA sequences up to nine base pairs in length can be specifically recognized by imidazole-pyrrole polyamides containing three to seven rings by 2:1 polyamide-DNA complex formation in the minor groove. Recognition of a nine base pair site defines the new lower limit of the binding site size that can be recognized by polyamides containing exclusively imidazole and pyrrolecarboxamides. The results of this study should provide useful guidelines for the design of new polyamides that bind longer DNA sites with enhanced affinity and specificity.

In Chapter 3 the design and synthesis of the hairpin polyamide Im-Py-Im-Py-γ-Im- Py-Im-Py-Dp is described. Quantitative DNase I footprint titration experiments reveal that Im-Py-Im-Py-γ-Im-Py-Im-Py-Dp binds six base pair 5'-(A,T)GCGC(A,T)-3' sequences with 30-fold higher affinity than the unlinked polyamide Im-Py-Im-Py-Dp. The hairpin polyamide does not discriminate between A•T and T•A at the first and sixth positions of the binding site as three sites 5'-TGCGCT-3', 5'-TGCGCA-3', and 5 'AGCGCT- 3' are bound with similar affinity. However, Im-Py-Im-Py-γ-Im-Py-Im-PyDp is specific for and discriminates between G•C and C•G base pairs in the 5'-GCGC-3' core as evidenced by lower affinities for the mismatched sites 5'-AACGCA-3', 5'- TGCGTT-3', 5'-TGCGGT-3', and 5'-ACCGCT-3'.

In Chapter 4, experiments are described in which a kinetically stable hexa-aza Schiff base La³⁺ complex is covalently attached to a Tat(49-72) peptide which has been shown to bind the HIV-1 TAR RNA sequence. Although these metallo-peptides cleave TAR site-specifically in the hexanucleotide loop to afford products consistent with hydrolysis, a series of control experiments suggests that the observed cleavage is not caused by a sequence-specifically bound Tat(49-72)-La(L)³⁺ peptide.

Understanding planet formation through high precision photometry and spectroscopy

From studies of protoplanetary disks to extrasolar planets and planetary debris, we aim to understand the full evolution of a planetary system. Observational constraints from ground- and space-based instrumentation allows us to measure the properties of objects near and far and are central to developing this understanding. We present here three observational campaigns that, when combined with theoretical models, reveal characteristics of different stages and remnants of planet formation. The Kuiper Belt provides evidence of chemical and dynamical activity that reveals clues to its primordial environment and subsequent evolution. Large samples of this population can only be assembled at optical wavelengths, with thermal measurements at infrared and sub-mm wavelengths currently available for only the largest and closest bodies. We measure the size and shape of one particular object precisely here, in hopes of better understanding its unique dynamical history and layered composition.

Molecular organic chemistry is one of the most fundamental and widespread facets of the universe, and plays a key role in planet formation. A host of carbon-containing molecules vibrationally emit in the near-infrared when excited by warm gas, T~1000 K. The NIRSPEC instrument at the W.M. Keck Observatory is uniquely configured to study large ranges of this wavelength region at high spectral resolution. Using this facility we present studies of warm CO gas in protoplanetary disks, with a new code for precise excitation modeling. A parameterized suite of models demonstrates the abilities of the code and matches observational constraints such as line strength and shape. We use the models to probe various disk parameters as well, which are easily extensible to others with known disk emission spectra such as water, carbon dioxide, acetylene, and hydrogen cyanide.

Lastly, the existence of molecules in extrasolar planets can also be studied with NIRSPEC and reveals a great deal about the evolution of the protoplanetary gas. The species we observe in protoplanetary disks are also often present in exoplanet atmospheres, and are abundant in Earth's atmosphere as well. Thus, a sophisticated telluric removal code is necessary to analyze these high dynamic range, high-resolution spectra. We present observations of a hot Jupiter, revealing water in its atmosphere and demonstrating a new technique for exoplanet mass determination and atmospheric characterization. We will also be applying this atmospheric removal code to the aforementioned disk observations, to improve our data analysis and probe less abundant species. Guiding models using observations is the only way to develop an accurate understanding of the timescales and processes involved. The futures of the modeling and of the observations are bright, and the end goal of realizing a unified model of planet formation will require both theory and data, from a diverse collection of sources.

Sequence-function relationships in E. coli transcriptional regulation

Understanding how transcriptional regulatory sequence maps to regulatory function remains a difficult problem in regulatory biology. Given a particular DNA sequence for a bacterial promoter region, we would like to be able to say which transcription factors bind there, how strongly they bind, and whether they interact with each other and/or RNA polymerase, with the ultimate objective of integrating knowledge of these parameters into a prediction of gene expression levels. The theoretical framework of statistical thermodynamics provides a useful framework for doing so, enabling us to predict how gene expression levels depend on transcription factor binding energies and concentrations. We used thermodynamic models, coupled with models of the sequence-dependent binding energies of transcription factors and RNAP, to construct a genotype to phenotype map for the level of repression exhibited by the lac promoter, and tested it experimentally using a set of promoter variants from E. coli strains isolated from different natural environments. For this work, we sought to ``reverse engineer'' naturally occurring promoter sequences to understand how variations in promoter sequence affects gene expression. The natural inverse of this approach is to ``forward engineer'' promoter sequences to obtain targeted levels of gene expression. We used a high precision model of RNAP-DNA sequence dependent binding energy, coupled with a thermodynamic model relating binding energy to gene expression, to predictively design and verify a suite of synthetic E. coli promoters whose expression varied over nearly three orders of magnitude.

However, although thermodynamic models enable predictions of mean levels of gene expression, it has become evident that cell-to-cell variability or ``noise'' in gene expression can also play a biologically important role. In order to address this aspect of gene regulation, we developed models based on the chemical master equation framework and used them to explore the noise properties of a number of common E. coli regulatory motifs; these properties included the dependence of the noise on parameters such as transcription factor binding strength and copy number. We then performed experiments in which these parameters were systematically varied and measured the level of variability using mRNA FISH. The results showed a clear dependence of the noise on these parameters, in accord with model predictions.

Finally, one shortcoming of the preceding modeling frameworks is that their applicability is largely limited to systems that are already well-characterized, such as the lac promoter. Motivated by this fact, we used a high throughput promoter mutagenesis assay called Sort-Seq to explore the completely uncharacterized transcriptional regulatory DNA of the E. coli mechanosensitive channel of large conductance (MscL). We identified several candidate transcription factor binding sites, and work is continuing to identify the associated proteins.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

Studies on T-even bacteriophage DNA

Part I. The regions of sequence homology and non-homology between the DNA molecules of T2, T4, and T6 have been mapped by the electron microscopic heteroduplex method. The heteroduplex maps have been oriented with respect to the T4 genetic map. They show characteristic, reproducible patterns of substitution and deletion loops. All heteroduplex molecules show more than 85% homology. Some of the loop patterns in T2/T4 heteroduplexes are similar to those in T4/T6.

We find that the rII, the lysozyme and ac genes, the D region, and gene 52 are homologous in T2, T4, and T6. Genes 43 and 47 are probably homologous between T2 and T4. The region of greatest homology is that bearing the late genes. The host range region, which comprises a part of gene 37 and all of gene 38, is heterologous in T2, T4, and T6. The remainder of gene 37 is partially homologous in the T2/T4 heteroduplex (Beckendorf, Kim and Lielausis, 1972) but it is heterologous in T4/T6 and in T2/T6. Some of the tRNA genes are homologous and some are not. The internal protein genes in general seem to be non-homologous.

The molecular lengths of the T-even DNAs are the same within the limit of experimental error; their calculated molecular weights are correspondingly different due to unequal glucosylation. The size of the T2 genome is smaller than that of T4 or T6, but the terminally repetitious region in T2 is larger. There is a length distribution of the terminal repetition for any one phage DNA, indicating a variability in length of the DNA molecules packaged within the phage.

Part II. E. coli cells infected with phage strains carrying extensive deletions encompassing the gene for the phage ser-tRNA are missing the phage tRNAs normally present in wild type infected cells. By DNA-RNA hybridization we have demonstrated that the DNA complementary to the missing tRNAs is also absent in such deletion mutants. Thus the genes for these tRNAs must be clustered in the same region of the genome as the ser-tRNA gene. Physical mapping of several deletions of the ser-tRNA and lysozyme genes, by examination of heteroduplex DNA in the electron microscope, has enabled us to locate the cluster, to define its maximum size, and to order a few of the tRNA genes within it. That such deletions can be isolated indicates that the phage-specific tRNAs from this cluster are dispensable.

Part III. Genes 37 and 38 between closely related phages T2 and T4 have been compared by genetic, biochemical, and hetero-duplex studies. Homologous, partially homologous and non-homologous regions of the gene 37 have been mapped. The host range determinant which interacts with the gene 38 product is identified.

Part IV. A population of double-stranded ØX-RF DNA molecules carrying a deletion of about 9% of the wild-type DNA has been discovered in a sample cultivated under conditions where the phage lysozyme gene is nonessential. The structures of deleted monomers, dimers, and trimers have been studied by the electron microscope heteroduplex method. The dimers and trimers are shown to be head-to-tail repeats of the deleted monomers. Some interesting examples of the dynamical phenomenon of branch migration in vitro have been observed in heteroduplexes of deleted dimer and trimer strands with undeleted wild-type monomer viral strands.