The surface viscosity of mixed monolayers

Summary The theory ofEyring of viscous flow, allows to describe the newtonian surface viscosity of a monolayer containing only one active component. This theory is extended to mixed monolayers with miscible components, allowing to calculate the surface viscosity of a surface mixture if the flow parameters of the single components are known. This theory is experimentally illustrated for the systems senegin/digitonin and cholesterol/phospholipids. The results of the last system are discussed in terms of the property of cholesterol being a liquifier in cell membranes.Next the surface viscosities of dilute cholesterol monolayers penetrated by digitonin are given. In this situation no agreement between theory and experiment is observed, indicating an interaction between these components as already known from other experimental techniques. This increased surface viscosity may be related to the strong hemolytic action of digitonin.Paper presented to the British Society of Rheology Conference on Rheology in Medicine and Pharmacy, London, April 14–15, 1970.     

Characterization of a new tailoring domain in polyketide biogenesis: the amine transferase domain of MycA in the mycosubtilin gene cluster

We report the expression and characterization of a truncated form of MycA from the Mycosubtilin gene cluster from Bacillus subtilis. The MycA fragment contains a new amino transferase (AMT) tailoring domain, allowing the first detailed study of a PLP-dependent enzyme operating in cis within the PKS and NRPS biosynthetic paradigm. As the AMT domain acts on covalently bound beta-ketothioesters, and is therefore a single-turnover system, electrospray ionization-Fourier transform mass spectrometry (ESI-FTMS) was used to observe the amine-transfer reaction both for amine donor substrate specificity and to regiospecifically determine enzyme-bound intermediates. We confirm the function of the AMT domain, dissect the mechanistic steps of amine transfer, identify the preferred amine source, and localize the beta-ketothioester substrate during amine transfer.     

Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.     

A fluorescent assay for chloride transport; identification of a synthetic anionophore with improved activity

A fluorescent assay based on the chloride-sensitive probe, lucigenin, is developed for monitoring chloride transport into vesicles, and used to compare the effectiveness of three steroid-derived transporters.     

Unusual coordination behavior of Cr3+ in microporous aluminophosphates

A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the AFI-type. A comparison of the XANES data, a preedge analysis with crystal field multiplet calculations and EXAFS data, pointed toward the presence of framework Cr3+ which, on dehydration, takes on a distorted tetrahedral coordination state. Due to the 3d3 configuration of Cr3+, this unusual tetrahedral coordination environment strongly tends to transform into the more stable 6-fold coordination geometry by binding two extraframework water molecules during hydration. In the presence of ammonia, tetrahedral Cr3+ readily transforms into a 5-fold coordination geometry by binding one ammonia molecule. Therefore, depending on the environmental conditions, the Cr3+ ions can occur in a 4-, 5-, or 6-fold coordination. This observation underlines the flexibility of transition metal ions, such as Cr3+, to cope with unusual coordination geometries in inorganic hosts, making them interesting as potential active sites in heterogeneous catalysis.     

Locally anisotropic toposes

This paper continues the investigation of isotropy theory for toposes. We develop the theory of isotropy quotients of toposes, culminating in a structure theorem for a class of toposes we call locally anisotropic. The theory has a natural interpretation for inverse semigroups, which clarifies some aspects of how inverse semigroups and toposes are related.     

The improper infinite derivatives of Takagi's nowhere-differentiable function

Let T be Takagi's continuous but nowhere-differentiable function. Using a representation in terms of Rademacher series due to N. Kono [Acta Math. Hungar. 49 (1987) 315-324], we give a complete characterization of those points where T has a left-sided, right-sided, or two-sided infinite derivative. This characterization is illustrated by several examples. A consequence of the main result is that the sets of points where T^′(x)=±∞ have Hausdorff dimension one. As a byproduct of the method of proof, some exact results concerning the modulus of continuity of T are also obtained.     

Computation of symbolic dynamics for one-dimensional maps

In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation.     

Synthesis and characterization of long perylenediimide polymer fibers: from bulk to the single-molecule level

The synthesis and characterization of perylenediimide polyisocyanides is reported. In addition to short oligomers, our synthetic approach results in the formation of extremely long, well-defined, and rigid perylenediimide polymers. Ordering and close-packing of the chromophores in these long polymers is guaranteed by attachment to a polyisocyanide backbone with amino acid side chains. Hydrogen bonding interactions between those groups stabilize and rigidify the helical polymer structure. The rodlike nature of the synthesized long perylenediimide pendant polyisocyanides as well as the helical arrangement of the chromophores is demonstrated by means of atomic force microscopy. Remarkably, polymer fibers up to 1 mum in length have been visualized, containing several thousands of perylenediimide molecules. Circular dichroism spectroscopy reveals the chiral organization of the chromophore units in the polymer, whereas absorption and emission measurements prove the occurrence of excited-state interactions between those moieties due to the close packing of the chromophore groups. However, an intricate optical behavior is encountered in bulk as a result of the coexistence of short oligomers and long polymers of perylenediimide, a situation subsequently uncovered by means of single-molecule experiments. Individual long helical perylenediimide polyisocyanides exhibit a typical red-shifted fluorescence spectrum, which, together with depolarized emission continuously decreasing in time, demonstrate that fluorescence arises from multiple excimer-like species in the polymer. Upon continuous irradiation of these long polymers, a fast decay in fluorescence lifetime is observed, a situation explained by photoinduced creation of quenching sites. Radical/ion formation by intramolecular electron transfer between close-by perylenediimide moieties is the most probable mechanism for this process. Appropriate control of the electron-transfer process might open the possibility of applying these polymers as perylenediimide-based supramolecular nanowires.