Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Stochastic comparability and dual q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.

Existence, uniqueness and constructions for stochastically monotone Q-processes

The key problems in discussing duality and monotonicity for continuous-time Markov chains are to find conditions for existence and uniqueness and then to construct corresponding processes in terms of infinitesimal characteristics, i.e., q-matrices. Such problems are solved in this paper under the assumption that the given q-matrix is conservative. Some general properties of stochastically monotone Q-process ( Q is not necessarily conservative) are also discussed.

Structure and denaturation of 4-chlorobenzoyl coenzyme A dehalogenase from Arthrobacter sp. strain TM-1

The secondary structure of the trimeric protein 4-chlorobenzoyl coenzyme A dehalogenase from Arthrobacter sp. strain TM-1, the second of three enzymes involved in the dechlorination of 4-chlorobenzoate to form 4-hydroxybenzoate, has been examined. E(mM) for the enzyme was 12.59. Analysis by circular dichroism spectrometry in the far uv indicated that 4-chlorobenzoyl coenzyme A dehalogenase was composed mostly of alpha-helix (56%) with lesser amounts of random coil (21%), beta-turn (13%) and beta-sheet (9%). These data are in close agreement with a computational prediction of secondary structure from the primary amino acid sequence, which indicated 55.8% alpha-helix, 33.7% random coil and 10.5% beta-sheet; the enzyme is, therefore, similar to the 4-chlorobenzoyl coenzyme A dehalogenase from Pseudomonas sp. CBS-3. The three-dimensional structure, including that of the presumed active site, predicted by computational analysis, is also closely similar to that of the Pseudomonas dehalogenase. Study of the stability and physicochemical properties revealed that at room temperature, the enzyme was stable for 24 h but was completely inactivated by heating to 60 degrees C for 5 min; thereafter by cooling at 1 degrees C min(-1) to 45 degrees C, 20.6% of the activity could be recovered. Mildly acidic (pH 5.2) or alkaline (pH 10.1) conditions caused complete inactivation, but activity was fully recovered on returning the enzyme to pH 7.4. Circular dichroism studies also indicated that secondary structure was little altered by heating to 60 degrees C, or by changing the pH from 7.4 to 6.0 or 9.2. Complete, irreversible destruction of, and maximal decrease in the fluorescence yield of the protein at 330-350 nm were brought about by 4.5 M urea or 1.1 M guanidinium chloride. Evidence was obtained to support the hypothetical three-dimensional model, that residues W140 and W167 are buried in a non-polar environment, whereas W182 appears at or close to the surface of the protein. At least one of the enzymes of the dehalogenase system (the combined 4-chlorobenzoate:CoA ligase, the dehalogenase and 4-hydroxybenzoyl coenzyme A thioesterase) appears to be capable of association with the cell membrane.