Characterising knotting properties of polymers in nanochannels.

Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either "local" or "non-local", based on a standard approach for measuring the "size" of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or "local"; otherwise, it is "non-local". Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed chains) in a tubular sublattice of the simple cubic lattice are "non-locally" knotted. This is shown to also hold for the case when the same polygons are subject to an external tensile force, as well as in the extreme case when they are as compact as possible (no empty lattice sites). We also provide numerical evidence for small tube sizes that at equilibrium non-local knotting is more likely than local knotting, regardless of the strength of the stretching or compressing force. The relevance of these results to other models and recent experiments involving DNA knots is also discussed.

Basolateral K channel activated by carbachol in the epithelial cell line T84.

Cholinergic stimulation of chloride secretion involves the activation of a basolateral membrane potassium conductance, which maintains the electrical gradient favoring apical Cl efflux and allows K to recycle at the basolateral membrane. We have used transepithelial short-circuit current (Isc), fluorescence imaging, and patch clamp studies to identify and characterize the K channel that mediates this response in T84 cells. Carbachol had little effect on Isc when added alone but produced large, transient currents if added to monolayers prestimulated with cAMP. cAMP also enhanced the subsequent Isc response to calcium ionophores. Carbachol (100 microM) transiently elevated intracellular free calcium ([Ca2+]i) by approximately 3-fold in confluent cells cultured on glass coverslips with a time course resembling the Isc response of confluent monolayers that had been grown on porous supports. In parallel patch clamp experiments, carbachol activated an inwardly rectifying potassium channel on the basolateral aspect of polarized monolayers which had been dissected from porous culture supports. The same channel was transiently activated on the surface of subconfluent monolayers during stimulation by carbachol. Activation was more prolonged when cells were exposed to calcium ionophores. The conductance of the inward rectifier in cell-attached patches was 55 pS near the resting membrane potential (-54 mV) with pipette solution containing 150 mM KCl (37 degrees C). This rectification persisted when patches were bathed in symmetrical 150 mM KCl solutions. The selectivity sequence was 1 K > 0.88 Rb > 0.18 Na >> Cs based on permeability ratios under bi-ionic conditions. The channel exhibited fast block by external sodium ions, was weakly inhibited by external TEA, was relatively insensitive to charybdotoxin, kaliotoxin, 4-aminopyridine and quinidine, and was unaffected by external 10 mM barium. It is referred to as the KBIC channel based on its most distinctive properties (Ba-insensitive, inwardly rectifying, Ca-activated). Like single KBIC channels, the carbachol-stimulated Isc was relatively insensitive to several blockers on the basolateral side and was unaffected by barium. These comparisons between the properties of the macroscopic current and single channels suggest that the KBIC channel mediates basolateral membrane K conductance in T84 cell monolayers during stimulation by cholinergic secretagogues.

Regulation of an inwardly rectifying K channel in the T84 epithelial cell line by calcium, nucleotides and kinases.

Agonists that elevate calcium in T84 cells stimulate chloride secretion by activating KBIC, an inwardly rectifying K channel in the basolateral membrane. We have studied the regulation of this channel by calcium, nucleotides and phosphorylation using patch clamp and short-circuit current (ISC) techniques. Open probability (Po) was independent of voltage but declined spontaneously with time after excision. Rundown was slower if patches were excised into a bath solution containing ATP (10 microM-5 mM), ATP (0.1 mM)+protein kinase A (PKA; 180 nM), or isobutylmethylxanthine (IBMX; 1 mM). Analysis of event durations suggested that the channel has at least two open and two closed states, and that rundown under control conditions is mainly due to prolongation of the long closed time. Channel activity was restimulated after rundown by exposure to ATP, the poorly hydrolyzable ATP analogue AMP-PNP, or ADP. Activity was further enhanced when PKA was added in the presence of MgATP, but only if free calcium concentration was elevated (400 nM). Nucleotide stimulation and inward rectification were both observed in nominally Mg-free solutions. cAMP modulation of basolateral potassium conductance in situ was confirmed by measuring currents generated by a transepithelial K gradient after permeabilization of the apical membrane using alpha-toxin. Finally, protein kinase C (PKC) inhibited single KBIC channels when it was added directly to excised patches. These results suggest that nonhydrolytic binding of nucleotides and phosphorylation by PKA and PKC modulate the responsiveness of the inwardly rectifying K channel to Ca-mediated secretagogues.