An intelligent liposome that may deliver drug molecules in a well controlled fashion

The passage of molecules, especially large ones, through the cellular membrane is a very important problem for some biotechnological applications, such as drug delivery. The appearance of pores in the lipid bilayer following some controlled mechanisms may be an adequate and interesting way. Some pores, named stochastic pores, can appear due to structural and dynamic properties of lipid bilayer, but others may be favored by mechanical tension induced by different ways. Recently, a sequence of 30-40 pores was observed in the same vesicle, a pore at a time, which can appear in vesicles stretched by optical induced mechanical tension. There are two very interesting biotechnological applications that require the increase of membrane permeability: gene therapy and targeted drug delivery. In the first one, the transport of DNA fragments through cellular and nuclear membranes is required. The second application uses drug molecules encapsulated in vesicles, which have to be transported to a target place. Having reached that point, one supposes that the liposome discharges its content by its breakdown. In this paper, we will write about how a lipid vesicle has to release the drug molecules in a well-controlled fashion. Such liposomes are named pulsatory liposomes and they induce cyclic activity. We will demonstrate that this liposome may be programmed to work a certain number of cycles, settled in advance. Also, we will calculate the amount of drug delivered during each cycle. In fact, a pulsatory liposome may be conceived as a drug dose micro device, which works according to a medical prescription established _a priori_

Analytic mappings between noncommutative pencil balls

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. In an earlier paper we characterized NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary; such maps we call "NC ball maps". In this paper we turn to a more general dimension-free ball B_L, called a "pencil ball", associated with a homogeneous linear pencil L(x):= A_1 x_1 + ... + A_m x_m, where A_j are complex matrices. For an m-tuple X of square matrices of the same size, define L(X):=\sum A_j \otimes X_j and let B_L denote the set of all such tuples X satisfying ||L(X)||<1. We study the generalization of NC ball maps to these pencil balls B_L, and call them "pencil ball maps". We show that every B_L has a minimal dimensional (in a certain sense) defining pencil L'. Up to normalization, a pencil ball map is the direct sum of L' with an NC analytic map of the pencil ball into the ball. That is, pencil ball maps are simple, in contrast to the classical result of D'Angelo on such analytic maps in C^m. To prove our main theorem, this paper uses the results of our previous paper mentioned above plus entirely different techniques, namely, those of completely contractive maps.Comment: 30 pages, final version. To appear in the Journal of Mathematical Analysis and Application