Intrinsic characteristics of the proton pump in the luminal membrane of a tight urinary epithelium. The relation between transport rate and delta mu H.

A number of tight urinary epithelia, as exemplified by the turtle bladder, acidify the luminal solution by active transport of H+ across the luminal cell membrane. The rate of active H+ transport (JH) decreases as the electrochemical potential difference for H+ [delta mu H = mu H(lumen) - mu H(serosa)] across the epithelium is increased. The luminal cell membrane has a low permeability for H+ equivalents and a high electrical resistance compared with the basolateral cell membrane. Changes in JH thus reflect changes in active H+ transport across the luminal membrane. To examine the control of JH by delta mu H in the turtle bladder, transepithelial electrical potential differences (delta psi) were imposed at constant acid-base conditions or the luminal pH was varied at delta psi = 0 and constant serosal PCO2 and pH. When the luminal compartment was acidified from pH 7 to 4 or was made electrically positive, JH decreased as a linear function of delta mu H as previously described. When the luminal compartment was made alkaline from pH 7 to 9 or was made electrically negative, JH reached a maximal value, which was the same whether the delta mu H was imposed as a delta pH or a delta psi. The nonlinear JH vs. delta mu H relation does not result from changes in the number of pumps in the luminal membrane or from changes in the intracellular pH, but is a characteristic of the H+ pumps themselves. We propose a general scheme, which, because of its structural features, can account for the nonlinearity of the JH vs. delta mu H relations and, more specifically, for the kinetic equivalence of the effects of the chemical and electrical components of delta mu H. According to this model, the pump complex consists of two components: a catalytic unit at the cytoplasmic side of the luminal membrane, which mediates the ATP-driven H+ translocation, and a transmembrane channel, which mediates the transfer of H+ from the catalytic unit to the luminal solution. These two components may be linked through a buffer compartment for H+ (an antechamber).

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.