Nonlinear indicial response of complex nonstationary oscillations as pulmonary hypertension responding to step hypoxia

This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.

Carbohydrates in Individual Cells of Epidermis, Mesophyll, and Bundle Sheath in Barley Leaves with Changed Export or Photosynthetic Rate1

Carbohydrate metabolism of barley (Hordeum vulgare) leaves induced to accumulate sucrose (Suc) and fructans was investigated at the single-cell level using single-cell sampling and analysis. Cooling of the root and shoot apical meristem of barley plants led to the accumulation of Suc and fructan in leaf tissue. Suc and fructan accumulated in both mesophyll and parenchymatous bundle-sheath (PBS) cells because of the reduced export of sugars from leaves under cooling and to increased photosynthesis under high photon fluence rates. The general trends of Suc and fructan accumulation were similar for mesophyll and PBS cells. The fructan-to-Suc ratio was higher for PBS cells than for mesophyll cells, suggesting that the threshold Suc concentration needed for the initiation of fructan synthesis was lower for PBS cells. Epidermal cells contained very low concentrations of sugar throughout the cooling experiment. The difference in Suc concentration between control and treated plants was much less if compared at the single-cell level rather than the whole-tissue level, suggesting that the vascular tissue contains a significant proportion of total leaf Suc. We discuss the importance of analyzing complex tissues at the resolution of individual cells to assign molecular mechanisms to phenomena observed at the whole-plant level.