A Method to Assess Granger Causality, Isolation and Autonomy in the Time and Frequency Domains: Theory and Application to Cerebrovascular Variability.

OBJECTIVE: Concepts of Granger causality (GC) and Granger autonomy (GA) are central to assess the dynamics of coupled physiologic processes. While causality measures have been already proposed and largely applied in time and frequency domains, measures quantifying self-dependencies are still limited to the time-domain formulation and lack of a clear spectral representation. METHODS: We embed into the classical linear parametric framework for computing GC from a driver random process X to a target process Y a measure of Granger Isolation (GI) quantifying the part of the dynamics of Y not originating from X, and a new spectral measure of GA assessing frequency-specific patterns of self-dependencies in Y. The framework is formulated in a way such that the full-frequency integration of the spectral GC, GI and GA measures returns the corresponding time-domain measures. The measures are illustrated in theoretical simulations and applied to time series of mean arterial pressure and cerebral blood flow velocity obtained in subjects prone to develop postural syncope and healthy controls. RESULTS: simulations show that GI is complementary to GC but not trivially related to it, while GA reflects the regularity of the internal dynamics of the analyzed target process. In the application to cerebrovascular interactions, spectral GA quantified the physiological response to postural stress of slow cerebral blood flow oscillations, while spectral GC and GI detected an altered response to postural stress in subjects prone to syncope, likely related to impaired cerebral autoregulation. CONCLUSION AND SIGNIFICANCE: The new spectral measures of GI and GA are useful complements to GC for the analysis of interacting oscillatory processes, and detect physiological and pathological responses to postural stress which cannot be traced in the time domain. The thorough assessment of causality, isolation and autonomy opens new perspectives for the analysis of coupled biological processes in both physiological and clinical investigations.

Capillary electrophoresis coupled with mass spectrometry for the evaluation of substance P enzymatic degradation by SaOS-2 human osteosarcoma.

A new analytical method for the detection and the quantitative evaluation of the undecapeptide substance P by capillary electrophoresis coupled with ion trap mass spectrometry (CE-MS) by a co-axial sheath liquid interface has been developed. Conditions of analysis employed an acidic buffer and a 60 cm fused silica capillary installed by overcoming the UV window position, thus allowing to perform the analysis in a brief time. The method has been applied to the evaluation of substance P enzymatic hydrolysis during incubation with the human osteosarcoma SaOS-2 cell line. The analysis of amino acids derived from the cleavage of substance P has been also carried out simultaneously under the same electrophoretic conditions allowing the description of a kinetic of amino acid formation, parallel with substance P disappearance. The amounts of intact substance P and of free amino acids were monitored along 600 s of incubation time. A steady decrease of substance P as function of reaction time was observed. Peptide's half-life was found to be about 4.3s, indicating an extremely fast hydrolysis in the presence of the SaOS-2 cells. Proline, phenilalanine and methionine were the predominant free amino acids recorded. Obtained results lead to hypothesize the occurrence of endopeptidases activity, followed by aminopeptidases responsible for the release of free amino acids originated after primary bond cleavage.

Hydrolysis of substance P in the presence of the osteosarcoma cell line SaOS-2: release of free amino acids.

The possible hydrolysis of substance P (Arg-Pro-Lys-Pro-Gln-Gln-Phe-Phe-Gly-Leu-Met) in presence of the osteoblastic cell line SaOS-2 was measured by capillary electrophoresis coupled to mass detection. The results obtained indicate that a very rapid disappearance of the intact undecapeptide was associated to a slower appearance of seven of its eight component amino acids. These results can be interpreted as indicating that an extremely fast hydrolysis of substance P by endopeptidases, which released peptidic by-products, was followed by a noticeably slower secondary degradation which released free amino acids. In decreasing quantitative importance, these phenomena appear to originate by the hydrolysis of the Pro(4)-Gln(5) bond, followed by C-terminal sequential degradation of the Arg(1)-Pro(4) tetrapeptide; by the hydrolysis of or Phe(7)-Phe(8) bond (or, possibly, of Gln(6)-Phe(7)) leading to release of free Phe and Gln; by hydrolysis of the Gly(9)-Leu(10) bond with subsequent release of Met and Leu. Results obtained appear to be compatible with the expression by SaOS-2 cells of enzymes already known to catalyze substance P hydrolysis, together with an apparent low efficiency of aminopeptidases. Because of the activity of C-terminal fragments on NK1 receptors, the delay between primary hydrolysis of substance P and secondary hydrolysis of its peptidic fragments indicated by the data shown implies a possible persistence of substance P physiological effects even after degradation of the intact peptide.