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The quantitation of buffering action II. Applications of the formal & general approach.

ABSTRACT: BACKGROUND: The paradigm of "buffering" originated in acid-base physiology, but was subsequently extended to other fields and is now used for a wide and diverse set of phenomena. In the preceding article, we have presented a formal and general approach to the quantitation of buffering action. Here, we use that buffering concept for a systematic treatment of selected classical and other buffering phenomena. RESULTS: H+ buffering by weak acids and "self-buffering" in pure water represent "conservative buffered systems" whose analysis reveals buffering properties that contrast in important aspects from classical textbook descriptions. The buffering of organ perfusion in the face of variable perfusion pressure (also termed "autoregulation") can be treated in terms of "non-conservative buffered systems", the general form of the concept. For the analysis of cytoplasmic Ca++ concentration transients (also termed "muffling"), we develop a related unit that is able to faithfully reflect the time-dependent quantitative aspect of buffering during the pre-steady state period. Steady-state buffering is shown to represent the limiting case of time-dependent muffling, namely for infinitely long time intervals and infinitely small perturbations. Finally, our buffering concept provides a stringent definition of "buffering" on the level of systems and control theory, resulting in four absolute ratio scales for control performance that are suited to measure disturbance rejection and setpoint tracking, and both their static and dynamic aspects. CONCLUSION: Our concept of buffering provides a powerful mathematical tool for the quantitation of buffering action in all its appearances.

SUBMITTER: Schmitt BM

PROVIDER: S-EPMC1079954 | biostudies-literature | 2005

REPOSITORIES: biostudies-literature

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The quantitation of buffering action II. Applications of the formal & general approach.

Schmitt Bernhard M BM

Theoretical biology & medical modelling 20050316

<h4>Background</h4>The paradigm of "buffering" originated in acid-base physiology, but was subsequently extended to other fields and is now used for a wide and diverse set of phenomena. In the preceding article, we have presented a formal and general approach to the quantitation of buffering action. Here, we use that buffering concept for a systematic treatment of selected classical and other buffering phenomena.<h4>Results</h4>H+ buffering by weak acids and "self-buffering" in pure water repres ...[more]

PMID: 15771784

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Project description:BackgroundAlthough "buffering" as a homeostatic mechanism is a universal phenomenon, the quantitation of buffering action remains controversial and problematic. Major shortcomings are: lack of a buffering strength unit for some buffering phenomena, multiple and mutually incommensurable units for others, and lack of a genuine ratio scale for buffering strength. Here, I present a concept of buffering that overcomes these shortcomings.TheoryBriefly, when, for instance, some "free" H+ ions are added to a solution (e.g. in the form of strong acid), buffering is said to be present when not all H+ ions remain "free" (i.e., bound to H2O), but some become "bound" (i.e., bound to molecules other than H2O). The greater the number of H+ ions that become "bound" in this process, the greater the buffering action. This number can be expressed in two ways: 1) With respect to the number of total free ions added as "buffering coefficient b", defined in differential form as b = d(bound)/d(total). This measure expresses buffering action from nil to complete by a dimensionless number between 0 and 1, analogous to probabilites. 2) With respect to the complementary number of added ions that remain free as "buffering ratio B", defined as the differential B = d(bound)/d(free). The buffering ratio B provides an absolute ratio scale, where buffering action from nil to perfect corresponds to dimensionless numbers between 0 and infinity, and where equal differences of buffering action result in equal intervals on the scale. Formulated in purely mathematical, axiomatic form, the concept reveals striking overlap with the mathematical concept of probability. However, the concept also allows one to devise simple physical models capable of visualizing buffered systems and their behavior in an exact yet intuitive way.ConclusionThese two measures of buffering action can be generalized easily to any arbitrary quantity that partitions into two compartments or states, and are thus suited to serve as standard units for buffering action. Some exemplary treatments of classical and non-classical buffering phenomena are presented in the accompanying paper.

Project description:An ability to efficiently compute the electrostatic potential produced by molecular charge distributions under realistic solvation conditions is essential for a variety of applications. Here, the simple closed-form analytical approximation to the Poisson equation rigorously derived in Part I for idealized spherical geometry is tested on realistic shapes. The effects of mobile ions are included at the Debye-Huckel level. The accuracy of the resulting closed-form expressions for electrostatic potential is assessed through comparisons with numerical Poisson-Boltzmann (NPB) reference solutions on a test set of 580 representative biomolecular structures under typical conditions of aqueous solvation. For each structure, the deviation from the reference is computed for a large number of test points placed near the dielectric boundary (molecular surface). The accuracy of the approximation, averaged over all test points in each structure, is within 0.6 kcal/mol/mid R:emid R: approximately kT per unit charge for all structures in the test set. For 91.5% of the individual test points, the deviation from the NPB potential is within 0.6 kcal/mol/mid R:emid R:. The deviations from the reference decrease with increasing distance from the dielectric boundary: The approximation is asymptotically exact far away from the source charges. Deviation of the overall shape of a structure from ideal spherical does not, by itself, appear to necessitate decreased accuracy of the approximation. The largest deviations from the NPB reference are found inside very deep and narrow indentations that occur on the dielectric boundaries of some structures. The dimensions of these pockets of locally highly negative curvature are comparable to the size of a water molecule; the applicability of a continuum dielectric models in these regions is discussed. The maximum deviations from the NPB are reduced substantially when the boundary is smoothed by using a larger probe radius (3 A) to generate the molecular surface. A detailed accuracy analysis is presented for several proteins of various shapes, including lysozyme whose surface features a functionally relevant region of negative curvature. The proposed analytical model is computationally inexpensive; this strength of the approach is demonstrated by computing and analyzing the electrostatic potential generated by a full capsid of the tobacco ring spot virus at atomic resolution (500 000 atoms). An analysis of the electrostatic potential of the inner surface of the capsid reveals what might be a RNA binding pocket. These results are generated with the modest computational power of a desktop personal computer.

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The quantitation of buffering action II. Applications of the formal & general approach.

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The quantitation of buffering action II. Applications of the formal & general approach.

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