Deciphering the Homeokinetic Code of Airway Smooth Muscle

CHENG-LI QUE, G. MAKSYM, and PETER T. MACKLEM

Inspiraplex, Respiratory Health Network of Centers of Excellence, Montreal Chest Institute, Montreal, Quebec, Canada

	INTRODUCTION

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We have found that short-term variation in airway caliber in unaffected subjects and subjects with asthma follows a power law (1, 2). To do this we measured respiratory impedance (Zrs) by the forced oscillation technique at 6 Hz while the subject breathed quietly for 15 min. We subtracted each individual value of Zrs from the mean value, squared the difference, and divided the squared differences (Zvar) into 20 bins and plotted frequency distribution curves in log₁₀-log₁₀ space. The data for all subjects were linear (Figure 1) and described by f = a · Zvar^b, where f is the fraction of the total number of measurements in a given bin, b is the slope of the log₁₀-log₁₀ plot and is negative, and log₁₀a is the intercept. Variable b is the same in unaffected subjects and subjects with asthma, but variable a was 2-5 orders of magnitude greater in subjects with asthma compared with the mean value in unaffected subjects (Figure 2).

View larger version (20K): [in this window] [in a new window]   Figure 1.   (A) Raw data of impedance for a healthy subject (RC) and for a subject with asthma (LC). (B) Frequency distribution curves. Ni/N = fraction of total number of measurements.

View larger version (23K): [in this window] [in a new window]   Figure 2.   Linear regression and 99% confidence intervals for healthy subjects and subjects with asthma.

When airway smooth muscle (ASM) was activated by methacholine (MCh) in healthy subjects and the muscle was simultaneously unloaded by assuming the supine position, variable b did not change, but log₁₀a was increased into the asthmatic range (Figure 3). Unloading in this sense means diminishing the tidal stresses below the level required to keep airways normally dilated (3). Thus, activated unloaded normal smooth muscle behaves in a manner almost identical to asthmatic smooth muscle (4, 5).

View larger version (30K): [in this window] [in a new window]   Figure 3.   (Top panel ) Slope comparisons of healthy subjects under different conditions. (Bottom panel ) Intercept comparison of healthy subjects under different conditions.

What does activation and unloading do to smooth muscle? The measurement of Zrs is the integrated result of uncountable trillions of ASM cross-bridges cycling in some 250,000 airways that contribute to the flow resistance of the lung (RL). In a given data set, a given value of Zrs or Zvar results from a set of tracheobronchial configurations that produce that particular value of Zrs or Zvar. For the same value of Zvar at different values of Zrs (in a healthy subject before and after MCh, for example) the configurations are different. That is to say that two different sets of configuration changes can produce the same Zvar. In fact, the airway configuration after the generalized airway narrowing produced by MCh would be possible in a normal lung but would be rarely found.

Assume that each of 250,000 airways has three possible configurations, normal, dilated, and constricted; the configuration present at a given time depends on the fraction of the total number of cross-bridges in that airway that is attached. The total number of possible configurations of the tracheobronchial tree is 3^250,000. If each airway could change its configuration in 1 ms, it would take longer than the age of the universe to cycle through all possible configurations. Assume that under normal circumstances the airways cycle mainly between the normal and dilated configurations and that when ASM is activated by MCh they are now biased to cycle mainly between the normal and constricted configurations. This will increase mean Zrs and simultaneously increase Zvar because RL will be more sensitive to further decrements of ASM length. However, the data produced by healthy subjects show that this is insufficient to account for the variability of airway caliber seen in asthma.

Because the data show that a given value of Zvar occurs 100 to 100,000 times more frequently in subjects with asthma, the increased variation in asthma would appear to be the result of a more rapid change in configuration. This would occur if the velocity of ASM shortening was increased so that there was a faster rate of cycling between the normal and constricted states in the subject with asthma than in the healthy subject. This is expected if the muscle is unloaded (6).

When any muscle, striated or smooth, is activated it generally produces power, the product of shortening velocity and force. However, the activator does not determine how much of the power is expressed as force and how much is expressed as velocity. It is the load the muscle is acting against that determines the partitioning between these two variables. As the load decreases, the force decreases with it and the velocity of shortening increases according to the muscle force-velocity relationship (6).

Thus the unloading resulting from the decreased lung volume in the supine position will increase the velocity of shortening, which in turn will increase the rate at which the airways will change their configuration. In healthy subjects, in the supine position, this did increase the value of log₁₀a without changing variable b, but the increase in log₁₀a was not sufficient to bring it into the asthmatic range. While unloading alone increased Zrs somewhat, its main effect was on Zvar. Thus its effect on rate of change of configuration was predominant. Its effect on the airways to cycle more frequently to the constricted configuration was less. With methacholine, in contrast, we believe the airways were biased to cycle more between the normal and constricted state, with a lesser change in velocity of shortening and cycling rate.

With simultaneous activation and unloading, normal smooth muscle behaved like asthmatic smooth muscle. This suggests that in asthma the velocity of airway smooth muscle is increased. This would occur if the muscle were unloaded because of peribronchial inflammation decreasing the local elastic recoil pressure and shear modulus. The effect of elastic recoil pressure on rate of change of RL has been studied by Bates and coworkers (7). We know that at a lung-distending pressure of 10 cm H₂O in humans, ASM contracts quasisometrically after methacholine administration, with no detectable increase in RL (8), and thus ASM has zero velocity of shortening. At distending pressures of 4 and 2 cm H₂O in the rat intravenous methacholine increases pulmonary resistance by ~ 4-fold and ~ 18-fold over the same time period, compared with 6 cm H₂O (7). Assuming that RL  1/r⁴, where r = radius, this corresponds to the velocities of shortening estimated relative to the velocity of shortening at a distending pressure of 6 cm H₂O, shown in Table 1. The effects of velocity of shortening on RL and Zvar are not trivial.

The study by Mandelbrot on the effects of the rate of change in stock market prices on stock market volatility (9) is directly applicable to the effects of velocity of shortening on airway stability. In his model, Mandelbrot increased the rate of price rises and lengthened the rate of price decreases so that the total time remained constant. He found that this increased volatility, with periods of relatively stable stock market behavior interspersed with periods of high volatility. This is strikingly similar to the increasing velocity of shortening of ASM but with the lengthening period determined by inspiratory time. Comparing our data with those of Mandelbrot, Zrs fluctuations in healthy upright subjects are similar to a relatively stable stock market when the rate of price increase is slow. On the other hand, Zrs fluctuations in healthy supine subjects, healthy supine subjects treated with methacholine, and subjects with asthma resemble a much more volatile stock market and do demonstrate periods of relative stability interspersed with much more volatile periods.

At thermodynamic equilibrium the entropy of a system is maximal. However, all living matter is complex and functions far from thermodynamic equilibrium (10). This requires a continuous supply and dissipation of energy. For a given system the greater the energy dissipation, the further it is from equilibrium. The further a system is from equilibrium the less its entropy will be. The less the entropy the more frequent will be the occurrence of rare, statistically improbable events (10). We know that in asthma the energy dissipation of ASM is increased because the smooth muscle is activated, presumably by inflammatory agonists. From the study by Prigogine and Stengers of systems far from equilibrium and irreversible nonlinear thermodynamics we can therefore predict what will be the result (10). Entropy will be lowered and there will be an increased appearance of rare, statistically improbable events. The data shown in Figures 1-3 show that these predictions are accurate. Indeed, log₁₀a should be a measure of distance from equilibrium and thus predict the probability of the statistically improbable event of a life-threatening attack of asthma.

	IMPORTANT QUESTIONS

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• Is airway smooth muscle unloaded in asthma and, if so, what is the mechanism?
• Is the increase in velocity of shortening sufficient to counteract the bronchodilation resulting from tidal stresses?
• What are the effects of inflammatory and genetic factors on cross-bridge kinetics?
• Can variations in impedance predict those individuals with asthma at risk of life-threatening attacks?

	Footnotes

Correspondence and requests for reprints should be addressed to P. T. Macklem, M.D., Montreal Chest Hospital Center, 3650 St. Urbain Street, Montreal, PQ, H2X 2P4 Canada.

	References

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6. Wang, J., H. Jiang, and N. L. Stephens. 1994. A modified force velocity equation for smooth muscle contraction. J. Appl. Physiol. 76: 253-258 [Abstract/Free Full Text].

7. Bates, J. H. T., J. H. T. Schuessler, C. Dolman, and D. H. Eidelman. 1997. Temporal dynamics of acute isovolume bronchoconstriction in the rat. J. Appl. Physiol. 82: 55-62 [Abstract/Free Full Text].

8. Sharma, A., W. J. Gibbons, and P. T. Macklem. 1994. Maximal bronchoconstriction and transpulmonary pressure in normals (abstract). Am. J. Respir. Crit. Care Med. 149: A586 .

9. Mandelbrot, B. B.. 1999. A multifractal walk down Wall Street. Sci. Am. 280: 70-73 [Medline].

10. Prigogine, I., and I. Stengers. 1984. Order out of Chaos: Man's New Dialogue with Nature. Bantam Books, New York.