To determine the contribution of microtubules to a hypothetical intracellular matrix, we have analyzed the space occupied by microtubules in vitro. Taxol-stabilized microtubules assembled from purified (three-times-cycled) bovine brain microtubule protein were pelleted by centrifugation under standardized conditions. The specific volume of the pellet, defined as the microliter volume per milligram protein, was 22.4. As suggested by others, this volume was strongly dependent on microtubule-associated proteins (MAPs), as shown by quantitation of the effects of purified MAP supplementation on specific volume. The specific volumes of microtubule pellets stripped of MAPs by high salt or chymotryptic digestion approached the mathematically optimal (least occupied space) and increased 14-fold with the highest MAP concentrations employed. Packing was also dependent on pH. Specific volumes comparable to those of MAP-depleted microtubules were attainable at pH's from 5.5 to 6.0, and specific volumes more than doubled at pH 7.5. MAP content was unaffected by pH. We present a theoretical analysis that suggests that as microtubules are centrifuged the mixture behaves as a liquid crystal. With packing, the mixture undergoes an isotropic-nematic phase transition in which the microtubules become oriented principally as parallel rods, mimicking their orientation in vivo. From the known concentration of microtubules in vivo, it can be inferred from our measurements that in some cells a large fraction, perhaps 40-50% of the cytosolic volume, is occupied by microtubules that form a mechanically irreducible space. Further theoretical analysis employing Ogston's formulation of the penetrability of fibrous networks suggests that the space between microtubules (in contrast to the extracellular matrix) imposes little barrier to the diffusion of macromolecules. A microtubule array thus achieves mechanical stability without affecting transport by diffusion. The space can accommodate other fibrous networks that could then affect transport, and, as we show, the space itself may be regulated by MAP content and intracellular pH.

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