PubMed · 5943387
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M ten Hoopen. 1966. Multimodal interval distributions.. https://doi.org/10.1007/bf00291086
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alpha-zeins of maize (Zea mays) that are storage proteins contain nine or ten tandem repeats comprising of about 20 amino acids. Small-angle X-ray scattering (SAXS) of alpha-zeins was measured in 70% (v/v) aqueous ethanol containing beta-mercaptoethanol or without reagent in a protein concentration range of 2.0 to 40.0 mg/ml. The overall radius of gyration of whole particles, Rg, and the corresponding radius of gyration of the cross-section, Rc, of reduced alpha-zeins are 4.00 +/- 0.03 nm and 1.39 +/- 0.05 nm, respectively, in the 70% (v/v) aqueous ethanol containing 2% (v/v) beta-mercaptoethanol. Analyses using the Rg and Rc values indicate that reduced alpha-zeins exist as asymmetric particles with the length of about 13 nm in the solution. A structural model is developed under assumption that each of tandem repeats units forms single alpha-helix and they are joined by glutamine-rich 'turns' or loops, as employed by Argos et al., [Argos, O., Pedersen, K., Marks, M.D. and Larkins, B.A. (1982) J. Biol. Chem. 257, 9984-9990] and Garratt et al. [Garratt, R., Oliva, G., Caracelli, I., Leite, A. and Arruda, P. (1993) Proteins Struc. Func. Genet. 15, 88-99], and that the longest dimension of 13 nm comes from linear stacking of the anti-parallel helices of tandem repeat in the direction perpendicular to the helical axis. The resultant model is presented by an elongated prism-like shape with an approximate axial ratio of 6:1.
In this work we present the development of the multiple sequence approximation (AGADIRms) and the standard one-sequence approximation (AGADIRls) within the framework of AGADIR's alpha-helix formation model. The extensive comparison between these new formulations and the original one [AGADIR; V. Muñoz and L. Serrano (1994). Nat. Struct. Biol., Vol. 1, pp. 399-409] indicates that the standard one-sequence approximation is virtually identical to the multiple sequence approximation, while the previously used residue partition function approximation [Muñoz and Serrano (1994); (1995), J. Mol. Biol., Vol. 245, pp. 275-296] is less precise. The calculations of the average helical content performed with AGADIR are precise for peptides of less than 30 residues and progressively diverge from the multiple sequence formulation for longer peptides. The helicity distribution of heteropolypeptides with less than 50% average helical content is also well described, while those of quasi-homopolymers with high helical content tend to be-flattened. These inaccuracies lead to an underestimation of 0.017 kcal/mol for the mean-residue enthalpic contribution in AGADIR, as compared to AGADIRms and AGADIRls. The other energy contributions to alpha-helix stability are not affected by the original statistical approximation. We also discuss the particularities of the model for alpha-helix formation utilized in AGADIR and compare it with the classical Zimm-Bragg and Lifson-Roig theories. Moreover, we develop the mathematical relationships between the basic AGADIR energy contributions and helix nucleation and elongation, which permit the quantitative comparison between formalisms. Remarkably, the comparison between AGADIRms and the Lifson-Roig formalism shows that, despite the differences on treating helix/coil cooperativity, both theories give virtually identical results when an equivalent set of parameters is used. This indicates that the helix/coil transition is a solid theory independent of the particularities of the model for alpha-helix formation.
During normal, voluntary movements, skeletal muscles typically contract in a highly dynamic manner; the length of the muscle and the speed of contraction change continuously. In this study, we present an approach to predict the accurate behavior of muscles for such dynamic contractions using Huxley's cross-bridge model. A numerical procedure is proposed to solye, without any assumptions, the partial differential equation that governs the attachment distribution function in Huxley's cross-bridge model. The predicted attachment distribution functions, and the corresponding force responses for shortening and stretching, were compared with those obtained using Zahalak's analytical solution and those obtained using the so-called "distribution moment model" in transient and steady-state contractions. Compared to the distribution moment model, the solutions obtained using our model are exact rather than approximate. The solutions obtained using the analytical approach and the present approach were virtually identical; however, in terms of CPU times, the present approach was 250-300 times faster than Zahalak's. From the results of this study, we concluded that the proposed solution is an exact and efficient way for solving the partial differential equation governing the cross-bridge model.