Polymerization of Rod-Like Macromolecular Monomers Studied by Stopped-Flow, Multiangle Light Scattering: Set-Up, Data Processing, and Application to Fibrin Formation

Abstract

Many biological supramolecular structures are formed by polymerization of macromolecular monomers. Light scattering techniques can provide structural information from such systems, if suitable procedures are used to collect the data and then to extract the relevant parameters. We present an experimental set-up in which a commercial multiangle laser light scattering photometer is linked to a stopped-flow mixer, allowing, in principle, the time-resolved extrapolation of the weight-average molecular weight M(w) and of the z-average square radius of gyration <R(g)(2)>(z) of the polymers from Zimm-like plots. However, if elongated structures are formed as the polymerization proceeds, curved plots rapidly arise, from which M(w) and <R(g)(2)>(z) cannot be recovered by linear fitting. To verify the correctness of a polynomial fitting procedure, polydisperse collections of rod-like or worm-like particles of different lengths, generated at various stages during bifunctional polycondensations of rod-like macromolecular monomers, were considered. Then, the angular dependence of their time-averaged scattered intensity was calculated in the Rayleigh-Gans-Debye approximation, with random and systematic noise also added to the data. For relatively narrow size distributions, a third-degree polynomial fitting gave satisfactory results across a broad range of conversion degrees, yielding M(w) and <R(g)(2)>(z) values within 2% and no greater than 10-20%, respectively, of the calculated values. When more broad size distributions were analyzed, the procedure still performed well for semiflexible polymers, but started to seriously underestimate both M(w) and <R(g)(2)>(z) when rigid rod-like particles were analyzed, even at relatively low conversion degrees. The data were also analyzed in the framework of the Casassa approximation, from which the mass per unit length of the polymers can be derived. These procedures were applied to a set of data taken on the early stages of the thrombin-catalyzed polymerization of fibrinogen, a rod-like macromolecule approximately 50 nm long. The polymers, grown in the absence of Ca(2+) by rate-limiting amounts of thrombin, appeared to be characterized by a much broader size distribution than the one expected for a classical Flory bifunctional polycondensation, and they seem to behave as relatively flexible worm-like double-stranded chains. Evidence for the formation of fibrinogen-fibrin monomer complexes is also inferred from the time dependence of the mass/length ratio. However, our data are also compatible with the presence of limited amounts of single-stranded structures in the very early stages, either as a secondary, less populated pathway, or as transient intermediates to the classical double-stranded fibrils.

A Comprehensive Mechanism of Fibrin Network Formation Involving Early Branching and Delayed Single- to Double-Strand Transition from Coupled Time-Resolved X-ray/Light-Scattering Detection

“…It has been previously shown 18,19,21,22 that FG polymerization WA-MALS data can be best interpreted by removing the time factor and plotting ⟨R g 2 ⟩ z and ⟨M/L⟩ w/z vs ⟨M⟩ w Similar plots, with ⟨R c 2 ⟩ z in place of ⟨M/L⟩ w/z , are presented in Figure 3 for the three FG polymerization runs of Figure 2. Confirming our previous reports, 21,22 the addition of Ca 2+ ions, while slowing down the process (see Figure 2), does not significantly affect its mechanism, as both the ⟨R g 2 ⟩ z vs ⟨M⟩ w and ⟨R c 2 ⟩ z vs ⟨M⟩ w plots ( Figure 3A,B, green symbols) follow the same course as the Ca 2+ -less data. Importantly, when the A knob competing inhibitor GPRP-NH 2 is added in a 500:1 molar ratio to FG, it completely impedes any polymer formation, as observed by both WA-MALS and SAXS (not shown), ruling out a previously hypothesized end-to-end/single-strand to halfstaggered/DS model.…”

“…Importantly, when the A knob competing inhibitor GPRP-NH 2 is added in a 500:1 molar ratio to FG, it completely impedes any polymer formation, as observed by both WA-MALS and SAXS (not shown), ruling out a previously hypothesized end-to-end/single-strand to halfstaggered/DS model. 21,22 However, at rate-limiting GPRP-NH 2 amounts (GPRP-NH 2 :FG 10:1), a difference arises between the ⟨R g 2 ⟩ z vs ⟨M⟩ w and ⟨R c 2 ⟩ z vs ⟨M⟩ w plots: while the former ( Figure 3A, blue squares) still nicely superimposes with the other datasets, the latter ( Figure 3B, blue circles) behaves differently, with ⟨R c 2 ⟩ z increasing somewhat faster as a function of ⟨M⟩ w than without GPRP-NH 2 .…”

“…21−24 For the initial stages, the coupled evolution of the z-average square radius of gyration ⟨R g 2 ⟩ z and of the weight-average molecular weight ⟨M⟩ w could be extracted from WA-MALS data. 21,22 Surprisingly, these data were incompatible with the classic halfstaggered RLDS mechanism when simulated using modified Flory bifunctional polycondensation distributions, 21,22,25 suggesting the formation of more elongated, thinner structures later coalescing into the classic RLDS/WLDS fibrils. 21,22 The data also implied that the ratio of release Q between the two FpA from any individual FG molecule was ≫1, meaning a faster cleavage of the second FpA and thus significantly skewing the distribution toward longer polymers.…”

“…21,22 Surprisingly, these data were incompatible with the classic halfstaggered RLDS mechanism when simulated using modified Flory bifunctional polycondensation distributions, 21,22,25 suggesting the formation of more elongated, thinner structures later coalescing into the classic RLDS/WLDS fibrils. 21,22 The data also implied that the ratio of release Q between the two FpA from any individual FG molecule was ≫1, meaning a faster cleavage of the second FpA and thus significantly skewing the distribution toward longer polymers. 21,22 However, a crucial parameter to prove this alternative mechanism, the coupled evolution of the fibrils' thickness (in the form of the mass/ length ratio ⟨M/L⟩ w/z ), could not be obtained from WA-MALS data until later in the reaction because of fundamental instrumental limitations.…”

“…21,22 However, a crucial parameter to prove this alternative mechanism, the coupled evolution of the fibrils' thickness (in the form of the mass/ length ratio ⟨M/L⟩ w/z ), could not be obtained from WA-MALS data until later in the reaction because of fundamental instrumental limitations. 21,22,26 Solution small-angle X-ray scattering (SAXS) can instead provide the solutes' z-average cross-sectional square radius of gyration ⟨R c 2 ⟩ z in a time-resolved manner. 27 However, it cannot simultaneously measure the ⟨R g 2 ⟩ z and ⟨M⟩ w beyond those of small oligomers, since their rapid growth quickly leads to values outside the setup's accessible length scales.…”