Cooperative ligand-mediated transitions in simple macromolecules

TL;DR

This work demonstrates that cooperative ligand-mediated transitions can arise in simple macromolecules by constraining conformational states with a two-phase oil–water environment, aligning with an extended Monod–Wyman–Changeux framework. Two systems are studied: hydrophobic polyelectrolytes, where ligand binding correlates with conformational partitioning, and terpyridine-containing oligomers that form coordinated gels upon metal binding; oligomeric templates show substantially higher cooperativity than monomeric analogs. The results highlight the crucial role of conformational reservoirs and composition dispersity in shaping transition sharpness, and show that dispersity can be manipulated through fractionation to tailor transition pH and width. The findings provide design principles for cooperative switching in non-biological macromolecules with potential applications in triggered release and self-healing materials.

Abstract

In biology, ligand mediated transitions (LMT), where the binding of a molecular ligand onto the binding site of a receptor molecule leads to a well-defined change in the conformation of the receptor, are often referred to as 'the second secret of life'. Sharp, cooperative transitions arise in many biological cases, while examples of synthetic cooperative systems are rare. This is because well-defined conformational states are hard to 'program' into a molecular design. Here, we impose an external constraint in the form of two immiscible liquids that effectively define and limit the available conformational states of two different synthetic and relatively simple macromolecules. We show that the mechanism of the observed cooperative transitions with ligand concentration is the coupling of ligand binding and conformation, similar to more complex biological systems. The systems studied are: (1) Hydrophobic polyelectrolytes (HPE), which are (bio) polymers that consist of hydrophobic as well as ionizable (proton and hydroxyl ligand-binding) functional groups. (2) Oligomeric metal chelators (OMC), which are oligomers composed of metal ion chelating repeating groups that are able to bind metal ions (considered as the 'ligands'), resulting in gel-like networks of oligomers crosslinked by coordinated metal ions. We find that in HPE, interactions between ligands and individual macromolecules explain the observed cooperative transitions. For OMC, coordinated bonds significantly enhance the degree of cooperativity, compared to HPE.

Figures (5)

• Figure 1: Sharp, cooperative, ligand mediated transitions are predicted for simple oligomeric species. (a) Plot of the fraction of hemoglobin in the Relaxed ($f_R$) and Tense ($f_T$) states, and the fraction of bound oxygen onto hemoglobin, $\theta_{MWC}$ as a function of $\lambda$. $\lambda$ is the oxygen fugacity and proportional to the partial oxygen pressure. For details see our previous work martin2023cooperative. The Langmuir isotherm $\theta_L$ is Eq. (\ref{['eq:theta_Langmuir']}), with $\beta g = -6$. $\Delta$ is a measure for the width, or sharpness, of the oxygen-ligand mediated transition (LMT). (b) Schematic of the analogy between a conformationally constrained oligomer and hemoglobin. The oligomer in isolation presents many thermally accessible conformations compared to the two main conformations for hemoglobin. However, when placed in a two-state oil and water system the oligomer is funneled into a reduced set of accessible conformations, which coupled to the preferential ion binding in the aqueous phase leads to sharp, cooperative transitions.
• Figure 2: Homopolymeric HPE present sharp, cooperative partitioning transitions.(a) Schematic of the comparison of the $pH$-dependent oil and water partitioning between a monoprotic acid (MPA) and the HPE PAHA. During a small change in $pH$ ($\Delta$) there is a complete transfer of HPE between phases, while there is only a small change in partitioning for the MPA.(b) Plot of $f_{aq}$ ($1-f_{H}$) (red squares) and $\theta$ (light red squares) for PAHA ($DP=18$). The data is a combination of two individual runs where all repeat measurements are plotted. The $f_{aq}$ curve is fit to Eq. (\ref{['eq:fractionHPE']}) (red line) and using the $pK_a$ value for propanoic acid: $4.69$harris_quantitative_2007. Fit parameters are shown in the legend. As a comparison a (calculated) non-cooperative transition with $M=1$ is plotted as a dotted blue line. Predicted $\theta$ curve (light red dashed line) using the fit parameters for Eq. (\ref{['eq:fractionHPE']}) of the $f_{H}$ data into Eq. (\ref{['eq:theta_HPE']}). (c) Hill plots for the fraction of ionized sites and the fraction of chains in the oil for PAHA. A straightline with a Hill parameter ($n_H$) of $7.2$ is consistent with the straightline section of this graph. See SI (Section \ref{['data_analysis_HPE']}) for details on data treatment and data scaling.
• Figure 3: Terpyridine oligomers shown much sharper, cooperative transitions than the corresponding monomer (a) Schematic of the comparison of the partition experiments of monomeric (T) and oligomeric (PT) terpyridine in oil (DCM) and water, with iron (II) ions in the aqueous phase as 'ligands'. (b) Fraction of terpyridine monomers (filled blue circles) and oligomeric terpyridine (filled red squares) in the aqueous state ($f_{aq}$) as a function of the free iron concentration in the water phase. The blue solid line represents the best fit to terpyridine to Eqs. (\ref{['eq:fractionOMC']},\ref{['foGCdim']}) with $\beta g = \beta (2g_H + g_2) = - 12.8$ and $M = 1$. The red line is the same equation with $\beta g = \beta (2g_H + g_2) = - 10.8$ and $M = 16$, which describes well the experimental data on poly(terpyridine). The independently measured fraction of occupied terpyridine sited (by iron (II) ions) in the water phase, $\theta$, are indicated by light blue circles for monomeric terpyridine and light red squares for PT16. (c) The corresponding Hill plots for terpyridine monomer and poly(terpyridine) where the blue and red lines represent Hill coefficients $M$ equal to $1$ and $16$, respectively.
• Figure 4: Chemically disperse copolymeric HPE presents broad, non-cooperative partitioning transitions. Fractionation can return sharp transitions. (a) Plot of $f_{aq}$ (red squares) and $\theta$ (light red squares) for PBA-AA. The data for each variable was independently collected from separate experimental systems. Repeat measurements of $f_{aq}$ are individually plotted to illustrate the experimental spread of the data. The curves are a fit using Eq. (\ref{['eq:fractionHPE']}) (dashed red) and SI Eq. (\ref{['eq:M_dispersity_fraction']}) (solid red), using the $pK_a$ values for acetic acid: $4.56$harris_quantitative_2007. Fit parameters are shown in the legend. As a comparison a (calculated) non-cooperative transition with $M=1$ is plotted as a dotted blue line. (b)$f_{aq}$ for the PBA-AA system and its corresponding fit (SI Eq. (\ref{['eq:M_dispersity_fraction']})) are shown as red squares and a red line. Note the asymmetric shape of the curve around the transition point ($f_{aq}=0.5$). The green dashed line shows a calculated $f_{aq}$ transition from the resulting HPE sample after the fractionation procedure (shown in (c)).
• Figure 5: (c) Schematic for a potential fractionation procedure using a two-phase oil and water system. After equilibration at each fractionation $pH$ point one of the phases of discarded (marked as a gray cross beside an arrow). Shades of red within a phase reflect polymer concentration. $pH_1>pH_2$(d) Distribution of the number of ionizable sites ($M$) on the polymer chains at different stages of the fractionation procedure. Only the distribution for the chains with 20 total monomers ($M_t$) is shown. Gaussian curves are plotted to guide the eye. See SI Section \ref{['data_analysis_HPE']} and \ref{['sec:fract_appen']} for details on data treatment and scaling, and fractionation calculations, respectively.