^{1}, D. Lairez

^{1,a)}, S. Combet

^{1}, G. C. Fadda

^{1,2}, S. Longeville

^{1}and G. Zalczer

^{3}

### Abstract

We report circular dichroism measurements on the helix-coil transition of poly(L-glutamic acid) in solution with polyethylene glycol (PEG) as a crowding agent. The PEG solutions have been characterized by small angle neutron scattering and are well described by the picture of a network of mesh size ξ, usual for semi-dilute chains in good solvent. We show that the increase of PEG concentration stabilizes the helices and increases the transition temperature. But more unexpectedly, we also notice that the increase of concentration of crowding agent reduces the mean helix extent at the transition, or in other words reduces its cooperativity. This result cannot be taken into account for by an entropic stabilization mechanism. Comparing the mean length of helices at the transition and the mesh size of the PEG network, our results strongly suggest two regimes: helices shorter or longer than the mesh size.

I. INTRODUCTION

II. RESULTS

A. Materials and methods

B. SANS characterization of PEG solutions

C. Circular dichroism

III. DISCUSSION

A. Zimm-Bragg model

B. Data analysis

C. Variation of the solvent quality

D. Entropic stabilization

E. Polymeric nature of the crowding agent

IV. CONCLUSION

## Figures

Coherent differential scattering cross section per unit volume and unit of PEG volume fraction *I*/ϕ_{PEG} vs. scattering vector *q* for PEG solutions at *T* = 20 °C. Lines are best fits following Eq. (2).

Coherent differential scattering cross section per unit volume and unit of PEG volume fraction *I*/ϕ_{PEG} vs. scattering vector *q* for PEG solutions at *T* = 20 °C. Lines are best fits following Eq. (2).

Mean short distance, ξ/*a*, and curvilinear distance, *g* = *m*(ξ)/*m* _{ a }, between neighboring PEG chains vs. volume fraction ϕ_{PEG}, measured at *T* = 20 °C, with *m* _{ a } the molar mass of the monomer and *a* its length from Ref. 15. Straight lines are best power law fits corresponding to and , respectively.

Mean short distance, ξ/*a*, and curvilinear distance, *g* = *m*(ξ)/*m* _{ a }, between neighboring PEG chains vs. volume fraction ϕ_{PEG}, measured at *T* = 20 °C, with *m* _{ a } the molar mass of the monomer and *a* its length from Ref. 15. Straight lines are best power law fits corresponding to and , respectively.

Molar ellipticity θ at 222 nm per amino acid of poly(L-glutamic acid) solutions vs. temperature for different pH. The horizontal dashed line has an ordinate θ_{1/2} corresponding to the helix fraction 1/2.

Molar ellipticity θ at 222 nm per amino acid of poly(L-glutamic acid) solutions vs. temperature for different pH. The horizontal dashed line has an ordinate θ_{1/2} corresponding to the helix fraction 1/2.

Ellipticity θ at 222 nm per amino acid of poly(L-glutamic acid) solutions at pH = 3.75 vs. temperature for different volume fractions of PEG. Full and open symbols correspond to rising and decreasing temperature curves, respectively. The horizontal line has an ordinate θ_{1/2} corresponding to the helix fraction *x* _{ h } = 1/2.

Ellipticity θ at 222 nm per amino acid of poly(L-glutamic acid) solutions at pH = 3.75 vs. temperature for different volume fractions of PEG. Full and open symbols correspond to rising and decreasing temperature curves, respectively. The horizontal line has an ordinate θ_{1/2} corresponding to the helix fraction *x* _{ h } = 1/2.

Helix fraction *x* _{ h } of poly(L-glutamic acid) solutions at pH = 3.75 vs. reduced temperature *T*/*T** for different volume fractions of PEG.

Helix fraction *x* _{ h } of poly(L-glutamic acid) solutions at pH = 3.75 vs. reduced temperature *T*/*T** for different volume fractions of PEG.

Reverse transition temperature 1/*T** vs. logarithm of the accessible volume fraction ln (1 − ϕ_{PEG}). Straight lines are guides for the eyes with slopes equal to 1/560 K (Ref. 30) for fully protonated (dashed lines) and 1/317 K (Ref. 31) for fully dissociated (full lines) glutamic acid monomers, respectively. Full symbols: present work (pH = 3.75). Open symbols: from Fig. 5 in Ref. 5 (pH = 5.8). At this latter pH, *T**(0) (intercept of dashed and full lines) is not accessible. It has been arbitrary set to 235 K in order the green dashed line fits the data points of Ref. 5.

Reverse transition temperature 1/*T** vs. logarithm of the accessible volume fraction ln (1 − ϕ_{PEG}). Straight lines are guides for the eyes with slopes equal to 1/560 K (Ref. 30) for fully protonated (dashed lines) and 1/317 K (Ref. 31) for fully dissociated (full lines) glutamic acid monomers, respectively. Full symbols: present work (pH = 3.75). Open symbols: from Fig. 5 in Ref. 5 (pH = 5.8). At this latter pH, *T**(0) (intercept of dashed and full lines) is not accessible. It has been arbitrary set to 235 K in order the green dashed line fits the data points of Ref. 5.

(Top) Reverse correlation length *L* _{ h }(*T**) of helices at the transition vs. reverse mesh size ξ of the PEG network. (Bottom) Average number *N* _{ h }(*T**) of amino acid per helix at the transition vs. the ratio *L* _{ h }(*T**)/ξ. The close symbol at x-coordinate equal to 0 corresponds to ϕ_{PEG} = 0 (i.e., ξ → ∞). Either ξ measured at 20 °C (circles) or ξ(*T**) (squares) calculated from Eq. (3) and Ref. 16 are used to compute the x-coordinate.

(Top) Reverse correlation length *L* _{ h }(*T**) of helices at the transition vs. reverse mesh size ξ of the PEG network. (Bottom) Average number *N* _{ h }(*T**) of amino acid per helix at the transition vs. the ratio *L* _{ h }(*T**)/ξ. The close symbol at x-coordinate equal to 0 corresponds to ϕ_{PEG} = 0 (i.e., ξ → ∞). Either ξ measured at 20 °C (circles) or ξ(*T**) (squares) calculated from Eq. (3) and Ref. 16 are used to compute the x-coordinate.

## Tables

Summary of the results obtained by circular dichroism measurements: transition temperature *T**; Zimm-Bragg parameter σ deduced from the slope at *T** of θ(*T*); extent *N* _{ h } and correlation length *L* _{ h } of helical domains at the transition.

Summary of the results obtained by circular dichroism measurements: transition temperature *T**; Zimm-Bragg parameter σ deduced from the slope at *T** of θ(*T*); extent *N* _{ h } and correlation length *L* _{ h } of helical domains at the transition.

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