Protein-like energetics of conformational transitions in a polyampholyte hydrogel

Polymer 179 (2019) 121617

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Protein-like energetics of conformational transitions in a polyampholyte hydrogel

T

Valerij Y. Grinberga,*, Tatiana V. Burovaa, Natalia V. Grinberga, Carmen Alvarez-Lorenzob, Alexei R. Khokhlovc a

A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Vavilov St. 28, Moscow, 119991, Russian Federation Department of Pharmacology, Pharmacy and Pharmaceutical Technology, R+DPharma Group (GI-1645), Faculty of Pharmacy and Health, Research Institute of Santiago de Compostela (IDIS), Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain c M.V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russian Federation b

H I GH L IG H T S

collapsed state is maximally stable at isoelectric point and stabilized by kosmotropic salt and ligands. • The polyampholyte hydrogel consists of independent cooperative domains. • The • The domain sizes (9–15 kDa) are comparable with those in globular proteins.

A R T I C LE I N FO

A B S T R A C T

Keywords: Polyampholyte Hydrogel Volume phase transition Differential scanning calorimetry

The volume phase transition of a hydrogel of the polyampholyte network N-isopropylacrylamide (6000) - N-(3aminopropylmethacrylamide) (120) - Acrylic acid (120) - N,N′-Methylenebisacrylamide (40) was investigated by high-sensitivity differential scanning calorimetry in relation to pH, concentrations of NaCl and two oppositely charged drug ligands (ibuprofen and propranolol). The transition temperature, enthalpy, heat capacity increment and width against these thermodynamic variables were determined. The experimental data were used for calculation of the excess free energy functions of the phase transition which are measures of the relative stability of the dense (collapsed) state of the polyampholyte network under different conditions. By analogy with globular proteins, the stability of the network dense state is maximal at the isoelectric point of the polyampholyte and is increased by the kosmotropic salt and specific ligands. We demonstrate that the polyampholyte hydrogel consists of independent cooperative domains. The sizes of these domains in the hydrogel (9–15 kDa) are comparable with those in globular proteins.

1. Introduction Polyampholyte hydrogels represent a unique class of polyelectrolyte networks combining in their structure both negatively and positively charged monomer units [1–7]. Due to attractive interactions of the opposite charges the polyampholytes in aqueous media reveal a variety of specific properties which can be entirely different from those of the corresponding polyelectrolytes containing the same charged groups but only of one sign [3,7–15]. Exceptional multifunctional properties of synthetic polyampholytes such as resistance to non-specific protein adsorption (non-fouling) [16–20], effective drug binding and release [21–24], stimuli responsivity [4,7,12,21–23,25–30], metal chelation [3,31–35], and mechanical properties [36–43] have been the focus of

*

several applied studies [16–18,24,29,30,44–47]. It is remarkable that these properties can be targeted and fine-tuned through a proper selection of the charged monomer subunits, polymer composition and architecture [6,7,16,21,29,30,48,49]. Thus, the application perspectives of polyampholytes in biotechnology, biomedicine, tissue engineering, protein separation, desalination and coatings are highly appreciated [3,5,19,23]. Polyampholyte chains and networks are also of crucial fundamental interest due to their ability to undergo diverse conformational transformations. As it was shown by both theoretical and experimental studies, polyampholytes in aqueous solutions are able to adopt ordered, globular, coil, helix or stretched conformations [3,50–56]. The transitions between these conformations are sensitive to chemical and

Corresponding author. E-mail address: [email protected] (V.Y. Grinberg).

https://doi.org/10.1016/j.polymer.2019.121617 Received 20 March 2019; Received in revised form 17 June 2019; Accepted 27 June 2019 Available online 27 June 2019 0032-3861/ © 2019 Elsevier Ltd. All rights reserved.

Polymer 179 (2019) 121617

V.Y. Grinberg, et al.

discussed.

physical external stimuli such as pH, ionic strength, solvent hydrophobicity, temperature, light and so on [4,7,12,21–24,26,28,30,36,57]. Due to the conformational adaptability, the polyampholytes can reproduce some principal structural and thermodynamic features of biomacromolecules [3,4,28,58–60]. A principal intrinsic feature of the polyampholytes which distinguishes them from the one-sign charged polyelectrolytes is the existence of so-called “frustrations”. This concept was introduced into the scientific lexicon in the physics of magnets [61,62] but has later been adapted and further developed in physical chemistry of polymers, particularly biopolymers. The long-range Coulomb attraction between opposite charges causes certain limitations (frustrations) in the chain flexibility and thus reduces a probability of the minimization of definite energy levels of a macromolecule. Indeed, the physical (electrostatic) bridges in polyampholytes act similarly to chemical cross-links. The frustrations were shown to notably affect the swelling, phase transitions and ligand binding of the cross-linked polyampholyte hydrogels [16,18,19,24,37,45,63–66]. In chemical sense frustrations in functional polymers are considered as some undesirable factor to be reduced either by chemical design or adding additives [65]. However, biophysicists consider the frustration analysis as a valuable instrument for understanding of folding mechanisms and organization of local functional structures in proteins [67–70]. The frustration concept constitutes the main principle of the Energy Landscape Theory of protein folding [71]. It has been shown that highly frustrated regions in a protein sequence, enforced by conflicting interactions, are mainly located on the globule surface and correspond to the functional domains of the protein [72]. The physical frustrations also affect the appearance of metastable states, the binding processes, catalysis and allosteric transitions in proteins [68]. In this regard synthetic stimuli-responsive polyampholyte hydrogels, in which the frustrations are easy to control and fine-tune, provide relevant models for elucidation of the structurefunction relations in biomacromolecules. Thermoresponsive cross-linked hydrogels are capable of the volume phase transition (collapse) in response to changes in temperature [73–75]. A rather large variety of thermoresponsive polyampholyte chains and networks were synthesized and investigated [10–12,24,28–30,36,45,65]. The polyampholytes containing monomers with weak ionizable groups revealed pH-dependent transition temperatures and a corresponding isoelectric point behaviour [4,7,12,28,40,76]. The collapse of a thermoresponsive hydrogel is accompanied by changes in conformations of the subchains. Ionizable groups in thermoresponsive polyampholyte hydrogels provide them with an affinity for ionic ligands that is conformationally controlled due to the thermotropic collapse [66,77,78]. The temperature and pHcontrolled conformational transitions of subchains and related conformation-dependent affinity of the thermoresponsive polyampholyte networks underlie their deep structural and functional analogy with the coil-globule transitions in proteins, enzymes in particular [4,28,79–81]. Accordingly, thermodynamic approaches developed in protein folding and binding can serve as a fruitful methodology of the investigation of synthetic thermoresponsive polyampholyte networks [78,82,83]. An advanced and powerful basis for thermodynamic analysis of the polymer transitions is provided by differential scanning calorimetry (DSC). The use of DSC techniques for studying the collapse of thermoresponsive hydrogels began in the early 90-th due to the pioneering works by Otake et al. [84] and Shibayama et al. [85,86]. In these studies, the enthalpy of the shrinking of hydrogels based on poly (N-isopropylacrylamide) was first directly measured and attributed to the polymer dehydration. In this paper we report detailed thermodynamic data on the thermotropic collapse of a polyampholyte copolymer hydrogel based on Nisopropylacrylamide. The effects of pH, NaCl and two ionic drugs (ibuprofen and propranolol) were investigated by high-sensitivity differential scanning calorimetry. Some basic parallels in thermodynamic behaviour of the polyampholyte hydrogel and globular proteins are

2. Experimental N-isopropylacrylamide (NIPA), N-aminopropylmethacrylamide (APMA), acrylic acid (AAc), N,N′-methylenbisacrylamide (BIS), 2,2′azobisisobutyronitrile, sodium ibuprofen (IBN) and propranolol hydrochloride (PPL) were from Sigma-Aldrich. Other chemicals were of an analytical grade. A polyampholyte copolymer gel NIPA-APMA-AAc with the comonomer ratio 6000:120:120 and a reference PNIPA gel were prepared by a free-radical polymerization in DMSO using N,N′-methylenbisacrylamide (40 mM) as a cross-linking agent [87]. After the reaction was completed, the gels were washed consecutively with solutions of HCl (100 mM), NaOH (100 mM) and deionized water to remove non-reacted monomers. The gels were swollen in water at 4 °C for one week. The equilibrium concentration of the NIPA-APMA-AAc and PNIPA hydrogels at 20 °C amounted to 10 ± 1%. This was determined by drying of the swollen gel samples at 105 °C to a constant weight. Based on the comonomer ratio in the reaction mixture, it has been calculated that the polyampholyte hydrogel subchain consists of an average of 156 units, involving three cationic and three anionic functional groups (Scheme 1). Energetics of the volume phase transition of the polyampholyte hydrogel NIPA-APMA-AAc as well as of the reference PNIPA hydrogel was investigated by high-sensitivity differential scanning calorimetry [88]. Stock suspensions of the swollen gel for calorimetric measurements were prepared in water using a glass Potter homogenizer for biological tissues as reported earlier [89]. Polymer concentration in the stock suspension was determined by weight after drying of the suspension at 105 °C. Stock solutions of NaCl, IBN and PPL were prepared in neat water. The gel suspensions for calorimetric measurements were prepared by adding of an equal volume of a buffer solution, a stock NaCl or ligand solution to the stock gel suspension. The following salts were used for preparation of the buffer solutions: glycine hydrochloride (pH 2–3 and pH 8–10), sodium acetate (pH 4–5) and potassium phosphate (pH 6–7.6). The polymer and buffer concentration in the calorimetric sample were 2 mg mL−1 and 5 mM, respectively. The samples were equilibrated for 40–42 h at 4 °C prior to calorimetric measurements. Calorimetric measurements were carried out with differential adiabatic scanning microcalorimeters DASM-4 and DASM-4A (NPO “Biopribor”, Russian Federation) within a temperature range of 10–80 °C under an excess pressure of 0.25 MPa. The heating rate in all experiments was 1 K min−1. Two or three successive scans were performed, and parameters of the second scan were used for analysis. The primary data processing and transformation of the temperature dependences of the apparent partial heat capacity of the polymer network to the excess heat capacity function of the gel collapse transition were

NIPA APMA

NIPA AAc

NIPA

Scheme 1. Apparent chemical structure of one third of a subchain of the NIPAAPMA-AAc polyampholyte hydrogel (x + y + z~50). 2

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. E

performed with the NAIRTA 2.0 software (A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Federation) using the spline-interpolation method for the calculation of the transition baseline. The temperature of a maximum of the excess heat capacity function was considered as a transition temperature, Tt . The specific transition enthalpy, Δt h , was determined by integration of the excess heat capacity function. The specific transition heat capacity increment, Δt cp , was calculated as a difference in apparent partial heat capacities of the gel network in the collapsed (shrunken) and in the swollen state at the transition temperature. The transition width, Δt T , was calculated as a ratio of the transition enthalpy to the maximal value of the excess heat capacity function. Dependences of the calorimetric transition parameters on pH, NaCl and drug ligand concentrations were obtained. These dependences were used for the calculation of the excess free energy of collapse, which is known to be a generalized measure of the effect of an intensive thermodynamic variable ( X ) such as the pH, salt or ligand concentration, on the volume phase transition of a polymer gel [78]:

Δt G E (Tt∘, X ) = Δt G (Tt∘, X ) − Δt G (Tt∘, X ∘)

4

where Δt G is the transition free energy, and Tt∘ and X ∘ are the reference values of temperature and the variable X . The calculations of the specific excess free energy of the transition were performed using the integrated Gibbs−Helmholtz equation [78]:

(

Δt g E (Tt∘, X ) = Δt h (X ) × 1 −

Tt∘ Tt (X )

) + Δ c (X )(T

∘ t

t p

⎜

(a) 4 3

2

2

1

1

0

0 0 20 E -1 cp , J g

40

60

80 (c) 4

3

3

2

2

1

1

0

0 0

20

40

60

80 o T, C

cp , J g

-1

0 20 E -1 cp , J g

0

20

(b)

40

60

80 (d)

40

60

80 o T, C

Fig. 2. Excess heat capacity functions of the NIPA-APMA-AAc polyampholyte hydrogel at different pHs: (a) pH 2.4 (5 mM glycine buffer); (b) pH 4.0 (5 mM acetate buffer); (c) pH 6.1 (5 mM phosphate buffer); (d) 9.6 (5 mM glycine buffer).

− Tt (X ))

T∘ − Δt cp (X ) Tt∘ ln⎛ t ⎞ ⎝ Tt (X ) ⎠

E

-1

3

4

(1)

cp , J g

⎟

(2)

the collapse of the polyampholyte gel is only slightly shifted by temperature relatively to the reference PNIPA gel, but their profiles differ drastically. The transition peak of the polyampholyte gel is broad and short while the transition peak of the PNIPA gel is narrow and tall. This suggests that the collapse of the polyampholyte gel is a transition of rather low cooperativity as compared with the transition of the PNIPA gel. Importantly, the apparent partial heat capacity of both gels in the collapsed state (at temperatures above the peak) is smaller than that one in the swollen state (at temperatures below the peak). Consequently, the transitions of both gels are accompanied by a substantial dehydration of non-polar groups of gel networks.

Depending on the analysis context of the experimental data the excess transition free energy was normalized either per mole of the monomer units Δt G0E = M0 × Δt g E or per a subchain of the polymer network Δt G E = NSC × Δt G0E where M0 and NSC are the molecular weight of the network monomer unit and the apparent polymerization degree of the network subchains, respectively. It was assumed that M0 is equal to the molecular weight of NIPA (113 g mol−1) and NSC=156. The latter was estimated from the composition of the feed mixture used for the synthesis of the NIPA-AMPA-AAc copolymer. The experimental data processing and fitting procedures were performed using the Mathcad 14 software.

3.1. Effects of pH on energetics of the collapse of polyampholyte hydrogel 3. Results and discussion

The NIPA-APMA-AAc copolymer involves weak ionogenic groups providing a pH-sensitivity of the copolymer hydrogel. Fig. 2 shows some examples of the excess heat capacity functions of the polyampholyte gel at different pHs. The pH-dependences of the thermodynamic transition parameters of the hydrogel are plotted in Fig. 3. Upon increasing pH the transition temperature passes through a minimum (Fig. 3a), while the transition enthalpy and heat capacity increment do not reveal significant variations at pH varying from 2 to 10. Their average values are equal to 34.3 ± 2.5 J g−1 and −0.72 ± 0.02 J g−1 K−1, respectively (Fig. 3b–c). For comparison, the PNIPA hydrogels of different cross-linking density are characterized by the transition enthalpy of 38.9 ± 4.4 J g−1 and the heat capacity increment of −0.63 ± 0.04 J g−1K−1 [83]. Thus, the introduction of minor fractions of opposite charges into the NIPA network does not affect notably the energetics of the gel collapse. The most appreciable pH-dependence is observed for the transition width (Fig. 3d) which demonstrates a distinct minimum at pH ~6. Using the obtained dependences of the transition parameters of the polyampholyte gel on pH, the excess free energy of the transition was calculated as a function of pH:

Thermograms of the NIPA-APMA-AAc polyampholyte hydrogel and of the reference PNIPA hydrogel are presented in Fig. 1a–b, respectively. Both hydrogels undergo the volume phase transition accompanied by an endothermic heat effect. The heat capacity peak related to -1

-1

-1

cp , J g K

(a)

20 10

Tt

-1

cp , J g K

(b)

Tt

c

c

t p

t p

0 10

20

30

40

50 o T, C

10

20

30

40

50 o T, C

Fig. 1. Apparent partial polymer heat capacities of the isoionic NIPA-APMAAAc polyampholyte hydrogel (a) and the reference PNIPA hydrogel (b). The thin black lines are linear approximations of the pre-transiton parts of the heat capacity functions. Tt and Δt cp are the transition temperature and heat capacity increment, respectively.

Δt G0E (Tt∘, pH ) = Δt G0 (Tt∘, pH ) − Δt G0 (Tt∘, pI) where pI is the isoelectric point of polyampholyte, and 3

(3)

Tt∘

is the

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. o

40

Tt , C

(a)

39

t

h, J g

-1

60 34.3+2.5

40

38

negative and positive charges in the subchain are f0 =0.019 and g0=0.019, respectively. The free energy of subchain in the coil (С) and globular (G) states can be expressed as a sum of the contributions of i intrinsic (hydrophobic) and electrostatic interactions, Gint and Gei , where i = C or G, respectively:

(b)

i Gi (T , pH ) = Gint (T ) + Gei (T , pH )

20

37

Accordingly, the free energy of subchain collapse, that is the coilglobule transition, could be written in the form:

0

36 2 4 6 -1 -1 c ,Jg K

8

10

t p

(c) 11

-0.4 -0.6

2 4 o T, C t

6

8

10

Δt G (T , pH ) = Δt Gint (T ) + Δt Ge (T , pH )

Δt G E (Tt∘, pH ) = Δt Ge (Tt∘, pH ) − Δt Ge (Tt∘, pI)

9

-0.8

is the transition temperature at pI . where According to Higgs et al. [91] the free energy of the polyampholyte chain is proportional to the concentration of monomer units in the coil or globule. Since the concentration of monomer units in the globule is much larger than that one in the coil, it can reasonably be assumed that

7 2

4

6

8

10 pH

2

4

6

8

10 pH

Δt G E (Tt∘, pH ) = GeG (Tt∘, pH ) − GeG (Tt∘, pI)

Δt G0E (Tt∘, pH ) ∝

transition temperature at pI. A value of pI 5.0 was roughly estimated as pH of the minimum of the smoothed dependence of the transition temperature on pH (Fig. 3a). At this point the transition temperature is equal to Tt∘= 37°С. The dependence of the excess free energy of transition on pH is shown in Fig. 4. It reveals a broad minimum at pH 4–6. The collapsed state of the hydrogel has a maximal stability within this pH range, i.e. in the extended vicinity of the isoelectric point of polyampholyte. The stability of the collapsed gel decreases notably to the left and to the right from the isoelectric point. It is worth to emphasize that in this respect the behaviour of the collapsed polyampholyte hydrogel reproduces the behaviour of globular proteins [90]. In a rough approximation, the polyampholyte gel can be considered as a network of identical subchains. As it follows from the apparent chemical composition of the polyampholyte gel (NIPA:APMA:AAc:BIS = 6000:120:120:40) the apparent polymerization degree of a subchain is N¯SC ≃ 156, and the maximal fractions of E

o

G0 (Tt ,pH), J mol

πl2 κb3

× [f (pH ) + g (pH )]2 +

⎨+ ⎩

πl2 κb3

× [f (pI ) + g (pI)]2

κ = [8πl × (10−3NA I )]0.5

b3 ≃

v0 M0 NA

f (pH ) = f0 αAAc (pH )

1 2

6

8

10

⎬ ⎭

(8)

(9)

(10)

where v0 and M0 are the specific volume and the molecular weight of the monomer unit for the given polymer. As NIPA is the dominant component of the gel network, we used the specific partial volume of PNIPA [92] and the molecular weight of its monomer unit (v0=0.87 cm3 g−1 and M0 = 113 g mol−1, respectively) for the calculation of the apparent volume of the monomer unit of polyampholyte chain. Dependences of the fractions of the negatively and positively charged monomer units of the polyampholyte on pH can be expressed as follows: (11)

and

g (pH ) = g0 αAMPA (pH )

4

× [f (pH ) − g (pH )]2 ⎫

where NA and I are the Avogadro number and the ionic strength, respectively. An apparent volume of the monomer unit could be approximately estimated as

0 2

4πl κ 2b3

where l=7 × 10 cm is the Bjerrum length in water; κ is the reciprocal of the Debye length; b3 is the volume of monomer unit; f and g are, respectively, the fractions of the negatively and positively charged monomer units in the polyampholyte chain. According to a definition

-1

pI

⎧−

−8

20 10

(7)

Further, following to Higgs et al. [91], we can obtain an expression for the excess transition free energy per mole of monomer units:

Fig. 3. Thermodynamic parameters of collapse of the NIPA-APMA-AAc polyampholyte hydrogel vs. pH: (a) transition temperature; (b) transition enthalpy; (c) transition heat capacity increment; (d) transition width. Each point of the plots is a result of at least three calorimetric experiments. The average values of the transition enthalpy and heat capacity increment are given in the corresponding panels.

t

(6)

Tt∘

8

-1.0

(5)

Then, the excess free energy of transition relative to the isoelectric point of polyampholyte can be determined as follows:

(d)

10

-0.72+0.02

(4)

(12)

where f0 and g0 are the fractions of AAc and APMA monomer units in the polyampholyte chain; αAAc is the dissociation degree of the AAс monomer units, and αAPMA is the protonation degree of the APMA units, while

pH

Fig. 4. Excess transition free energy of the NIPA-APMA-AAc polyampholyte hydrogel vs. pH: (1) experimental; (2) fitted by equation (8)−(15) at pKa 2.3 ± 0.2 and pKa 7.4 ± 0.1 for AAc and APMA monomer units, respectively. The Pearson's correlation coefficient is 0.998. pI 4.9 is calculated by equation (15). Tt∘ = 37 °C is a reference temperature. The free energy is expressed per monomer unit of the gel network. 4

AAc αAAc = 10−pKa + pH 1 − αAAc

(13)

APMA αAPMA + pH = 10−pKa 1 − αAPMA

(14)

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. o

pI =

(15)

E

(a)

15 10

1 2

5 0

cp , J g

40

5

15

(c) 15

10

10

5

5

0

0 20

40

60 o T, C

40

0 1.5 (c) 10

-1

5

-2

0 0.1

0.01 o T, C t

1 Cs , M

0.0

0.1

1 (d)

0.5

1.0

1.5 Cs , M

capacity peak to lower temperatures is observed upon increasing NaCl concentration. Fig. 6 shows the dependences of the transition parameters for the NIPA-APMA-AAc polyampholyte hydrogel and the reference PNIPA hydrogel on the concentration of NaCl. The transition temperature of the PNIPA gel is a decreasing linear function of the salt concentration. This could be explained by the lyotropic effect of NaCl. The dependence of the transition temperature on the salt concentration for the polyampholyte gel reveals some deviations from the linearity at the lowest salt concentrations. The transition enthalpies and heat capacity increments of the gels are quite similar and do not significantly change with the change in NaCl concentration. The transition width of the PNIPA gel is insensitive to the salt, while the transition width of the polyampholyte gel passes through a maximum and is substantially larger than that of the PNIPA gel within the whole range of NaCl concentrations. A further analysis of the salt effect on the polyampholyte gel collapse was performed using the dependence of the excess transition free energy on the salt concentration referred to the transition temperature of the reference PNIPA gel (Tt∘=31 °C):

(b)

0 20 E -1 cp , J g

25.1+0.9

Fig. 6. Thermodynamic transition parameters of the isoionic NIPA-APMA-AAc polyampholyte hydrogel (1) and the reference PNIPA hydrogel (2) vs. NaCl concentration: (a) transition temperature; (b) transition enthalpy; (c) transition heat capacity increment; (c) transition width. The thin line in the insert of panel (a) is obtained by linear extrapolation of the data obtained at 0.2 M ≤ Cs ≤ 1.5 M . The average values of the transition enthalpy and heat capacity increment for both hydrogels are presented in the corresponding panels.

10

60

(b)

50

-0.62+0.03

0.01

-1

15

h, J g

25

0

0

0

38

0.0 0.5 1.0 -1 -1 c ,Jg K t p

The excess heat capacity functions for the NIPA-APMA-AAc polyampholyte hydrogel in isoionic conditions at different concentrations of NaCl are shown in Fig. 5 in comparison with the curves of the reference PNIPA hydrogel. For both hydrogels, a shift of the transition heat -1

t

0.6

1 2

15

3.2. Salt effects on energetics of the collapse of polyampholyte hydrogel

0 20 E -1 cp , J g

0.3

30

25

Equation (8)−(15) were used for the approximation of the experimental pH-dependence of the excess transition free energy of the NIPAAPMA-AAc polyampholyte hydrogel at an average ionic strength of the buffer solutions applied (I =0.005 mol L−1). Values of pK aAAc and pK aAPMA were used as the adjustable parameters (Fig. 4). A successful fitting was achieved at the ionization exponents pK aAAc 2.3 ± 0.2 and pK aAPMA 7.4 ± 0.1. These values differ markedly from the values of the ionization exponents of the corresponding monomers: pK a 4.26 for AAc [94] and pK a ~9 for APMA [29]. Similar discrepancies are typical of globular proteins. For example, the ionization exponents of carboxylic groups of asparagine and glutamine acids and of amino group of lysine are known to vary in different proteins within the intervals pK a 0.5–9.2 and pK a 5.7–12.1, respectively [95]. These variations are caused by a number of local effects typical of the densely packed protein globule possessing a hydrophobic interior. In particular, the participance of a carboxylate anion in the H-bond formation as a proton acceptor is manifested as a decrease in pK a of the carboxylic group. The hydrophobic micro-surroundings having a rather low dielectric constant provides a decrease in pK a of the lysine amino group due to the Born effect. It is highly probable that similar factors are realized in the collapsed state of the NIPA-AAс-APMA polyampholyte gel which also has a hydrophobic interior. A decrease in the dielectric constant of micro-surroundings of the ionogenic groups of the polymer network as a result of the collapse is supported by the fact that the collapse of hydrogels of some basic copolymers of NIPA is accompanied by a decrease in pK a of the constituting amino groups [76,96].

E

(a)

35

0.0

34

pK aAAc + pK aAPMA 2

cp , J g

-1

Tt , C

and pK aAAc and pK aAPMA are the ionization exponents of the AAс and APMA monomer units. Additionally, it can be assumed in the first approximation [93] that

60 (d)

Δt G E (Tt∘, Cs ) = Δt Gint (Tt∘) + Δt GeE (Tt∘, Cs ) + Δt GsE (Tt∘, Cs )

(16)

Δt Gint (Tt∘)

is the intrinsic transition free energy, defined by the where chemical structure of polymer network; Δt GeE (Tt∘, Cs ) and Δt GsE (Tt∘, Cs ) are the electrostatic and lyotropic contributions into the excess free energy of transition, respectively. By definition

Δt GeE (Tt∘, Cs ) = Δt Ge (Tt∘, Cs ) − Δt Ge (Tt∘, 0)

0

20

40

60 o T, C

(17)

and

Δt GsE (Tt∘, Cs ) = Δt Gs (Tt∘, Cs ) − Δt G (Tt∘, 0)

Fig. 5. Excess heat capacity functions of the NIPA-APMA-AAc isoionic polyampholyte hydrogel (1) and the reference PNIPA hydrogel (2) at different NaCl concentrations, M: (a) 0; (b) 0.05; (c) 0.1; (d) 1.5.

(18)

Cs ) и Cs ) are the electrostatic and lyotropic where contributions into the transition free energy. Δt Ge (Tt∘,

5

Δt Gs (Tt∘,

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. -1

10

The electrostatic contribution can be expressed via electrostatic free energies of the gel subchain in the coil and globule states, GeC (Tt∘, Cs ) and GeG (Tt∘, Cs ) , respectively:

Δt Ge (Tt∘, Cs ) = GeG (Tt∘, Cs ) − GeC (Tt∘, Cs )

5

2;

3;

4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 E o -1 -1 E o -1 G ( T t ,Cs ), J mol 10 tG0 ( T t ,Cs ), J mol t (c) (b) 5

-1

10 7 6

(21)

5

0

5

-5

4

-10

(22)

0.0

0.1

0.2 Cs , M

0.5

1.0

1.5 Cs , M

Fig. 7. (a) Excess transition free energies of the isoionic polyampholyte NIPAAPMA-AAc hydrogel (1) and the reference PNIPA hydrogel (2) vs. NaCl concentration at the transition temperature of the reference hydrogel without the salt (Tt∘=31°С): (1) and (2) experimental; (3) fitted by equation (24) at K e=0.337 J mol−1M0.5, Cs∘=2.8 × 10−3 M and Δt Ks=−110 ± 1 J mol−1 M−1 (the standard fit error and Pearson's correlation coefficient are ± 1.3 J mol−1 and 0.999, respectively); (4) fitted by equation (23) at Δt Ks=−92 ± 2 J mol−1 M−1 (the standard fit error and Pearson's correlation coefficient are ± 2.4 J mol−1 and 0.999, respectively). (b) and (c) Excess transition free energy of the NIPA-APMA-AAc polyampholyte hydrogel at small and large concentrations of the salt: (5) the lyotropic contribution to the excess transition free energy ( Δt Ks=−110 ± 1 J mol−1 M−1). The free energies are expressed per monomer units of the polymer networks.

(23)

where Δt Ks is the transition increment of the lyotropic constant, which depends on the salt nature, but does not practically depend on temperature. Combining eqs (16), (21) and (23) we can get the dependence of the excess transition free energy of the polyampholyte gel on the salt concentration:

Δt G E (Tt∘) = Δt Gint (Tt∘) − K e [(I0 + Cs )−0.5 − I00.5] + Δt Ks Cs

1;

-15

It is well known [97] that the lyotropic contribution into the free energy of a solute is proportional to the salt concentration, i.e. Gsi = Ksi Cs (i = G, C ) . Consequently, we can express:

Δt GsE (Tt∘, Cs ) = Δt Ks Cs

(a)

-10

(20)

where K e is a constant and I0 is the apparent contribution of the polyampholyte counterions to the ionic strength. By analogy, the lyotropic contribution into the transition free energy can be given in the form:

Δt Gs (Tt∘, Cs ) = GsG (Tt∘, Cs ) − GsC (Tt∘, Cs )

-1

-5

Using the expression for the free energy of polyampholyte chain in the globule state [91] and taking into account that the ionic strength of the 1-1 electrolyte solution is equal to its molar concentration, we can derive the dependence of the electrostatic contribution into the excess transition free energy on the salt concentration at pI:

Δt GeE = −K e [(I0 + Cs )−0.5 − I0−0.5]

o

G0 ( T t ,Cs ), J mol

0

(19)

Since by the absolute value Δt GeG > > Δt GeC because of a larger density of monomer units in the globule

Δt Ge (Tt∘, Cs ) ≃ GeG (Tt∘, Cs )

E

t

(24)

Eqs (23) and (24) were successfully used for the approximation of the dependences of the excess transition free energy on the concentration of NaCl for the reference PNIPA gel and the NIPA-APMA-AAc gel, respectively (Fig. 7). As a result, the following values of the transition increments of the lyotropic constant were derived: Δt Ks=−92 ± 2 J mol−1M−1 for the PNIPA gel and Δt Ks=−110 ± 1 J mol−1M−1 for the NIPA-APMA-AAc gel. First of all, it is evident that under comparable conditions at a fixed temperature the transition free energy of the polyampholyte gel is larger than that one of the reference PNIPA gel. Consequently, the presence of opposite charged monomeric units in the gel network hinders the collapse. A nature of this effect is well known [98]. The collapse of such a network leads to a localization of counterions of the charged units within a limited volume. Naturally, this localization decreases the transition entropy and thus raises thermodynamic cost of the collapse. There is another important difference between the dependences of the excess transition free energy on the salt concentration for the polyampholyte gel and the reference PNIPA gel. In the case of the PNIPA gel, this dependence is strictly linear within the whole range of salt concentrations that is typical of the lyotropic effect [99]. For the polyampholyte gel, the dependence of the transition free energy on the salt concentration becomes strictly linear only at Cs >0.5 М. At low salt concentrations, this dependence passes through a weak maximum, gradually approaching a linear function at high salt concentrations. This specific behaviour of the excess transition free energy at low salt concentrations most likely is a result of the salt screening of electrostatic interactions of charge fluctuations of the polyampholyte network. A solvophobic theory of solutions [100], extended by Melander and Horvath [97] to the description of the salting-out phenomenon, relates the lyotropic constant increment to changes in the hydrophobic (nonpolar) accessible surface area and dipole moment of a solute. In our terms this relation looks as follows:

Δt Ks =

1000 RTt∘ [σΔt Ω − Δt λ] 18

(25)

where σ is the molal surface tension increment of the salt (σ =1.64 × 10−3 dyn g cm−1 mol−1 for NaCl [97]); Δt Ω and Δt λ are the transition increments of the intrinsic salting-out and salting-in coefficients, respectively. The transition intrinsic salting-out coefficient Δt Ω correlates with the transition increment of the non-polar accessible surface area ( Δt ASAnpl , Å2):

Δt Ω =

Δt ASAnpl 411

(26)

and the transition intrinsic salting-in coefficient Δt λ having an electrostatic origin is approximately proportional to the transition increment of the dipole moment of network subchains ( Δt μ ). Evidently, Δt λ is negligible for the neutral PNIPA gel. Therefore we can calculate the transition ASA increment by equation (25)−(26) Δt Ks using the experimental value of the increment (−92 ± 2 J mol−1M−1). We obtained that Δt ASAnpl =−164 ± 4 Å2 for the PNIPA gel. On the other hand, the calculations by the VEGA ZZ 3.1.1.42 program [101] have shown that the accessible surface area of the hydrophobic part of the PNIPA side branch is equal to 162 ± 7 Å2. Thus, it can be concluded that the collapse of PNIPA gel is accompanied by a practically total burial of the non-polar side groups of the polymer. The application of equation (25) to the polyampholyte gel is problematic since in this case we can not ignore the contribution of the dipole-charge interaction between the polymer network and salt. Nevertheless, there is a reason to believe that the polyampholyte and reference gels are comparable by the degree of burial of non-polar side groups in the collapsed state. If we accept that the transition increment 6

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. E

of ASA of the polyampholyte gel is also equal to −164 Å2, then we can get from equation (25) that the electrostatic increment Δt λ is approximately equal to 1.3 × 10−4 kg mol−1. A detailed analysis of this parameter is difficult. However, it is important that Δt λ > 0. It means that the dipole moment of the network subchain in the globule state is larger than that one in the coil state. Such a relation between the dipole moments of the polymer globule and coil seems to be supported by the comparison of the dipole moments of globular proteins in the random coil state [102] and in the native state [103]. Such estimations are available for lysozyme, myoglobin, RNase and chymotrypsinogen. The dipole moment of these proteins in the native state is varied from 122 to 444 D but in the random coil state it equals to only 35 ± 5 D. These estimates support our suggestion that the folding of subchains of the polyampholyte gel in the course of the collapse is accompanied by an increase in their dipole moment. In other words, it could be really expected that Δt λ > 0 and, correspondingly, the lyotropic increment Δt Ks of the polyampholyte gel should be larger by absolute value than that one of the reference PNIPA gel. It should be noted that our approximated analysis does not take into account changes in the contribution of the osmotic pressure of counterions into the free energy of collapse with the increased concentration of a supporting electrolyte [98] This contribution increases the transition free energy of the polyampholyte gel in comparison with the transition free energy of the reference PNIPA gel. Evidently, it is maximal at isoionic conditions, i.e. in the absence of the supporting electrolyte (Cs = 0 ). When the hydrogel, containing counterions of the polyelectrolyte network, is in equilibrium with a neat solvent it is subjected to a rather high osmotic pressure, which hinders the gel collapse. When the hydrogel is placed into a salt solution, the osmotic pressure of the network is partially compensated by the osmotic pressure of the solution. This effect is enhanced by the increased salt concentration that should manifest itself as a decrease in the free energy of collapse. Such a decrease is superposed on decreasing the free energy of collapse caused by the lyotropic effect, so as a result, the slope of the final segment of the dependence of the transition free energy of the polyampholyte gel on the salt concentration could exceed the slope expected only from the lyotropic effect. We should note that the theory of the osmotic pressure effect of counterions on the volume phase transition of polyampholyte gels is not sufficiently developed [104,105]. For this reason, a quantitative analysis of contributions of this effect into energetics of the volume phase transition of polyampholyte gels is hardly possible on this stage.

4

(a) 4

1

3 1 2 2 3 1

0

0 10

30

(a)

38

10

-1

(b)

30

50

70 o T, C

t

50

h,Jg

-1

(b) 25.9+0.9

25

36 1 2

34

0

0 20 40 60 80 100 0 20 40 60 80 100 o -1 -1 T, C c , J K g t t P (d) (c) 14 0 -0.62+0.03 12 -1

10 8

-2

6 0 20 40 60 80 100 L, mM

0 20 40 60 80 100 L, mM

Fig. 9. Thermodynamic transition parameters of the isoionic NIPA-APMA-AAc polyampholyte hydrogel vs. the ibuprofen (1) and propranolol (2) concentrations: (a) transition temperature; (b) transition enthalpy; (c) transition heat capacity increment; (c) transition width. The average values of the transition enthalpy and heat capacity increment for both ligands are given in the corresponding panels.

parameters of the gel collapse on the concentration of the ligands are shown in Fig. 9. Firstly, note that the data for both ligands do not differ significantly and can be combined in a common array for each parameter. The transition temperature decreases slightly, the enthalpy and heat capacity increment do not depend on the ligand concentration, while the transition width increases distinctly. Fig. 10 shows the dependence of the excess transition free energy of the NIPA-APMA-AAc polyampholyte gel on the ligand concentration. For comparison, we also show the analogous dependences obtained

HO

C H3 N C H3

I

70 o T, C

o

Tt , C

H

C H3

50

cp , J g

Fig. 8. Excess heat capacity functions of the isoionic NIPA-APMA-AAc polyampholyte hydrogel at different ibuprofen (a) and propranolol (b) concentrations, mM: 0 (1), 10 (2), 100 (3).

O OH

E

2

For elucidation of a ligand binding potential of the polyampholyte hydrogel in view of its application in drug delivery systems we have investigated effects of pharmacologically significant anionic and cationic ligands, ibuprofen and propranolol (Scheme 2), on the collapse of the NIPA-APMA-AAc gel.. The excess heat capacity functions of the isoionic NIPA-APMA-AAc gel at different concentrations of ibuprofen and propranolol are given in Fig. 8. The effects of both ligands on the transition thermograms relays mostly to the peak width while the peak position is only slightly affected. The corresponding dependences of the thermodynamic

H 3C

-1

3

3.3. Effects of ligand binding on energetics of the collapse of polyampholyte hydrogel

C H3

cp , J g

O

II 7

Scheme 2. Chemical structure of ibuprofen (I) and propranolol (II).

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. E

t

o

G (Tt ,L) / RTt

o

charged ligand, and their interaction weakens upon addition of a salt for increasing the ionic strength of the solvent. This all leads to a disintegration of the domains, i.e. to a decrease in their sizes. The decrease in the domain size can be judged by the broadening of the transition of the polyampholyte gel (Figs. 3d and 6d for Cs < 0.2 M, and 9d), since the transition width is a measure of the cooperativity of the system, i.e. sizes of its domains [107]. We can formalize these conceptions for a quantitative comparison with the experimental data on the transition energetics of the polyampholyte gel. For this purpose, we will accept two important approximations. The domains are identical, and the transition of the domain from a swollen (C) into collapsed (G) state follows the “all-ornothing”mechanism as in small globular proteins, that is described by the two-state model [90]:

1 2 3 4 5

0.0 -0.2 -0.4 -0.6 0

25

50

75

100 L, mM

Fig. 10. Excess transition free energies of the NIPA-AMPA-AAc (1), NIPAAPMA (2) and NIPA-AAc (3) hydrogels vs. ligand concentration for ibuprofen (4), and propranolol (5). Tt∘ is the reference transition temperature (without ligand).

d Δt G E ( )= dL RTt∘

−6.2 (1), −42.4 (2) and −96.2 (3) M−1. The free energies

K* C ⇄ G

are expressed per network subchain. The data for the NIPA-APMA and NIPAAAc gels are taken from the work [87].

The second approximation means that the transition is described by one equilibrium constant K *which is a simple function of temperature:

early for the NIPA-APMA and NIPA-AAc polyelectrolyte hydrogels in the presence of ibuprofen and propranolol, respectively [87]. The ligand effects on the excess transition free energy of a polymer gel is determined by the difference in the free energies of ligand binding to the network subchains in the globule and coil states, Δb GG and Δb GC , respectively [78]:

Δt G E = Δb GG − Δb GC = Δb G E

K * = exp(−Δt G */ RT )

(28)

and

Δt G * = M * × Δt g

(29)

where M* is the molecular weight of the domain, and Δt g is the specific transition free energy of the gel network, which is a function of the experimental transition parameters Tt , Δt h and Δt cp :

(26)

where Δb G E can be regarded as an increment of the binding free energy assigned to the transition. By analogy with the work by Ito et al. [80], the initial slope of the dependence of the excess transition free energy on the ligand concentration could be used to estimate the transition increment of the total binding affinity Δt Q of gel:

d Δt G E Δt Q ≃ − ( ) dL RTt∘

(27)

Δt g = Δt h (1 −

T T ) + Δt cp (T − Tt ) − TΔt cp ln( ) Tt Tt

(30)

Then we can get an expression for the specific excess heat capacity of the gel [88]:

cpE = M *

[Δt h + Δt cp (T − Tt )]2 RT 2

×

K* (1 + K *)2

(31)

(27) Equation (28)−(31) were successfully used for the approximation of the experimental excess heat capacity functions of the polyampholyte gel at different pH and different concentrations of NaCl and ligands. The domain molecular weight and the transition temperature were used as the fitting parameters. The fitting examples with the average fit standard error of ± 0.063 J g−1K−1 and Pearson's correlation coefficient of 0.997 are given in Fig. 11. An evolution of the domain structure of the polyampholyte hydrogel upon changes in external conditions represents a particular interest. It can be judged by analyzing relative changes in the domain size of the polyampholyte gel in dependence on pH, and salt and ligand concentrations (Fig. 12). The domain size is maximal in the vicinity of the isoelectric point of the polyampholyte, where its overall charge fluctuations and electrostatic interactions between them are maximal. The increase in the ionic strength of solvent produces screening of these interactions and, consequently, a decrease in the domain size. However, at a rather high salt concentration a lyotropic effect begins to appear. The hydrophobic interaction between the NIPA monomer units enhances, and the domain size again increases. The ligand binding is equivalent to a partial neutralization of the network charges of a definite sign. The network acquires an excess charge, the charge fluctuations are suppressed and their interactions is reduced. All this leads to a disintegration of the initial domains to the smaller ones. In general, the effect of ligand binding on the domain structure of the polyampholyte gel is similar to the effects of the pH changes. Scheme 3 illustrates the evolution of the domain structure of a polyampholyte hydrogel. It is known that the domain structure has been ascertained for some thermoresponsive polyelectrolyte hydrogels by means of small-angle neutron scattering [108,109] and light scattering [110]. The domain size was shown to depend on pH, the concentration of supporting

A positive value of the total affinity increment points to a preferential binding of the ligand by the collapsed gel. Data in Fig. 10 reveal that under comparable conditions the affinity of ibuprofen and propranolol to the NIPA-APMA-AAс polyampholyte gel in the collapsed state is substantially less than their affinity to the collapsed NIPA-AMPA and NIPA-AAс polyelectrolyte gels. Alvarez-Lorenzo et al. [65] observed a similar behaviour upon investigation of binding of an anionic ligand (pyranine-4) to a polyampholyte gel of NIPA - methacrylic acid (MA) - methacrylamidopropyltrimethylammonium chloride (MAPTAC). In contrast to the NIPAMAPTAC polyelectrolyte gel, the polyampholyte gel demonstrated an extremely low affinity for pyranine-4 in the collapsed state despite of the presence in the gel of strong cationic MAPTAC groups. It was shown that this specific property of the polyampholyte gel caused by the existence of conformational frustrations of the polymer network as a result of formation of ionic pairs between the oppositely charged MAPTAC and MA sites. In addition, our data convincingly demonstrate the existence of similar frustrations in the NIPA-APMA-AAс polyampholyte gel. 3.4. Domain structure of polyampholyte hydrogel Based on the chemical structure of the polymer network of polyampholyte gels, it is reasonable to suggest that these gels consist of subsystems, i.e. structural domains. A coherency of these domains is provided by electrostatic interactions of charge fluctuations of the network subchains. The charge fluctuations are maximal at the isoelectric point of polyampholyte [106]. Accordingly, a maximal size of the domains seems to be reached at this point. The charge fluctuations are attenuated upon pH deviations from pI or upon the effect of a 8

Polymer 179 (2019) 121617

V.Y. Grinberg, et al. E

-1

cp , J g K

-1

E

(a)

4

-1

cp , J g K

Domain boundaries

-1

(b)

Electrostatic interactions pH=pI,Cs=0.15 M, L=100 mM

3

pI, Cs=0, L=0

2 1

M* > 0

0

( tT) < 0 280 300 -1 -1 cp , J g K

320

340

E

(c)

4

280 300 E -1 -1 cp , J g K

320

340 (d)

-

-

+

+

-

APMA-NIPA domains

3

AAc-NIPA domains

2

Scheme 3. Evolutions of domain structure of the NIPA-APMA-AAc polyampholyte hydrogel vs. pH, NaCl and ligand (ibuprofen or propranolol) concentrations. pI is the isoelectric point of the polyampholyte; Cs and L are the salt and ligand concentrations, respectively. ΔM* and Δ (Δt T ) are corresponding increments of the domain size and the transition width of the gel.

1 0 280

300

320

340 T, K

280

300

320

340 T, K

Table 1 Thermoresponsive polyampholyte hydrogels vs proteins: conformational stability and domain structure.

Fig. 11. Two-state model approximation of the collapse transition for the NIPAAPMA-AAc polyampholyte hydrogel (points, experimental; curves, fitted by equation (28)−(31)) under different conditions: (a) pI, salt- and ligand-free (Tt =310.89 ± 0.03 K, M*=11.7 ± 0.1 kDa; (b) pI, 50 mM NaCl, ligand-free (Tt =310.07 ± 0.03 K, M*=15.0 ± 0.1 kDa; (c) pI, salt-free, 100 mM ibuprofen (Tt =309.94 ± 0.03 K, M*=9.05 ± 0.04 kDa; (d) pI, salt-free, 100 mM propranolol (Tt =310.54 ± 0.04 K, M*=8.9 ± 0.1 kDa). A part of the experimental points is omitted for more clear presentation of the experimental data. *

*

*

M (pH) / M (pI) 1.0

+

(a)

*

M (Cs ) / M (0)

*

Systems

pH

NIPA-APMA-AAc gel Proteins

M (L) / M (0) (c)

a b

0.8

0.0 0.5 1.0 1.5 Cs , M

0

50

Domain size [kDa]

L

b

Max at pI

Increased

Increased

9–15

Max at pI [90]

Increased [113]

Increased [114]

11-16 [112]

Concentration of a lyotropic salt. Concentration of a specific ligand.

coincidence discloses a primitive, but fundamental generality of mechanisms of the structure formation in polyampholyte gels and globular proteins. In particular, this generality manifests itself in the conformational behaviour of the gels and proteins (Table 1). For both types of polymer structure, the conformational stability of the compact folded state is maximal at the isoelectric point and is increased by lyotropic salts and specific ligands.

0.6 2 4 6 8 10 pH

Cs

a

Stability of folded state

*

(b)

Thermodynamic variables

100 L, mM

Fig. 12. Reduced domain size of the NIPA-AMPA-AAc polyampholyte hydrogel vs. pH (a); NaCl concentration (b) and ligand (ibuprofen and propranolol) concentration (c) at pI of the gel.

4. Conclusion We have shown that a copolymer hydrogel composed of thermoresponsive polyampholyte subchains when undergoing a cooperative transition between a swollen and condensed state reproduces some basic energetic features of the coil-globule transition of globular proteins. Similarly to the majority of globular proteins, the stability of the collapsed (apparently folded) state of the hydrogel subchains is maximal at the isoelectric point of the polyampholyte network and decreases upon deviation of pH from that point. The analysis of the pH-dependence of the transition free energy for the polyampholyte gel reveals intrinsic deviations of the pKa values of both acidic and basic side groups of the copolymer network in the folded state from those of the corresponding non-interacting monomers. The existence of so-called “anomalous ionogenic groups” is typical of the native folding in proteins. This anomaly is caused by a series of local effects such as H-bonds and salt bridges formation typical of the densely packed protein globule possessing a hydrophobic interior. It is highly probable that similar factors are realized in the collapsed state of the

electrolyte and cross-linking density. Importantly, the domain organization of the collapsed gel state appears most distinctly for the networks of a rather small content of charges and low cross-linking density. Finally, it should be noted that the domain structure organization is typical of globular proteins with a molecular weight larger than 20 kDa, while a number of the domains in the protein molecule can reach several tens [111]. This phenomenon has a fundamental origin [112]. The entropy cost of the polymer chain folding into a globule increases proportionally to the square of the polymerization degree of the chain, and a gain in the folding enthalpy due to formation of dense contacts between the chain monomer units linearly depends on the polymerization degree. According to theoretical and experimental estimations the average values of the molecular weight of domains in globular proteins lie within the interval 11–16 kDa [112]. It is noteworthy that depending on the conditions the molecular weight of domains in the polyampholyte gel varies in a similar interval 9–15 kDa. This apparent 9

Polymer 179 (2019) 121617

V.Y. Grinberg, et al.

NIPA-AAс-APMA polyampholyte gel which also has a hydrophobic interior. Thermodynamic analysis of the collapse transition profile of the polyampholyte gel supports the idea of a gel organization as an ensemble of independent in thermodynamic sense cooperative units (domains). The domain structure organization is typical of globular proteins with a molecular weight larger than 20 kDa. Estimations of average values of the domain sizes in globular proteins give 11–16 kDa, while our estimations of the domain size in the polyampholyte gel amount to 9–15 kDa. We believe that such a coincidence discloses a fundamental generality of mechanisms of the structure formation in polyampholyte gels and globular proteins. Similarly to native globular conformation in proteins the collapsed state of the polyampholyte gel is stabilized by ligand binding. However, the binding affinity of the polyampholyte gel with respect to ionic ligands is marginal compared with proteins and even with the polyelectrolyte gels of a similar composition. This evidently reflects conformational restrictions (frustrations) of the polymer network as a result of ionic pairing between the oppositely charged sites of the polyampholyte network. Physical frustrations are believed to play an important role in evolution of protein structure and functions affecting metastable states, binding processes, catalysis and allosteric transitions. Remarkably, highly frustrated regions in a protein sequence, enforced by conflicting interactions, correspond to functional domains of the protein. Our data on energetics of the polyampholyte gel underpin the intriguing analogies of the thermodynamic behaviour of globular proteins and their primitive but adequate models such as thermoresponsive polyampholyte hydrogels.

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