## 1 Introduction  
Hydrogels are three-dimensional polymer networks that are capable of retaining large amounts of water or biological fluids, and simulating biological tissue [1, 2]. Hydrogels have been obtained from various polymers of natural origin, for example, polysaccharides, as well as from numerous synthetic polymers, such as poly(ethylene glycol) [3]. On the basis of the cross-linking mechanism, hydrogels can be classified into two categories, physical and chemical [1]. Physical cross-links have been formed by ionic interaction, hydrogen bonding, or crystallite formation. In chemically cross-linked hydrogels, covalent bonds have been present between polymer chains, e.g., as a result of reactions of functional groups occurring along polymeric chains with bi- or multifunctional cross-linkers [4]. Hydrogels, due to their similarity to natural tissue, are suitable for various biomedical applications, such as drug-delivery systems, scaffolds for tissue engineering, wound dressings, or contact lenses [5, 6]. In addition, an important area of hydrogel application is personal-hygiene products such as nappies, sanitary pads, or adult-incontinence products [7]. Moreover, due to their unique properties, hydrogels could also find applications in many other fields, e.g., the food industry [8] or agriculture [9]. Poly-\(\gamma\)-glutamic acid (\(\gamma\)-PGA), a biopolymer produced by bacteria, is made of D- and L-glutamic acid units connected by amide linkages [10]. \(\gamma\)-PGA is produced on an industrial scale (mostly from biomass by microbial fermentation), so it is relatively easily available. This naturally occurring polyamide is water-soluble, biodegradable, nontoxic to humans and the environment, and safe for human consumption [11]. Due to its edibility, \(\gamma\)-PGA has been tested for various food-related applications, e.g., as a texture modifier for baked foods, bitterness-relieving agent, or cryoprotectant for probiotic bacteria [12; 13]. \(\gamma\)-PGA has also been used for medical applications, e.g., in tissue engineering [14] or delivery systems [15]. In addition, \(\gamma\)-PGA could be used to prepare hydrogels with properties suitable for pharmaceutical applications [16]. \(\gamma\)-PGA-based hydrogels are not limited to only medical applications; they could also be used to purify turbid water [17] or as electrolytes in organic electrochemical supercapacitors [18]. Poly(ethylene glycol) (PEG) is a water-soluble and nontoxic polymer, approved by the United States Food and Drug Administration (FDA). PEG has been extensively used in a variety of medical applications, such as drug-delivery systems or tissue engineering [19]. Moreover, PEG has been used to obtain hydrogels suitable for biomedical applications, e.g., in delivery systems [20], tissue engineering [21], or wound dressings [22]. Despite intensive research interest in poly-\(\gamma\)-glutamic acid, there are limited literature data on hydrogels made of poly-\(\gamma\)-glutamic acid and poly(ethylene glycol). One of the few examples is hydrogels obtained via photopolymerisation from methacrylated poly(\(\gamma\)-glutamic acid) and poly(ethylene glycol) diacrylate; on the basis of a cytotoxicity assay of these pH-sensitive hydrogels, they were found suitable for biomedical applications (as a matrix for pH-dependent drug release or scaffolding material in tissue engineering) [23]. Another example of \(\gamma\)-PGA-PEG hydrogels was prepared in a reaction between \(\gamma\)-PGA-containing maleimide groups and PEG-containing terminal thiol groups. This \(\gamma\)-PGA-PEG hydrogel has the potential to be used as a drug-delivery system [24]. The synthesis of known \(\gamma\)-PGA-PEG hydrogels was preceded by a modification of \(\gamma\)-PGA biopolymers in which additional functional groups were introduced. The protocol reported in the current study allows to prepare \(\gamma\)-PGA-PEG hydrogels in a one-step method under mild conditions.