A model describing swelling changes of covalently crosslinked gels caused by unfolding of crosslinks of folded chains built-in in the gel matrix was proposed. By unfolding, a new interacting surface is exposed which may differ from the interacting sites of the gel polymer. Non-ionic as well as ionic interactions are considered. A certain force generated by the swelling pressure acts on the ends of the folded crosslinks and unfolding starts when this force exceeds a certain limiting value. The continuation or arrest of unfolding depends on whether the exposure of the new interacting surface decreases or increases this force. The unfolding process is considered to be irreversible but possible reversibility can be considered. This model relates to biohybrid gels in which the folded domain of the crosslink is composed of elements of the muscle protein titin. The model is based on the statistical-mechanical theory of swelling of crosslinked polymers. A change in external variables such as temperature or degree of ionization can cause an abrupt change in volume of the swollen gel (transition) within a certain range of parameters characterizing the gel and polymer-solvent interactions.