## 1 Introduction  
In recent years, the spotlight in the realms of biology, chemistry, and medicine has intensified on short peptides, which have captivated the scientific community with their distinctive features [1, 2]. Apart from their low molecular weight and facile synthesis, these types of peptides are recognized for their biocompatibility and the ability to target specific cells or organelles with minimal side effects [3]. These distinct attributes make them exceptionally well suited for an extensive array of applications, such as cell culture [4], tissue regeneration processes [5], drug delivery [6], and biosensors [7]. Noteworthy is that short peptides were proven to play pivotal roles in the advanced gene therapy area [8, 9]. Peptides can serve as smart delivery vehicles due to their capability to bind, conjugate, or encapsulate DNA or RNA [9]. Additionally, they are utilized in diagnostic imaging due to their inherent targeting ability [10, 11]. Self-assembly represents an innate and intricate mechanism observed across numerous essential biological processes, underscoring its fundamental role in nature [12]. Within this context, peptides demonstrate a remarkable capability to autonomously organize and undergo self-assembly, particularly under specific environmental conditions [1; 2; 3; 4]. The molecular self-assembly process implies the formation of physical hydrogels, also known as supramolecular hydrogels [13]. The predominant mechanism in peptide supramolecular gelation is primarily catalyzed by fundamental physical forces, such as hydrogen bonding, hydrophobic interactions, aromatic \(\pi\)-\(\pi\) stacking interactions, and electrostatic interactions, which are weak and reversible [14]. Such noncovalent interactions are known for imparting order and directionality to peptide self-assembly into fibril-like structures and hence play a critical role in building the final 3D architecture [15; 16]. The inherent biocompatibility, high water content, and exceptional hydrogenation propensity brought on by the unidirectional amide H-bonding and \(\pi\)-\(\pi\) stacking interactions can provide peptide-based hydrogels significant unique properties [17]. These special features, when harmonized with the inherent bioactivity intrinsic to the peptide sequences, pave the way for the creation of distinct and specialized biomaterials. It was previously reported that peptides consisting of fewer than eight amino acids can spontaneously self-assemble into hydrogels [18]. The ability of peptides consisting of only two amino acids (shortest self-assembling motif of peptides) to form linear dipeptide hydrogels was also shown, employing different synthesis strategies [13]. Chemical synthesis of peptides can be achieved either by solution- or solid-phase strategies. However, the solid-phase peptide synthesis (SPPS) method (in which a peptide is anchored to an insoluble solid support, typically made of a polymer matrix), has lately seen consistent advancements and refinements in order to produce peptides with high purity [19]. Thus, the exploration of amino acids and their ability to form specific sequences and implicitly supramolecular structures have paved the way for pioneering advancements in materials science [20; 21]. Due to the intriguing structures formed by short hybrid peptides, there is growing interest in leveraging self-assembly principles to design and forecast peptide hydrogels. Therefore, understanding the underlying mechanisms and microscopic behavior involved in peptide self-assembly is essential. Computational techniques have increasingly become instrumental in elucidating the interplay between molecular structures, as well as the potential for supramolecular gelation [22]. Furthermore, the computational methodologies are expected to be critical for researchers exploring and innovating in the realm of peptide hydrogel materials.