A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks

Inclusion of Cationic Amphiphilic Peptides in Fmoc-FF Generates Multicomponent Functional Hydrogels

Peptide building blocks have been recently proposed for the fabrication of supramolecular nanostructures able to encapsulate and in vivo deliver drugs of a different nature. The primary sequence design is essential for nanostructure property modulation, directing and affecting affinity for specific drugs. For instance, the presence of positively charged residues of lysine (K) or arginine (R) could allow improving electrostatic interactions and, in turn, the encapsulation of negatively charged active pharmaceutical ingredients, including nucleic acids. In this context, here, we describe the formulation and the multiscale structural characterization of hybrid cationic peptide containing hydrogels (HGs). In these matrices, the well-known low-molecular-weight hydrogelator, Fmoc-diphenylalanine (Fmoc-FF, Fmoc = fluorenyl methoxycarbonyl), was mixed with a library of cationic amphiphilic peptides (CAPs) differing for their alkyl chain (from C8 to C18) in a 1/1 mol/mol ratio. The structural characterization highlighted that in mixed HGs, the aggregation is guided by Fmoc-FF, whereas the cationic peptides are only partially immobilized into the hydrogelated matrix. Moreover, morphology, stiffness, topography, and toxicity are significantly affected by the length of the alkyl chain. The capability of the hydrogels to encapsulate negative drugs was evaluated using the 5-carboxyfluorescein (5-FAM) dye as a model.

A scale-invariant log-normal droplet size distribution below the critical concentration for protein phase separation

Many proteins have been recently shown to undergo a process of phase separation that leads to the formation of biomolecular condensates. Intriguingly, it has been observed that some of these proteins form dense droplets of sizeable dimensions already below the critical concentration, which is the concentration at which phase separation occurs. To understand this phenomenon, which is not readily compatible with classical nucleation theory, we investigated the properties of the droplet size distributions as a function of protein concentration. We found that these distributions can be described by a scale-invariant log-normal function with an average that increases progressively as the concentration approaches the critical concentration from below. The results of this scaling analysis suggest the existence of a universal behaviour independent of the sequences and structures of the proteins undergoing phase separation. While we refrain from proposing a theoretical model here, we suggest that any model of protein phase separation should predict the scaling exponents that we reported here from the fitting of experimental measurements of droplet size distributions. Furthermore, based on these observations, we show that it is possible to use the scale invariance to estimate the critical concentration for protein phase separation.

Topological Considerations in Biomolecular Condensation

Biomolecular condensation and phase separation are increasingly understood to play crucial roles in cellular compartmentalization and spatiotemporal regulation of cell machinery implicated in function and pathology. A key aspect of current research is to gain insight into the underlying physical mechanisms of these processes. Accordingly, concepts of soft matter and polymer physics, the thermodynamics of mixing, and material science have been utilized for understanding condensation mechanisms of multivalent macromolecules resulting in viscoelastic mesoscopic supramolecular assemblies. Here, we focus on two topological concepts that have recently been providing key mechanistic understanding in the field. First, we will discuss how percolation provides a network-topology-related framework that offers an interesting paradigm to understand the complex networking of dense 'connected' condensate structures and, therefore, their phase behavior. Second, we will discuss the idea of entanglement as another topological concept that has deep roots in polymer physics and important implications for biomolecular condensates. We will first review some historical developments and fundamentals of these concepts, then we will discuss current advancements and recent examples. Our discussion ends with a few open questions and the challenges to address them, hinting at unveiling fresh possibilities for the modification of existing knowledge as well as the development of new concepts relevant to condensate science.