Multivalent binding interactions are commonly found throughout biology to enhance weak monovalent binding such as between glycoligands and protein receptors. Designing multivalent polymers to bind to viruses and toxic proteins is a promising avenue for inhibiting their attachment and subsequent infection of cells. Several studies have focused on oligomeric multivalent inhibitors and how changing parameters such as ligand shape, size, linker length, and flexibility affect binding. However, experimental studies of how larger structural parameters of multivalent polymers, such as degree of polymerization, affect binding avidity to targets have mixed results, with some finding an improvement with longer polymers and some finding no effect. Here, we use Brownian dynamics simulations to provide a theoretical understanding of how the degree of polymerization affects the binding avidity of multivalent polymers. We show that longer polymers increase binding avidity to multivalent targets but reach a limit in binding avidity at high degrees of polymerization. We also show that when interacting with multiple targets simultaneously, longer polymers are able to use intertarget interactions to promote clustering and improve binding efficiency. We expect our results to narrow the design space for optimizing the structure and effectiveness of multivalent inhibitors as well as be useful to understand biological design strategies for multivalent binding.

Multivalent binding is essential to many biological processes because it builds high affinity bonds by using several weak binding interactions simultaneously. Multivalent polymers have shown promise as inhibitors of toxins and other pathogens, and they are important components in the formation of biocondensates. Explaining how structural features of these polymers change their binding and subsequent control of phase separation is critical to designing better pathogen inhibitors and also to understanding diseases associated with membraneless organelles. In this work, we will examine the binding of a multivalent polymer to a small target. This scenario could represent a polymeric inhibitor binding to a toxic protein or RNA binding to an RNA-binding protein in the case of liquid-liquid phase separation. We use simulation and theory to show that flexible randomcoil polymers bind more strongly than stiff rod-like polymers and that flexible polymers nucleate condensed phases at lower energies than their rigid analogues. We hope these results will provide insight into the rational design of polymeric inhibitors and improve understanding of membraneless organelles.

Using inspiration from biology, we can leverage multivalent binding interactions to enhance weak, monovalent binding between molecules. While most previous studies have focused on multivalent binders with uniform binding sites, new synthetic polymers might find it desirable to have multiple binding moieties along the chain. Here, we probe how patterning of heterogeneous binding sites along a polymer chain controls the binding affinity of a polymer using a reactive Brownian dynamics scheme. Unlike monovalent binders that are pattern-agnostic, we find that divalent binding is dependent on both the polymer pattern and binding target concentration. For dilute targets, blocky polymers provide high local concentrations of high-affinity sites, but at high target concentrations, competition for binding sites makes alternating polymers the strongest binders. Subsequently, we show that random copolymers are robust to target concentration fluctuations. These results will assist in the rational design of multivalent polymer therapeutics and materials.

Multivalent polymers are a key structural component of many biocondensates. When interacting with their cognate binding proteins, multivalent polymers such as RNA and modular proteins have been shown to influence the liquid-liquid phase separation (LLPS) boundary to both control condensate formation and to influence condensate dynamics after phase separation. Much is still unknown about the function and formation of these condensed droplets, but changes in their dynamics or phase separation are associated with neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS) and Alzheimer’s Disease. Therefore, investigation into how the structure of multivalent polymers relates to changes in biocondensate formation and maturation is essential to understanding and treating these diseases. Here, we use a coarse-grain, Brownian Dynamics simulation with reactive binding that mimics specific interactions in order to investigate the difference between non-specific and specific multivalent binding polymers. We show that non-specific binding interactions can lead to much larger changes in droplet formation at lower protein-polymer interaction energies than their specific, valence-limited counterparts. We also demonstrate the effects of solvent conditions and polymer length on phase separation, and we present how modulating binding energy to the polymer can change the organization of a droplet in a three component system of polymer, binding protein, and solvent. Finally, we compare the effects of surface tension and polymer binding on the condensed phase dynamics, and show that both lower protein solubilities and higher attraction/affinity of the protein to the polymer result in slower droplet dynamics. This research will help to better understand experimental systems and provides additional insight into how multivalent polymers can control LLPS.

A system for actively changing the stiffness of a long, thin, flexible robotic manipulator has been designed for cardiologists to use in a range of diagnosis and treatment procedures. Low-stiffness manipulators, such as catheters, are ideal for steering through vasculature with low risk of tissue injury. However, such instruments are not well-suited for applying force to tissue. The proposed system solves this problem by using a series of bead-shaped vertebrae containing pull wires to actively change the stiffness of the catheter, similar to gooseneck surgical retractors. Individual wires steer the catheter to a desired location. All wires are then tensioned to create friction between each vertebra and prevent sliding, therefore resisting motion. While this design concept has been implemented manually in various settings for decades, fine robotic control of the friction and stiffness of the system relies on a thorough understanding of the friction properties between vertebral segments. We have developed an analytical model to understand the interactions between vertebrae and determine the relationships between system parameters and the overall stiffness of the catheter. Experiments validated the calculations from the model and the functionality of the system by applying known loads to the tip of the catheter and measuring the catheter displacement. The catheter stiffness was measured to range from 100 N/m to 800 N/m, which is sufficient for performing many surgical tasks on tissue. This system can be useful in minimally invasive procedures involving direct instrument contact with tissue by improving accuracy, safety, and work flow.