Elastohydrodynamics and Kinetics of Protein Patterning in the Immunological Synapse

Leveraging Covalency to Stabilize Ternary Complex Formation For Cell-Cell "Induced Proximity"

Recent advances in the field of translational chemical biology use diverse "proximity-inducing" synthetic modalities to elicit new modes of "event driven" pharmacology. These include mechanisms of targeted protein degradation and immune clearance of pathogenic cells. Heterobifunctional "chimeric" compounds like Proteolysis TArgeting Chimeras (PROTACs) and Antibody Recruiting Molecules (ARMs) leverage these mechanisms, respectively. Both systems function through the formation of reversible "ternary" or higher-order biomolecular complexes. Critical to function are key parameters, such as bifunctional molecule affinity for endogenous proteins, target residence time, and turnover. To probe the mechanism and enhance function, covalent chemical approaches have been developed to kinetically stabilize ternary complexes. These include electrophilic PROTACs and Covalent Immune Recruiters (CIRs), the latter designed to uniquely enforce cell-cell induced proximity. Inducing cell-cell proximity is associated with key challenges arising from a combination of steric and/or mechanical based destabilizing forces on the ternary complex. These factors can attenuate the formation of ternary complexes driven by high affinity bifunctional/proximity inducing molecules. This Account describes initial efforts in our lab to address these challenges using the CIR strategy in antibody recruitment or receptor engineered T cell model systems of cell-cell induced proximity. ARMs form ternary complexes with serum antibodies and surface protein antigens on tumor cells that subsequently engage immune cells via Fc receptors. Binding and clustering of Fc receptors trigger immune cell killing of the tumor cell. We applied the CIR strategy to convert ARMs to covalent chimeras, which "irreversibly" recruit serum antibodies to tumor cells. These covalent chimeras leverage electrophile preorganization and kinetic effective molarity to achieve fast and selective covalent engagement of the target ternary complex protein, e.g., serum antibody. Importantly, covalent engagement can proceed via diverse binding site amino acids beyond cysteine. Covalent chimeras demonstrated striking functional enhancements compared to noncovalent ARM analogs in functional immune assays. We revealed this enhancement was in fact due to the increased kinetic stability and not concentration, of ternary complexes. This finding was recapitulated using analogous CIR modalities that integrate peptidic or carbohydrate binding ligands with Sulfur(VI) Fluoride Exchange (SuFEx) electrophiles to induce cell-cell proximity. Mechanistic studies in a distinct model system that uses T cells engineered with receptors that recognize covalent chimeras or ARMs, revealed covalent receptor engagement uniquely enforces downstream activation signaling. Finally, this Account discusses potential challenges and future directions for adapting and optimizing covalent chimeric/bifunctional molecules for diverse applications in cell-cell induced proximity.

Design of Crosslinking Antibodies For T-Cell Activation: Experimental and Computational Analysis of PD-1/CD137 Bispecific Agents

Bispecific and multispecific agents have become increasingly utilized in cancer treatment and immunotherapy, yet their complex design parameters present a challenge in developing successful therapeutics. Bispecifics that crosslink receptors on two opposing cells can provide specific activation of a receptor only when these cells are in close spatial proximity, such as an immune cell and cancer cell in a tumor. These agents, including T cell activating bispecifics, can avoid off-tumor toxicity through activation only in the tumor microenvironment by utilizing a tumor target to cluster T-cell receptors for a selective costimulatory signal. Here, we investigate a panel of PD-1/CD137 targeted Humabody VH domains to determine the key factors for T cell activation, such as affinity, valency, expression level, domain orientation, and epitope location. Target expression is a dominant factor determining both specificity and potency of T cell activation. Given an intrinsic expression level, the affinity can be tuned to modulate the level of activation and IC50 and achieve specificity between low and high expression levels. Changing the epitope location and linker length showed minor improvements to activation at low expression levels, but increasing the valency for the target decreased activation at all expression levels. By combining non-overlapping epitopes for the target, we achieved higher receptor activation at low expression levels. A kinetic model was able to capture these trends, offering support for the mechanistic interpretation. This work provides a framework to quantify factors for T cell activation by cell-crosslinking bispecific agents and guiding principles for the design of new agents.

Mechanical forces amplify TCR mechanotransduction in T cell activation and function

Adoptive T cell immunotherapies, including engineered T cell receptor (eTCR) and chimeric antigen receptor (CAR) T cell immunotherapies, have shown efficacy in treating a subset of hematologic malignancies, exhibit promise in solid tumors, and have many other potential applications, such as in fibrosis, autoimmunity, and regenerative medicine. While immunoengineering has focused on designing biomaterials to present biochemical cues to manipulate T cells ex vivo and in vivo, mechanical cues that regulate their biology have been largely underappreciated. This review highlights the contributions of mechanical force to several receptor-ligand interactions critical to T cell function, with central focus on the TCR-peptide-loaded major histocompatibility complex (pMHC). We then emphasize the role of mechanical forces in (i) allosteric strengthening of the TCR-pMHC interaction in amplifying ligand discrimination during T cell antigen recognition prior to activation and (ii) T cell interactions with the extracellular matrix. We then describe approaches to design eTCRs, CARs, and biomaterials to exploit TCR mechanosensitivity in order to potentiate T cell manufacturing and function in adoptive T cell immunotherapy.

Coalescence of Elastic Blisters Filled with a Viscous Fluid

Pockets of viscous fluid coalescing beneath an elastic sheet are encountered in a wide range of natural phenomena and engineering processes, spanning across scales. As the pockets merge, a bridge is formed with a height increasing as the sheet relaxes. We study the spatiotemporal dynamics of such an elastohydrodynamic coalescence process by combining experiments, lubrication theory, and numerical simulations. The bridge height exhibits an exponential growth with time, which corresponds to a self-similar solution of the bending-driven thin-film equation. We address this unique self-similarity and the self-similar shape of the bridge, both of which are corroborated in numerical simulations and experiments.

Characterization of mechanisms positioning costimulatory complexes in immune synapses

Small immunoglobulin superfamily (sIGSF) adhesion complexes form a corolla of microdomains around an integrin ring and secretory core during immunological synapse (IS) formation. The corolla recruits and retains major costimulatory/checkpoint complexes, such as CD28, making forces that govern corolla formation of particular interest. Here, we investigated the mechanisms underlying molecular reorganization of CD2, an adhesion and costimulatory molecule of the sIGSF family during IS formation. Computer simulations showed passive distal exclusion of CD2 complexes under weak interactions with the ramified F-actin transport network. Attractive forces between CD2 and CD28 complexes relocate CD28 from the IS center to the corolla. Size-based sorting interactions with large glycocalyx components, such as CD45, or short-range CD2 self-attraction successfully explain the corolla 'petals.' This establishes a general simulation framework for complex pattern formation observed in cell-bilayer and cell-cell interfaces, and the suggestion of new therapeutic targets, where boosting or impairing characteristic pattern formation can be pivotal.

Diffuso-kinetic membrane budding dynamics

A wide range of proteins are known to create shape transformations of biological membranes, where the remodelling is a coupling between the energetic costs from deforming the membrane, the recruitment of proteins that induce a local spontaneous curvature C₀ and the diffusion of proteins along the membrane. We propose a minimal mathematical model that accounts for these processes to describe the diffuso-kinetic dynamics of membrane budding processes. By deploying numerical simulations we map out the membrane shapes, the time for vesicle formation and the vesicle size as a function of the dimensionless kinetic recruitment parameter K₁ and the proteins sensitivity to mean curvature. We derive a time for scission that follows a power law ∼K₁^-2/3, a consequence of the interplay between the spreading of proteins by diffusion and the kinetic-limited increase of the protein density on the membrane. We also find a scaling law for the vesicle size ∼1/([small sigma, Greek, macron]_avC₀), with [small sigma, Greek, macron]_av the average protein density in the vesicle, which is confirmed in the numerical simulations. Rescaling all the membrane profiles at the time of vesicle formation highlights that the membrane adopts a self-similar shape.

F-Actin-Driven CD28-CD80 Localization in the Immune Synapse

During immunological synapse (IS) formation, T cell receptor (TCR) signaling complexes, integrins, and costimulatory molecules exhibit a particular spatial localization. Here, we develop an agent-based model for the IS formation based on TCR peptide-bound major histocompatibility complex (pMHC) and leukocyte-function-associated antigen 1 (LFA-1) intracellular activation molecule 1 (ICAM-1) dynamics, including CD28 binding to a costimulatory ligand, coupling of molecules to the centripetal actin flow, and size-based segregation (SBS). A radial gradient of LFA-1 in the peripheral supramolecular activation cluster (pSMAC) toward the central supramolecular activation cluster (cSMAC) emerged as a combined consequence of actin binding and diffusion and modified the positioning of other molecules. The simulations predict a mechanism of CD28 movement, according to which CD28-CD80 complexes passively follow TCR-pMHC microclusters. However, the characteristic CD28-CD80 localization in a ring pattern around the cSMAC only emerges with a particular CD28-actin coupling strength that induces a centripetal motion. These results have implications for the understanding of T cell activation and fate decisions.

Mechanisms for bacterial gliding motility on soft substrates

The motility mechanism of certain prokaryotes has long been a mystery, since their motion, known as gliding, involves no external appendages. The physical principles behind gliding still remain poorly understood. Using myxobacteria as an example of such organisms, we identify here the physical principles behind gliding motility and develop a theoretical model that predicts a 2-regime behavior of the gliding speed as a function of the substrate stiffness. Our theory describes the elasto-capillary-hydrodynamic interactions between the membrane of the bacteria, the slime it secretes, and the soft substrate underneath. Defining gliding as the horizontal translation under zero net force, we find the 2-regime behavior is due to 2 distinct mechanisms of motility thrust. On mildly soft substrates, the thrust arises from bacterial shape deformations creating a flow of slime that exerts a pressure along the bacterial length. This pressure in conjunction with the bacterial shape provides the necessary thrust for propulsion. On very soft substrates, however, we show that capillary effects must be considered that lead to the formation of a ridge at the slime-substrate-air interface, thereby creating a thrust in the form of a localized pressure gradient at the bacterial leading edge. To test our theory, we perform experiments with isolated cells on agar substrates of varying stiffness and find the measured gliding speeds in good agreement with the predictions from our elasto-capillary-hydrodynamic model. The mechanisms reported here serve as an important step toward an accurate theory of friction and substrate-mediated interactions between bacteria proliferating in soft media.

Numerical investigation of adhesion dynamics of a deformable cell pair on an adhesive substrate in shear flow

Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper, we numerically investigate the dynamic adhesion of a deformable cell pair to a flat substrate under shear flow. Specifically, the immersed boundary-lattice Boltzmann method is utilized as the flow solver, and the stochastic receptor-ligand kinetics model is implemented to recover cell-substrate and cell-cell adhesive interactions. Special attention is paid to the roles of the cell deformability and adhesion strengths in cellular motion. Four distinct adhesion states, namely, rolling, tumbling, firm adhesion, and detachment, are identified and presented in phase diagrams as a function of the adhesion strengths for cell pairs with different deformabilities. The simulation results suggest that both the cell-cell and cell-substrate adhesion strengths act as the resistance to the rolling motion, and dominate the transition among various adhesion states. The cell deformability not only enhances the resistance effect, but also contributes to detachment or fast tumbling of the cell pair. These findings enrich the understanding of adhesion dynamics of cell aggregates, which could shed light on complex adhesion processes and provide instructions in developing adhesion-based applications.

Efficient simulation of thermally fluctuating biopolymers immersed in fluids on 1-micron, 1-second scales

The combination of fluid-structure interactions with stochasticity, due to thermal fluctuations, remains a challenging problem in computational fluid dynamics. We develop an efficient scheme based on the stochastic immersed boundary method, Stokeslets, and multiple timestepping. We test our method for spherical particles and filaments under purely thermal and deterministic forces and find good agreement with theoretical predictions for Brownian Motion of a particle and equilibrium thermal undulations of a semi-flexible filament. As an initial application, we simulate bio-filaments with the properties of F-actin. We specifically study the average time for two nearby parallel filaments to bundle together. Interestingly, we find a two-fold acceleration in this time between simulations that account for long-range hydrodynamics compared to those that do not, suggesting that our method will reveal significant hydrodynamic effects in biological phenomena.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

Irreversible thermodynamics of curved lipid membranes

The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intramembrane lipid flow, intramembrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.

Interplay between membrane elasticity and active cytoskeleton forces regulates the aggregation dynamics of the immunological synapse

Adhesion between a T cell and an antigen presenting cell is achieved by TCR-pMHC and LFA1-ICAM1 protein complexes. These segregate to form a special pattern, known as the immunological synapse (IS), consisting of a central quasi-circular domain of TCR-pMHC bonds surrounded by a peripheral domain of LFA1-ICAM1 complexes. Insights gained from imaging studies had led to the conclusion that the formation of the central adhesion domain in the IS is driven by active (ATP-driven) mechanisms. Recent studies, however, suggested that passive (thermodynamic) mechanisms may also play an important role in this process. Here, we present a simple physical model, taking into account the membrane-mediated thermodynamic attraction between the TCR-pMHC bonds and the effective forces that they experience due to ATP-driven actin retrograde flow and transport by dynein motor proteins. Monte Carlo simulations of the model exhibit a good spatio-temporal agreement with the experimentally observed pattern evolution of the TCR-pMHC microclusters. The agreement is lost when one of the aggregation mechanisms is "muted", which helps to identify their respective roles in the process. We conclude that actin retrograde flow drives the centripetal motion of TCR-pMHC bonds, while the membrane-mediated interactions facilitate microcluster formation and growth. In the absence of dynein motors, the system evolves into a ring-shaped pattern, which highlights the role of dynein motors in the formation of the final concentric pattern. The interplay between the passive and active mechanisms regulates the rate of the accumulation process, which in the absence of one them proceeds either too quickly or slowly.

Mathematical Modeling of Synaptic Patterns

During antigen recognition by T cells, a specific spatial structure is formed at the contact face to an antigen-presenting cell (APC), called an immunological synapse (IS). The IS supports bidirectional signaling and release of effector molecules and is widely studied both biologically and numerically, in order to understand the process of T cell activation and signaling. This specialized structure harbors a central area (central supramolecular activation cluster, cSMAC) populated by T cell receptor-peptide-major histocompatibility complex (TCR-pMHC ) interactions, hedged by a peripheral ring (peripheral supramolecular activation cluster, pSMAC) of integrin lymphocyte function associated-1 interactions with its immunoglobulin superfamily ligand intercellular adhesion molecule-1 (LFA-1-ICAM-1). These two regions form the "bull's eye" pattern characteristic of the mature IS.In theoretical studies, different modeling architectures, including partial differential equations (PDE) and agent-based models , have been developed with the purpose to answer mechanistic questions about the IS dynamics. In this chapter, we explain possible physiological mechanisms that lead to the formation of ISs and technical issues that may occur in the course of development of agent-based models.

Cell Surface Mechanochemistry and the Determinants of Bleb Formation, Healing, and Travel Velocity

Blebs are pressure-driven cell protrusions implicated in cellular functions such as cell division, apoptosis, and cell motility, including motility of protease-inhibited cancer cells. Because of their mechanical nature, blebs inform us about general cell-surface mechanics, including membrane dynamics, pressure propagation throughout the cytoplasm, and the architecture and dynamics of the actin cortex. Mathematical models including detailed fluid dynamics have previously been used to understand bleb expansion. Here, we develop mathematical models in two and three dimensions on longer timescales that recapitulate the full bleb life cycle, including both expansion and healing by cortex reformation, in terms of experimentally accessible biophysical parameters such as myosin contractility, osmotic pressure, and turnover of actin and ezrin. The model provides conditions under which blebbing occurs, and naturally gives rise to traveling blebs. The model predicts conditions under which blebs travel or remain stationary, as well as the bleb traveling velocity, a quantity that has remained elusive in previous models. As previous studies have used blebs as reporters of membrane tension and pressure dynamics within the cell, we have used our system to investigate various pressure equilibration models and dynamic, nonuniform membrane tension to account for the shape of a traveling bleb. We also find that traveling blebs tend to expand in all directions unless otherwise constrained. One possible constraint could be provided by spatial heterogeneity in, for example, adhesion density.

Formation of semi-dilute adhesion domains driven by weak elasticity-mediated interactions

Cell-cell adhesion is established by specific binding of receptor and ligand proteins anchored in the cell membranes. The adhesion bonds attract each other and often aggregate into large clusters that are central to many biological processes. One possible origin of attractive interactions between adhesion bonds is the elastic response of the membranes to their deformation by the bonds. Here, we analyze these elasticity-mediated interactions using a novel mean-field approach. Our analysis of systems at different densities of bonds, ϕ, reveals that the phase diagram, i.e., the binodal and spinodal lines, exhibit a nearly universal behavior when the temperature T is plotted against the scaled density x = ϕξ(2), where ξ is the linear size of the membrane's region affected by the presence of a single isolated bond. The critical point (ϕc , Tc) is located at very low densities, and slightly below Tc we identify phase coexistence between two low-density phases. Dense adhesion domains are observed only when the height by which the bonds deform the membranes, h0, is much larger than their thermal roughness, Δ, which occurs at very low temperatures T≪Tc. We, thus, conclude that the elasticity-mediated interactions are weak and cannot be regarded as responsible for the formation of dense adhesion domains. The weakness of the elasticity-mediated effect and its relevance to dilute systems only can be attributed to the fact that the membrane's elastic energy saturates in the semi-dilute regime, when the typical spacing between the bonds r≳ξ, i.e., for x≲ 1. Therefore, at higher densities, only the mixing entropy of the bonds (which always favors uniform distributions) is thermodynamically relevant. We discuss the implications of our results for the question of immunological synapse formation, and demonstrate that the elasticity-mediated interactions may be involved in the aggregation of these semi-dilute membrane domains.