A coarse-grained model for the simulations of biomolecular interactions in cellular environments

How does the same ligand activate signaling of different receptors in TNFR superfamily: a computational study

TNFα is a highly pleiotropic cytokine inducing inflammatory signaling pathways. It is initially presented on plasma membrane of cells (mTNFα), and also exists in a soluble variant (sTNFα) after cleavage. The ligand is shared by two structurally similar receptors, TNFR1 and TNFR2. Interestingly, while sTNFα preferentially stimulates TNFR1, TNFR2 signaling can only be activated by mTNFα. How can two similar receptors respond to the same ligand in such a different way? We employed computational simulations in multiple scales to address this question. We found that both mTNFα and sTNFα can trigger the clustering of TNFR1. The size of clusters induced by sTNFα is constantly larger than the clusters induced by mTNFα. The systems of TNFR2, on the other hand, show very different behaviors. Only when the interactions between TNFR2 are very weak, mTNFα can trigger the receptors to form very large clusters. Given the same weak binding affinity, only small oligomers were obtained in the system of sTNFα. Considering that TNF-mediated signaling is modulated by the ligand-induced clustering of receptors on cell surface, our study provided the mechanistic foundation to the phenomenon that different isoforms of the ligand can lead to highly distinctive signaling patterns for its receptors.

Understanding the General Principles of T Cell Engagement by Multiscale Computational Simulations

The use of bispecific antibodies as T cell engagers can bypass the normal TCR-MHC interaction, redirect the cytotoxic activity of T-cells, and lead to highly efficient tumor cell killing. However, this immunotherapy also causes significant on-target off-tumor toxicologic effects, especially when they were used to treat solid tumors. In order to avoid these adverse events, it is necessary to understand the fundamental mechanisms during the physical process of T cell engagement. We developed a multiscale computational framework to reach this goal. The framework combines simulations on the intercellular and multicellular levels. On the intercellular level, we simulated the spatial-temporal dynamics of three-body interactions among bispecific antibodies, CD3 and TAA. The derived number of intercellular bonds formed between CD3 and TAA were further transferred into the multicellular simulations as the input parameter of adhesive density between cells. Through the simulations under various molecular and cellular conditions, we were able to gain new insights of how to adopt the most appropriate strategy to maximize the drug efficacy and avoid the off-target effect. For instance, we discovered that the low antibody binding affinity resulted in the formation of large clusters at the cell-cell interface, which could be important to control the downstream signaling pathways. We also tested different molecular architectures of the bispecific antibody and suggested the existence of an optimal length in regulating the T cell engagement. Overall, the current multiscale simulations serve as a prove-of-concept study to help the future design of new biological therapeutics.

SIGNIFICANCE

T-cell engagers are a class of anti-cancer drugs that can directly kill tumor cells by bringing T cells next to them. However, current treatments using T-cell engagers can cause serious side-effects. In order to reduce these effects, it is necessary to understand how T cells and tumor cells interact together through the connection of T-cell engagers. Unfortunately, this process is not well studied due to the limitations in current experimental techniques. We developed computational models on two different scales to simulate the physical process of T cell engagement. Our simulation results provide new insights into the general properties of T cell engagers. The new simulation methods can therefore serve as a useful tool to design novel antibodies for cancer immunotherapy.

Elucidating activation and deactivation dynamics of VEGFR-2 transmembrane domain with coarse-grained molecular dynamics simulations

The vascular endothelial growth factor receptor 2 (VEGFR-2) is a member of receptor tyrosine kinases (RTKs) and is a dimeric membrane protein that functions as a primary regulator of angiogenesis. As is usual with RTKs, spatial alignment of its transmembrane domain (TMD) is essential toward VEGFR-2 activation. Experimentally, the helix rotations within TMD around their own helical axes are known to participate importantly toward the activation process in VEGFR-2, but the detailed dynamics of the interconversion between the active and inactive TMD forms have not been clearly elucidated at the molecular level. Here, we attempt to elucidate the process by using coarse grained (CG) molecular dynamics (MD) simulations. We observe that inactive dimeric TMD in separation is structurally stable over tens of microseconds, suggesting that TMD itself is passive and does not allow spontaneous signaling of VEGFR-2. By starting from the active conformation, we reveal the mechanism of TMD inactivation through analyzing the CG MD trajectories. We observe that interconversions between a left-handed overlay and a right-handed one are essential for the process of going from an active TMD structure to the inactive form. In addition, our simulations find that the helices can rotate properly when the overlaying structure of the helices interconverts and when the crossing angle of the two helices changes by larger than ~40 degrees. As the activation right after the ligand attachment on VEGFR-2 will take place in the reverse manner of this inactivation process, these structural aspects will also appear importantly for the activation process. The rather large change in helix configuration for activation also explains why VEGFR-2 rarely self-activate and how the activating ligand structurally drive the whole VEGFR-2. This mechanism of TMD activation / inactivation within VEGFR-2 may help in further understanding the overall activation processes of other RTKs.

Dissecting the general mechanisms of protein cage self-assembly by coarse-grained simulations

The development of artificial protein cages has recently gained massive attention due to their promising application prospect as novel delivery vehicles for therapeutics. These nanoparticles are formed through a process called self-assembly, in which individual subunits spontaneously arrange into highly ordered patterns via non-covalent but specific interactions. Therefore, the first step toward the design of novel engineered protein cages is to understand the general mechanisms of their self-assembling dynamics. Here we have developed a new computational method to tackle this problem. Our method is based on a coarse-grained model and a diffusion-reaction simulation algorithm. Using a tetrahedral cage as test model, we showed that self-assembly of protein cage requires of a seeding process in which specific configurations of kinetic intermediate states are identified. We further found that there is a critical concentration to trigger self-assembly of protein cages. This critical concentration allows that cages can only be successfully assembled under a persistently high concentration. Additionally, phase diagram of self-assembly has been constructed by systematically testing the model across a wide range of binding parameters. Finally, our simulations demonstrated the importance of protein's structural flexibility in regulating the dynamics of cage assembly. In summary, this study throws lights on the general principles underlying self-assembly of large cage-like protein complexes and thus provides insights to design new nanomaterials.

On the formation of ordered protein assemblies in cell-cell interfaces

Crystal structures of many cell-cell adhesion receptors reveal the formation of linear "molecular zippers" comprising an ordered one-dimensional array of proteins that form both intercellular (trans) and intracellular (cis) interactions. The clustered protocadherins (cPcdhs) provide an exemplar of this phenomenon and use it as a basis of barcoding of vertebrate neurons. Here, we report both Metropolis and kinetic Monte Carlo simulations of cPcdh zipper formation using simplified models of cPcdhs that nevertheless capture essential features of their three-dimensional structure. The simulations reveal that the formation of long zippers is an implicit feature of cPcdh structure and is driven by their cis and trans interactions that have been quantitatively characterized in previous work. Moreover, in agreement with cryo-electron tomography studies, the zippers are found to organize into two-dimensional arrays even in the absence of attractive interactions between individual zippers. Our results suggest that the formation of ordered two-dimensional arrays of linear zippers of adhesion proteins is a common feature of cell-cell interfaces. From the perspective of simulations, they demonstrate the importance of a realistic depiction of adhesion protein structure and interactions if important biological phenomena are to be properly captured.

Understanding the functional role of membrane confinements in TNF-mediated signaling by multiscale simulations

The interaction between TNFα and TNFR1 is essential in maintaining tissue development and immune responses. While TNFR1 is a cell surface receptor, TNFα exists in both soluble and membrane-bound forms. Interestingly, it was found that the activation of TNFR1-mediated signaling pathways is preferentially through the soluble form of TNFα, which can also induce the clustering of TNFR1 on plasma membrane of living cells. We developed a multiscale simulation framework to compare receptor clustering induced by soluble and membrane-bound ligands. Comparing with the freely diffusive soluble ligands, we hypothesize that the conformational dynamics of membrane-bound ligands are restricted, which affects the clustering of ligand-receptor complexes at cell-cell interfaces. Our simulation revealed that only small clusters can form if TNFα is bound on cell surface. In contrast, the clustering triggered by soluble TNFα is more dynamic, and the size of clusters is statistically larger. We therefore demonstrated the impact of membrane-bound ligand on dynamics of receptor clustering. Moreover, considering that larger TNFα-TNFR1 clusters is more likely to provide spatial platform for downstream signaling pathway, our studies offer new mechanistic insights about why the activation of TNFR1-mediated signaling pathways is not preferred by membrane-bound form of TNFα.

Mechanistic dissection of spatial organization in NF-κB signaling pathways by hybrid simulations

The nuclear factor kappa-light-chain-enhancer of activated B cells (NF-κB) is one of the most important transcription factors involved in the regulation of inflammatory signaling pathways. Inappropriate activation of these pathways has been linked to autoimmunity and cancers. Emerging experimental evidences have been showing the existence of elaborate spatial organizations for various molecular components in the pathways. One example is the scaffold protein tumor necrosis factor receptor associated factor (TRAF). While most TRAF proteins form trimeric quaternary structure through their coiled-coil regions, the N-terminal region of some members in the family can further be dimerized. This dimerization of TRAF trimers can drive them into higher-order clusters as a response to receptor stimulation, which functions as a spatial platform to mediate the downstream poly-ubiquitination. However, the molecular mechanism underlying the TRAF protein clustering and its functional impacts are not well-understood. In this article, we developed a hybrid simulation method to tackle this problem. The assembly of TRAF-based signaling platform at the membrane-proximal region is modeled with spatial resolution, while the dynamics of downstream signaling network, including the negative feedbacks through various signaling inhibitors, is simulated as stochastic chemical reactions. These two algorithms are further synchronized under a multiscale simulation framework. Using this computational model, we illustrated that the formation of TRAF signaling platform can trigger an oscillatory NF-κB response. We further demonstrated that the temporal patterns of downstream signal oscillations are closely regulated by the spatial factors of TRAF clustering, such as the geometry and energy of dimerization between TRAF trimers. In general, our study sheds light on the basic mechanism of NF-κB signaling pathway and highlights the functional importance of spatial regulation within the pathway. The simulation framework also showcases its potential of application to other signaling pathways in cells.

A multiscale study on the mechanisms of spatial organization in ligand-receptor interactions on cell surfaces

The binding of cell surface receptors with extracellular ligands triggers distinctive signaling pathways, leading into the corresponding phenotypic variation of cells. It has been found that in many systems, these ligand-receptor complexes can further oligomerize into higher-order structures. This ligand-induced oligomerization of receptors on cell surfaces plays an important role in regulating the functions of cell signaling. The underlying mechanism, however, is not well understood. One typical example is proteins that belong to the tumor necrosis factor receptor (TNFR) superfamily. Using a generic multiscale simulation platform that spans from atomic to subcellular levels, we compared the detailed physical process of ligand-receptor oligomerization for two specific members in the TNFR superfamily: the complex formed between ligand TNFα and receptor TNFR1 versus the complex formed between ligand TNFβ and receptor TNFR2. Interestingly, although these two systems share high similarity on the tertiary and quaternary structural levels, our results indicate that their oligomers are formed with very different dynamic properties and spatial patterns. We demonstrated that the changes of receptor’s conformational fluctuations due to the membrane confinements are closely related to such difference. Consistent to previous experiments, our simulations also showed that TNFR can preassemble into dimers prior to ligand binding, while the introduction of TNF ligands induced higher-order oligomerization due to a multivalent effect. This study, therefore, provides the molecular basis to TNFR oligomerization and reveals new insights to TNFR-mediated signal transduction. Moreover, our multiscale simulation framework serves as a prototype that paves the way to study higher-order assembly of cell surface receptors in many other bio-systems.

A computational study of co-inhibitory immune complex assembly at the interface between T cells and antigen presenting cells

The activation and differentiation of T-cells are mainly directly by their co-regulatory receptors. T lymphocyte-associated protein-4 (CTLA-4) and programed cell death-1 (PD-1) are two of the most important co-regulatory receptors. Binding of PD-1 and CTLA-4 with their corresponding ligands programed cell death-ligand 1 (PD-L1) and B7 on the antigen presenting cells (APC) activates two central co-inhibitory signaling pathways to suppress T cell functions. Interestingly, recent experiments have identified a new cis-interaction between PD-L1 and B7, suggesting that a crosstalk exists between two co-inhibitory receptors and the two pairs of ligand-receptor complexes can undergo dynamic oligomerization. Inspired by these experimental evidences, we developed a coarse-grained model to characterize the assembling of an immune complex consisting of CLTA-4, B7, PD-L1 and PD-1. These four proteins and their interactions form a small network motif. The temporal dynamics and spatial pattern formation of this network was simulated by a diffusion-reaction algorithm. Our simulation method incorporates the membrane confinement of cell surface proteins and geometric arrangement of different binding interfaces between these proteins. A wide range of binding constants was tested for the interactions involved in the network. Interestingly, we show that the CTLA-4/B7 ligand-receptor complexes can first form linear oligomers, while these oligomers further align together into two-dimensional clusters. Similar phenomenon has also been observed in other systems of cell surface proteins. Our test results further indicate that both co-inhibitory signaling pathways activated by B7 and PD-L1 can be down-regulated by the new cis-interaction between these two ligands, consistent with previous experimental evidences. Finally, the simulations also suggest that the dynamic and the spatial properties of the immune complex assembly are highly determined by the energetics of molecular interactions in the network. Our study, therefore, brings new insights to the co-regulatory mechanisms of T cell activation.

The activation of a T cell can be regulated by the receptors on its surface, such as CTLA-4 and PD-1. People used to think that these two receptors inhibit T cell activation through distinct pathways. However, recent experiments discovered that the ligands of these two receptors, B7 and PD-L1, can interact with each other on the same surface of antigen presenting cells. Here we utilized computational simulations to investigate functional roles of this newly discovered interaction in T cell coregulation. The specific environment of interface between T cell and antigen presenting cell has been taken into account of our model. Ligand and receptors randomly diffuse within this interface area. They further involve in different types of interactions, with each other from the same side or the opposite side of cell surface. Using this method, we found ligands and receptors can not only form complexes, but also aggregate into large-scale clusters. We also demonstrated that the engagement between B7 and PD-L1 can reduce the interactions with their corresponding receptors. This study, therefore, offers new insights to our understanding of signal regulation in T cells.

Understanding the impacts of cellular environments on ligand binding of membrane receptors by computational simulations

Binding of cell surface receptors with their extracellular ligands initiates various intracellular signaling pathways. However, our understanding of the cellular functions of these receptors is very limited due to the fact that in vivo binding between ligands and receptors has only been successfully measured in a very small number of cases. In living cells, receptors are anchored on surfaces of the plasma membrane, which undergoes thermal undulations. Moreover, it has been observed in various systems that receptors can be organized into oligomers prior to ligand binding. It is not well understood how these cellular factors play roles in regulating the dynamics of ligand-receptor interactions. Here, we tackled these problems by using a coarse-grained kinetic Monte Carlo simulation method. Using this method, we demonstrated that the membrane undulations cause a negative effect on ligand-receptor interactions. We further found that the preassembly of membrane receptors on the cell surface can not only accelerate the kinetics of ligand binding but also reduce the noises during the process. In general, our study highlights the importance of membrane environments in regulating the function of membrane receptors in cells. The simulation method can be potentially applied to specific receptor systems involved in cell signaling.

A Multiscale and Comparative Model for Receptor Binding of 2019 Novel Coronavirus and the Implication of its Life Cycle in Host Cells

The respiratory syndrome caused by a new type of coronavirus has been emerging from China and caused more than one million death globally since December 2019. This new virus, called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) uses the same receptor called Angiotensin-converting enzyme 2 (ACE2) to attack humans as the coronavirus that caused the severe acute respiratory syndrome (SARS) seventeen years ago. Both viruses recognize ACE2 through the spike proteins (S-protein) on their surfaces. It was found that the S-protein from the SARS coronavirus (SARS-CoV) bind stronger to ACE2 than SARS-CoV-2. However, function of a bio-system is often under kinetic, rather than thermodynamic, control. To address this issue, we constructed a structural model for complex formed between ACE2 and the S-protein from SARS-CoV-2, so that the rate of their association can be estimated and compared with the binding of S-protein from SARS-CoV by a multiscale simulation method. Our simulation results suggest that the association of new virus to the receptor is slower than SARS, which is consistent with the experimental data obtained very recently. We further integrated this difference of association rate between virus and receptor into a mathematical model which describes the life cycle of virus in host cells and its interplay with the innate immune system. Interestingly, we found that the slower association between virus and receptor can result in longer incubation period, while still maintaining a relatively higher level of viral concentration in human body. Our computational study therefore provides, from the molecular level, one possible explanation that this new pandemic by far spread much faster than SARS.

Understand the Functions of Scaffold Proteins in Cell Signaling by a Mesoscopic Simulation Method

Scaffold proteins are central players in regulating the spatial-temporal organization of many important signaling pathways in cells. They offer physical platforms to downstream signaling proteins so that their transient interactions in a crowded and heterogeneous environment of cytosol can be greatly facilitated. However, most scaffold proteins tend to simultaneously bind more than one signaling molecule, which leads to the spatial assembly of multimeric protein complexes. The kinetics of these protein oligomerizations are difficult to quantify by traditional experimental approaches. To understand the functions of scaffold proteins in cell signaling, we developed a, to our knowledge, new hybrid simulation algorithm in which both spatial organization and binding kinetics of proteins were implemented. We applied this new technique to a simple network system that contains three molecules. One molecule in the network is a scaffold protein, whereas the other two are its binding targets in the downstream signaling pathway. Each of the three molecules in the system contains two binding motifs that can interact with each other and are connected by a flexible linker. By applying the new simulation method to the model, we show that the scaffold proteins will promote not only thermodynamics but also kinetics of cell signaling given the premise that the interaction between the two signaling molecules is transient. Moreover, by changing the flexibility of the linker between two binding motifs, our results suggest that the conformational fluctuations in a scaffold protein play a positive role in recruiting downstream signaling molecules. In summary, this study showcases the capability of computational simulation in understanding the general principles of scaffold protein functions.

Cadherin clusters stabilized by a combination of specific and nonspecific cis-interactions

We demonstrate a combined experimental and computational approach for the quantitative characterization of lateral interactions between membrane-associated proteins. In particular, weak, lateral (cis) interactions between E-cadherin extracellular domains tethered to supported lipid bilayers, were studied using a combination of dynamic single-molecule Förster Resonance Energy Transfer (FRET) and kinetic Monte Carlo (kMC) simulations. Cadherins are intercellular adhesion proteins that assemble into clusters at cell-cell contacts through cis- and trans- (adhesive) interactions. A detailed and quantitative understanding of cis-clustering has been hindered by a lack of experimental approaches capable of detecting and quantifying lateral interactions between proteins on membranes. Here single-molecule intermolecular FRET measurements of wild-type E-cadherin and cis-interaction mutants combined with simulations demonstrate that both nonspecific and specific cis-interactions contribute to lateral clustering on lipid bilayers. Moreover, the intermolecular binding and dissociation rate constants are quantitatively and independently determined, demonstrating an approach that is generalizable for other interacting proteins.

A computational model for understanding the oligomerization mechanisms of TNF receptor superfamily

By recognizing members in the tumor necrosis factor (TNF) receptor superfamily, TNF ligand proteins function as extracellular cytokines to activate various signaling pathways involved in inflammation, proliferation, and apoptosis. Most ligands in TNF superfamily are trimeric and can simultaneously bind to three receptors on cell surfaces. It has been experimentally observed that the formation of these molecular complexes further triggers the oligomerization of TNF receptors, which in turn regulate the intracellular signaling processes by providing transient compartmentalization in the membrane proximal regions of cytoplasm. In order to decode the molecular mechanisms of oligomerization in TNF receptor superfamily, we developed a new computational method that can physically simulate the spatial-temporal process of binding between TNF ligands and their receptors. The simulations show that the TNF receptors can be organized into hexagonal oligomers. The formation of this spatial pattern is highly dependent not only on the molecular properties such as the affinities of trans and cis binding, but also on the cellular factors such as the concentration of TNF ligands in the extracellular area or the density of TNF receptors on cell surfaces. Moreover, our model suggests that if TNF receptors are pre-organized into dimers before ligand binding, these lateral interactions between receptor monomers can play a positive role in stabilizing the ligand-receptor interactions, as well as in regulating the kinetics of receptor oligomerization. Altogether, this method throws lights on the mechanisms of TNF ligand-receptor interactions in cellular environments.

Multiscale simulation unravel the kinetic mechanisms of inflammasome assembly

In the innate immune system, the host defense from the invasion of external pathogens triggers the inflammatory responses. Proteins involved in the inflammatory pathways were often found to aggregate into supramolecular oligomers, called 'inflammasome', mostly through the homotypic interaction between their domains that belong to the death domain superfamily. Although much has been known about the formation of these helical molecular machineries, the detailed correlation between the dynamics of their assembly and the structure of each domain is still not well understood. Using the filament formed by the PYD domains of adaptor molecule ASC as a test system, we constructed a new multiscale simulation framework to study the kinetics of inflammasome assembly. We found that the filament assembly is a multi-step, but highly cooperative process. Moreover, there are three types of binding interfaces between domain subunits in the ASC^PYD filament. The multiscale simulation results suggest that dynamics of domain assembly are rooted in the primary protein sequence which defines the energetics of molecular recognition through three binding interfaces. Interface I plays a more regulatory role than the other two in mediating both the kinetics and the thermodynamics of assembly. Finally, the efficiency of our computational framework allows us to design mutants on a systematic scale and predict their impacts on filament assembly. In summary, this is, to the best of our knowledge, the first simulation method to model the spatial-temporal process of inflammasome assembly. Our work is a useful addition to a suite of existing experimental techniques to study the functions of inflammasome in innate immune system.

A Multiscale Model for the Self-Assembly of Coat Proteins in Bacteriophage MS2

The self-assembly of viral capsids is an essential step to the formation of infectious viruses. Elucidating the kinetic mechanisms of how a capsid or virus-like particle assembles could advance our knowledge about the viral lifecycle, as well as the general principles in self-assembly of biomaterials. However, current understanding of capsid assembly remains incomplete for many viruses due to the fact that the transient intermediates along the assembling pathways are experimentally difficult to be detected. In this paper, we constructed a new multiscale computational framework to simulate the self-assembly of virus-like particles. We applied our method to the coat proteins of bacteriophage MS2 as a specific model system. This virus-like particle of bacteriophage MS2 has a unique feature that its 90 sequence-identical dimers can be classified into two structurally various groups: one is the symmetric CC dimer, and the other is the asymmetric AB dimer. The homotypic interactions between AB dimers result in a 5-fold symmetric contact, while the heterotypic interactions between AB and CC dimers result in 6-fold symmetric contact. We found that the assembly can be described as a physical process of phase transition that is regulated by various factors such as concentration and specific stoichiometry between AB and CC dimers. Our simulations also demonstrate that heterotypic and homotypic interfaces play distinctive roles in modulating the assembling kinetics. The interaction between AB and CC dimers is much more dynamic than that between two AB dimers. We therefore suggest that the alternate growth of viral capsid through the heterotypic dimer interactions dominates the assembling pathways. This is, to the best of our knowledge, the first multiscale model to simulate the assembling process of coat proteins in bacteriophage MS2. The generality of this approach opens the door to its further applications in assembly of other viral capsids, virus-like particles, and novel drug delivery systems.

A Multiscale Computational Model for Simulating the Kinetics of Protein Complex Assembly

Proteins fulfill versatile biological functions by interacting with each other and forming high-order complexes. Although the order in which protein subunits assemble is important for the biological function of their final complex, this kinetic information has received comparatively little attention in recent years. Here we describe a multiscale framework that can be used to simulate the kinetics of protein complex assembly. There are two levels of models in the framework. The structural details of a protein complex are reflected by the residue-based model, while a lower-resolution model uses a rigid-body (RB) representation to simulate the process of complex assembly. These two levels of models are integrated together, so that we are able to provide the kinetic information about complex assembly with both structural details and computational efficiency.

Integrating Structural Information to Study the Dynamics of Protein-Protein Interactions in Cells

The information of how two proteins interact is embedded in the atomic details of their binding interfaces. These interactions, spatial-temporally coordinating each other as a network in a variable cytoplasmic environment, dominate almost all biological functions. A feasible and reliable computational model is highly demanded to realistically simulate these cellular processes and unravel the complexities beneath them. We therefore present a multiscale framework that integrates simulations on two different scales. The higher-resolution model incorporates structural information of proteins and energetics of their binding, while the lower-resolution model uses a highly simplified representation of proteins to capture the long-time-scale dynamics of a system with multiple proteins. Through a systematic benchmark test and two practical applications of biomolecular systems with specific cellular functions, we demonstrated that this method could be a powerful approach to understand molecular mechanisms of dynamic interactions between biomolecules and their functional impacts with high computational efficiency.

General principles of binding between cell surface receptors and multi-specific ligands: A computational study

The interactions between membrane receptors and extracellular ligands control cell-cell and cell-substrate adhesion, and environmental responsiveness by representing the initial steps of cell signaling pathways. These interactions can be spatial-temporally regulated when different extracellular ligands are tethered. The detailed mechanisms of this spatial-temporal regulation, including the competition between distinct ligands with overlapping binding sites and the conformational flexibility in multi-specific ligand assemblies have not been quantitatively evaluated. We present a new coarse-grained model to realistically simulate the binding process between multi-specific ligands and membrane receptors on cell surfaces. The model simplifies each receptor and each binding site in a multi-specific ligand as a rigid body. Different numbers or types of ligands are spatially organized together in the simulation. These designs were used to test the relation between the overall binding of a multi-specific ligand and the affinity of its cognate binding site. When a variety of ligands are exposed to cells expressing different densities of surface receptors, we demonstrated that ligands with reduced affinities have higher specificity to distinguish cells based on the relative concentrations of their receptors. Finally, modification of intramolecular flexibility was shown to play a role in optimizing the binding between receptors and ligands. In summary, our studies bring new insights to the general principles of ligand-receptor interactions. Future applications of our method will pave the way for new strategies to generate next-generation biologics.

In order to adapt to surrounding environments, multiple signaling pathways have been evolved in cells. The first step of these pathways is to detect external stimuli, which is conducted by the dynamic interactions between cell surface receptors and extracellular ligands. As a result, recognition of extracellular ligands by cell surface receptors is an indispensable component of many physiological or pathological activities. In both natural selection and drug design, the presence of multiple binding sites in extracellular ligand complexes (so-called multi-specific ligands) is a common strategy to target different receptors on surface of the same cell. Such spatial organization of ligand binding sites can elaborately modulate the downstream signaling pathways. However, our understanding to the interactions between multi-specific ligands and membrane receptors is largely limited by the fact that these interactions are difficult to quantify and they have only been successfully measured in a very small number of cases in vivo. Using a simple computational model, we can realistically simulate the binding process between specially designed multi-specific ligands and membrane receptors on cell surfaces. This study therefore provides a useful pathway to unravel basic mechanisms of ligand-receptor interactions and design principles for new drug candidates.

A Computational Model for Kinetic Studies of Cadherin Binding and Clustering

Cadherin is a cell-surface transmembrane receptor that mediates calcium-dependent cell-cell adhesion and is a major component of adhesive junctions. The formation of intercellular adhesive junctions is initiated by trans binding between cadherins on adjacent cells, which is followed by the clustering of cadherins via the formation of cis interactions between cadherins on the same cell membranes. Moreover, classical cadherins have multiple glycosylation sites along their extracellular regions. It was found that aberrant glycosylation affects the adhesive function of cadherins and correlates with metastatic phenotypes of several cancers. However, a mechanistic understanding of cadherin clustering during cell adhesion and the role of glycosylation in this process is still lacking. Here, we designed a kinetic model that includes multistep reaction pathways for cadherin clustering. We further applied a diffusion-reaction algorithm to numerically simulate the clustering process using a recently developed coarse-grained model. Using experimentally measured rates of trans binding between soluble E-cadherin extracellular domains, we conducted simulations of cadherin-mediated cell-cell binding kinetics, and the results are quantitatively comparable to experimental data from micropipette experiments. In addition, we show that incorporating cadherin clustering via cis interactions further increases intercellular binding. Interestingly, a two-phase kinetic profile was derived under the assumption that glycosylation regulates the kinetic rates of cis interactions. This two-phase profile is qualitatively consistent with experimental results from micropipette measurements. Therefore, our computational studies provide new, to our knowledge, insights into the molecular mechanism of cadherin-based cell adhesion.

Predicting Protein-protein Association Rates using Coarse-grained Simulation and Machine Learning

Protein–protein interactions dominate all major biological processes in living cells. We have developed a new Monte Carlo-based simulation algorithm to study the kinetic process of protein association. We tested our method on a previously used large benchmark set of 49 protein complexes. The predicted rate was overestimated in the benchmark test compared to the experimental results for a group of protein complexes. We hypothesized that this resulted from molecular flexibility at the interface regions of the interacting proteins. After applying a machine learning algorithm with input variables that accounted for both the conformational flexibility and the energetic factor of binding, we successfully identified most of the protein complexes with overestimated association rates and improved our final prediction by using a cross-validation test. This method was then applied to a new independent test set and resulted in a similar prediction accuracy to that obtained using the training set. It has been thought that diffusion-limited protein association is dominated by long-range interactions. Our results provide strong evidence that the conformational flexibility also plays an important role in regulating protein association. Our studies provide new insights into the mechanism of protein association and offer a computationally efficient tool for predicting its rate.

Excluded volume effects in on- and off-lattice reaction-diffusion models

Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics become computationally expensive in crowded environments. In this study, the authors therefore investigate to which extent on-lattice approximations, the so-called cellular automata models, can be used to simulate reactions and diffusion in the presence of crowding molecules. They show that the diffusion is most severely slowed down in the off-lattice model, since randomly distributed obstacles effectively exclude more volume than those ordered on an artificial grid. Crowded reaction rates can be both increased and decreased by the grid structure and it proves important to model the molecules with realistic sizes when excluded volume is taken into account. The grid artefacts increase with increasing crowder density and they conclude that the computationally more efficient on-lattice simulations are accurate approximations only for low crowder densities.

Modeling somite scaling in small embryos in the framework of Turing patterns

The adaptation of prevertebra size to embryo size is investigated in the framework of a reaction-diffusion model involving a Turing pattern. The reaction scheme and Fick's first law of diffusion are modified in order to take into account the departure from dilute conditions induced by confinement in smaller embryos. In agreement with the experimental observations of scaling in somitogenesis, our model predicts the formation of smaller prevertebrae or somites in smaller embryos. These results suggest that models based on Turing patterns cannot be automatically disregarded by invoking the question of maintaining proportions in embryonic development. Our approach highlights the nontrivial role that the solvent can play in biology.

Elucidating the general principles of cell adhesion with a coarse-grained simulation model

Coarse-grained simulation of interplay between cell adhesion and cell signaling.

Computational modeling of the interplay between cadherin-mediated cell adhesion and Wnt signaling pathway

Wnt signaling and cadherin-mediated adhesion have been implicated in both processes of embryonic development and the progression of carcinomas. Recent experimental studies revealed that Wnt signaling and cadherin-mediated cell adhesion have close crosstalk with each other. A comprehensive model that investigates the dynamic balance of β-catenins in Wnt signaling and cell adhesion will improve our understanding to embryonic development and carcinomas. We constructed a network model to evaluate the dynamic interplay between adhesion and Wnt signaling. The network is decomposed into three interdependent modules: the cell adhesion, the degradation circle and the transcriptional regulation. In the cell adhesion module, we consider the effect of cadherin’s lateral clustering. We found adhesion negatively contributes to Wnt signaling through competition for cytoplasmic β-catenins. In the network of degradation circle, we incorporated features from various existing models. Our simulations reproduced the most recent experimental phenomena with semi-quantitative accuracy. Finally, in the transcriptional regulation module, we developed a function selection strategy to analyze the outcomes of genetic feedback loops in modulating the gene expression of Wnt targets. The specific cellular phenomena such as cadherin switch and Axin oscillation were archived and their biological insights were discussed. Our model provides the theoretical basis of how spatial organization regulates the dynamics of cellular signaling pathways. We suggest that cell adhesion affects Wnt signaling in both negative and positive ways. Cadherins can inhibit Wnt signaling not only in a way as a stoichiometric binding partner of β-catenins that sequesters them from signaling, but also in a way through their clustering to impacts the rate at which β-catenins are involved in the destruction loop. Additionally, cadherin clustering increases the phosphorylation rate of β-catenins and promotes its signaling in nucleus.