Neeraj J. Agrawal

Systems biology and physical biology of clathrin-mediated endocytosis

In this review, we describe the application of experimental data and modeling of intracellular endocytic trafficking mechanisms with a focus on the process of clathrin-mediated endocytosis. A detailed parts-list for the protein-protein interactions in clathrin-mediated endocytosis has been available for some time. However, recent experimental, theoretical, and computational tools have proved to be critical in establishing a sequence of events, cooperative dynamics, and energetics of the intracellular process. On the experimental front, total internal reflection fluorescence microscopy, photo-activated localization microscopy, and spinning-disk confocal microscopy have focused on assembly and patterning of endocytic proteins at the membrane, while on the theory front, minimal theoretical models for clathrin nucleation, biophysical models for membrane curvature and bending elasticity, as well as methods from computational structural and systems biology, have proved insightful in describing membrane topologies, curvature mechanisms, and energetics.

Multivalent Binding of Nanocarrier to Endothelial Cells under Shear Flow

We investigate the effects of particle size, shear flow, and resistance due to the glycocalyx on the multivalent binding of functionalized nanocarriers (NC) to endothelial cells (ECs). We address the much- debated issue of shear-enhanced binding by computing the binding free-energy landscapes of NC binding to the EC surface when the system is subjected to shear, using a model and simulation methodology based on the Metropolis Monte Carlo approach. The binding affinities calculated based on the free-energy profiles are found to be in excellent agreement with experimental measurements for different-sized NCs. The model suggests that increasing the size of NCs significantly increases the multivalency but only moderately enhances the binding affinities due to the entropy loss associated with bound receptors on the EC surface. A significant prediction of our model is that under flow conditions, the binding free energies of NCs are a nonmonotonic function of the shear force. They show a well-defined minimum at a critical shear value, and thus quantitatively mimic the shear-enhanced binding behavior observed in various experiments. More significantly, our results indicate that the interplay between multivalent binding and shear force can reproduce the shear-enhanced binding phenomenon, which suggests that under certain conditions, this phenomenon can also occur in systems that do not show a catch-bond behavior. In addition, the model also suggests that the impact of the glycocalyx thickness on NC binding affinity is exponential, implying a highly nonlinear effect of the glycocalyx on binding.

A Multiscale Computational Approach to Dissect Early Events in the Erb Family Receptor Mediated Activation, Differential Signaling, and Relevance to Oncogenic Transformations

We describe a hierarchical multiscale computational approach based on molecular dynamics simulations, free energy-based molecular docking simulations, deterministic network-based kinetic modeling, and hybrid discrete/continuum stochastic dynamics protocols to study the dimer-mediated receptor activation characteristics of the Erb family receptors, specifically the epidermal growth factor receptor (EGFR). Through these modeling approaches, we are able to extend the prior modeling of EGF-mediated signal transduction by considering specific EGFR tyrosine kinase (EGFRTK) docking interactions mediated by differential binding and phosphorylation of different C-terminal peptide tyrosines on the RTK tail. By modeling signal flows through branching pathways of the EGFRTK resolved on a molecular basis, we are able to transcribe the effects of molecular alterations in the receptor (e.g., mutant forms of the receptor) to differing kinetic behavior and downstream signaling response. Our molecular dynamics simulations show that the drug sensitizing mutation (L834R) of EGFR stabilizes the active conformation to make the system constitutively active. Docking simulations show preferential characteristics (for wildtype vs. mutant receptors) in inhibitor binding as well as preferential enhancement of phosphorylation of particular substrate tyrosines over others. We find that in comparison to the wildtype system, the L834R mutant RTK preferentially binds the inhibitor erlotinib, as well as preferentially phosphorylates the substrate tyrosine Y1068 but not Y1173. We predict that these molecular level changes result in preferential activation of the Akt signaling pathway in comparison to the Erk signaling pathway for cells with normal EGFR expression. For cells with EGFR over expression, the mutant over activates both Erk and Akt pathways, in comparison to wildtype. These results are consistent with qualitative experimental measurements reported in the literature. We discuss these consequences in light of how the network topology and signaling characteristics of altered (mutant) cell lines are shaped differently in relationship to native cell lines.

Minimal Mesoscale Model for Protein-Mediated Vesiculation in Clathrin-Dependent Endocytosis

In eukaryotic cells, the internalization of extracellular cargo via the endocytic machinery is an important regulatory process required for many essential cellular functions. The role of cooperative protein-protein and protein-membrane interactions in the ubiquitous endocytic pathway in mammalian cells, namely the clathrin-dependent endocytosis, remains unresolved. We employ the Helfrich membrane Hamiltonian together with surface evolution methodology to address how the shapes and energetics of vesicular-bud formation in a planar membrane are stabilized by presence of the clathrin-coat assembly. Our results identify a unique dual role for the tubulating protein epsin: multiple epsins localized spatially and orientationally collectively play the role of a curvature inducing capsid; in addition, epsin serves the role of an adapter in binding the clathrin coat to the membrane. Our results also suggest an important role for the clathrin lattice, namely in the spatial- and orientational-templating of epsins. We suggest that there exists a critical size of the coat above which a vesicular bud with a constricted neck resembling a mature vesicle is stabilized. Based on the observed strong dependence of the vesicle diameter on the bending rigidity, we suggest that the variability in bending stiffness due to variations in membrane composition with cell type can explain the experimentally observed variability on the size of clathrin-coated vesicles, which typically range 50–100 nm. Our model also provides estimates for the number of epsins involved in stabilizing a coated vesicle, and without any direct fitting reproduces the experimentally observed shapes of vesicular intermediates as well as their probability distributions quantitatively, in wildtype as well as CLAP IgG injected neuronal cell experiments. We have presented a minimal mesoscale model which quantitatively explains several experimental observations on the process of vesicle nucleation induced by the clathrin-coated assembly prior to vesicle scission in clathrin dependent endocytosis.

Geometry of Mediating Protein Affects the Probability of Loop Formation in DNA

Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.

Mesoscale simulations of curvature-inducing protein partitioning on lipid bilayer membranes in the presence of mean curvature fields.

The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable ‘neck-region’ (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated.

Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model.

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein–membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.

A flexible-protein molecular docking study of the binding of ruthenium complex compounds to PIM1, GSK-3β, and CDK2/Cyclin A protein kinases

AbstractWe employ ensemble docking simulations to characterize the interactions of two enantiomeric forms of a Ru-complex compound (1-R and 1-S) with three protein kinases, namely PIM1, GSK-3β, and CDK2/cyclin A. We show that our ensemble docking computational protocol adequately models the structural features of these interactions and discriminates between competing conformational clusters of ligand-bound protein structures. Using the determined X-ray crystal structure of PIM1 complexed to the compound 1-R as a control, we discuss the importance of including the protein flexibility inherent in the ensemble docking protocol, for the accuracy of the structure prediction of the bound state. A comparison of our ensemble docking results suggests that PIM1 and GSK-3β bind the two enantiomers in similar fashion, through two primary binding modes: conformation I, which is very similar to the conformation presented in the existing PIM1/compound 1-R crystal structure; conformation II, which represents a 180° flip about an axis through the NH group of the pyridocarbazole moiety, relative to conformation I. In contrast, the binding of the enantiomers to CDK2 is found to have a different structural profile including a suggested bound conformation, which lacks the conserved hydrogen bond between the kinase and the ligand (i.e., ATP, staurosporine, Ru-complex compound). The top scoring conformation of the inhibitor bound to CDK2 is not present among the top-scoring conformations of the inhibitor bound to either PIM1 or GSK-3β and vice-versa. Collectively, our results help provide atomic-level insights into inhibitor selectivity among the three kinases.n FigureTop cluster of predicted conformations based on ensemble docking simulations of a Ruthenium based compound to protein kinases

Chapter 11:Top-down Mesoscale Models and Free Energy Calculations of Multivalent Protein-Protein and Protein-Membrane Interactions in Nanocarrier Adhesion and Receptor Trafficking

In this chapter we present a summary of recent applications of top-down mesoscale modeling to two biologically relevant problems: (1) adhesion of nanocarriers to cells mediated by multivalent receptor-ligand interactions in targeted drug delivery; (2) internalization of cell surface receptors in cells via the biological process of endocytosis. In particular, we focus on methods for computing absolute/relative free energies using these mesoscale models in order to facilitate direct comparison with experimental data.