Kinetics of enzymatic reactions in lipid membranes containing domains

Modeling the distribution of enzymes on lipid vesicles: A novel framework for surface-mediated reactions in coagulation

Blood coagulation is a network of biochemical reactions wherein dozens of proteins act collectively to initiate a rapid clotting response. Coagulation reactions are lipid-surface dependent, and this dependence is thought to help localize coagulation to the site of injury and enhance the association between reactants. Current mathematical models of coagulation either do not consider lipid as a variable or do not agree with experiments where lipid concentrations were varied. Since there is no analytic rate law that depends on lipid, only apparent rate constants can be derived from enzyme kinetic experiments. We developed a new mathematical framework for modeling enzymes reactions in the presence of lipid vesicles. Here the concentrations are such that only a fraction of the vesicles harbor bound enzymes and the rest remain empty. We call the lipid vesicles with and without enzyme TF:VIIa+ and TF:VIIa- lipid, respectively. Since substrate binds to both TF:VIIa+ and TF:VIIa- lipid, our model shows that excess empty lipid acts as a strong sink for substrate. We used our framework to derive an analytic rate equation and performed constrained optimization to estimate a single, global set of intrinsic rates for the enzyme-substrate pair. Results agree with experiments and reveal a critical lipid concentration where the conversion rate of the substrate is maximized, a phenomenon known as the template effect. Next, we included product inhibition of the enzyme and derived the corresponding rate equations, which enables kinetic studies of more complex reactions. Our combined experimental and mathematical study provides a general framework for uncovering the mechanisms by which lipid mediated reactions impact coagulation processes.

Lipid environment modulates processivity and kinetics of a presenilin homolog acting on multiple substrates in vitro

Intramembrane proteases (IPs) hydrolyze peptides in the lipid membrane. IPs participate in a number of cellular pathways including immune response and surveillance, and cholesterol biosynthesis, and they are exploited by viruses for replication. Despite their broad importance across biology, how activity is regulated in the cell to control protein maturation and release of specific bioactive peptides at the right place and right time remains largely unanswered, particularly for the intramembrane aspartyl protease (IAP) subtype. At a molecular biochemical level, different IAP homologs can cleave non-biological substrates, and there is no sequence recognition motif among the nearly 150 substrates identified for just one IAP, presenilin-1, the catalytic component of γ-secretase known for its involvement in the production of amyloid-β plaques associated with Alzheimer disease. Here we used gel-based assays combined with quantitative mass spectrometry and FRET-based kinetics assays to probe the cleavage profile of the presenilin homolog from the methanogen Methanoculleus marisnigri JR1 as a function of the surrounding lipid-mimicking environment, either detergent micelles or bicelles. We selected four biological IAP substrates that have not undergone extensive cleavage profiling previously, namely, the viral core protein of Hepatitis C virus, the viral core protein of Classical Swine Fever virus, the transmembrane segment of Notch-1, and the tyrosine receptor kinase ErbB4. Our study demonstrates a proclivity toward cleavage of substrates at positions of low average hydrophobicity and a consistent role for the lipid environment in modulating kinetic properties.

Real-time monitoring of peptidoglycan synthesis by membrane-reconstituted penicillin-binding proteins

Peptidoglycan is an essential component of the bacterial cell envelope that surrounds the cytoplasmic membrane to protect the cell from osmotic lysis. Important antibiotics such as β-lactams and glycopeptides target peptidoglycan biosynthesis. Class A penicillin-binding proteins (PBPs) are bifunctional membrane-bound peptidoglycan synthases that polymerize glycan chains and connect adjacent stem peptides by transpeptidation. How these enzymes work in their physiological membrane environment is poorly understood. Here, we developed a novel Förster resonance energy transfer-based assay to follow in real time both reactions of class A PBPs reconstituted in liposomes or supported lipid bilayers and applied this assay with PBP1B homologues from Escherichia coli, Pseudomonas aeruginosa, and Acinetobacter baumannii in the presence or absence of their cognate lipoprotein activator. Our assay will allow unravelling the mechanisms of peptidoglycan synthesis in a lipid-bilayer environment and can be further developed to be used for high-throughput screening for new antimicrobials.

Surface reaction-diffusion kinetics on lattice at the microscopic scale

Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.

Assembly of Lyotropic Liquid Crystals with Solid Crystal's Structural Order Translated from the Lipid Rafts in Cell Membranes

Self-assembly offers a powerful way to control the complexity and hierarchy of nanoscale materials, and promises to create a diverse range of emergent properties. Successful syntheses that allow a delicate structural design of building units play an important role. However, as can be learned from many cellular processes and functions, coself-assembly using logically chosen additives should be equally effective in designing self-assembly. Herein I show that, translated from the dynamic nanoscale assemblies in cell membranes known as lipid rafts, coself-assembly of 1-decanol into cetyltrimethylammonium chloride micelles for the assembly of lyotropic liquid crystals generates new structural complexity and hierarchy, and a surprising property that is emerging from it. Designing the intermolecular forces in the way that cholesterol interacts with sphingolipids promotes the synergistic balance between the flexibility and rigidity, and the unique molecular recognition for silicic acid, followed by the micelle coalescence. This very much resembles the assembly process of the lipid rafts in cell membranes and triggers orders of magnitude of sharp increases in X-ray diffraction intensity. The analysis of the diffraction patterns shows that the structural order of these liquid crystals matches that of solid crystals, often of single crystals. Furthermore, the assembly of the liquid crystals promotes a substantial increase in the condensation rate of silicic acids by guiding them to form a silicate trimer along the surface of micelles. This very much resembles the role of the lipid rafts that sharply increases the reaction rate of biomolecules by guiding them to form discrete species along the surface of membranes. This finding demonstrates that it is possible to translate the key features of cellular processes and functions into artificial self-assembling systems of our choice using the building units that are readily available, thus creating novel soft materials.

Geodesic curvature driven surface microdomain formation

Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.

Effects of soft interactions and bound mobility on diffusion in crowded environments: a model of sticky and slippery obstacles

Crowded environments modify the diffusion of macromolecules, generally slowing their movement and inducing transient anomalous subdiffusion. The presence of obstacles also modifies the kinetics and equilibrium behavior of tracers. While previous theoretical studies of particle diffusion have typically assumed either impenetrable obstacles or binding interactions that immobilize the particle, in many cellular contexts bound particles remain mobile. Examples include membrane proteins or lipids with some entry and diffusion within lipid domains and proteins that can enter into membraneless organelles or compartments such as the nucleolus. Using a lattice model, we studied the diffusive movement of tracer particles which bind to soft obstacles, allowing tracers and obstacles to occupy the same lattice site. For sticky obstacles, bound tracer particles are immobile, while for slippery obstacles, bound tracers can hop without penalty to adjacent obstacles. In both models, binding significantly alters tracer motion. The type and degree of motion while bound is a key determinant of the tracer mobility: slippery obstacles can allow nearly unhindered diffusion, even at high obstacle filling fraction. To mimic compartmentalization in a cell, we examined how obstacle size and a range of bound diffusion coefficients affect tracer dynamics. The behavior of the model is similar in two and three spatial dimensions. Our work has implications for protein movement and interactions within cells.

Kinetic aspects of enzyme-mediated repair of DNA single-strand breaks

In cells and bacteria, DNA can be damaged in different ways. The efficient damage repair, mediated by various enzymes, is crucial for their survival. Most frequently, the damage is reduced to single-strand breaks. In human cells, according to the experiments, the repair of such breaks can mechanistically be divided into four steps including (i) the break detection, (ii) processing of damaged ends, (iii) gap filling, and (iv) ligation of unbound ends of the broken strand. The first and second steps run in parallel while the third and fourth steps are sequential. The author proposes a kinetic model describing these steps. It allows one to understand the likely dependence of the number of breaks in different states on enzyme concentrations. The dependence of these concentrations on the rate of the formation of breaks can be understood as well. In addition, the likely role of unzipping and zipping of the fragments of broken ends of the strand in the ligation step has been scrutinized taking the specifics of binding of DNA stands into account.

Nonspecific Binding Domains in Lipid Membranes Induced by Phospholipase A2

Phospholipase A2 (PLA2) is a peripheral membrane protein that can hydrolyze phospholipids to produce lysolipids and fatty acids. It has been found to play crucial roles in various cellular processes and is thought as a potential candidate for triggering drug release from liposomes for medical treatment. Here, we directly observed that PLA2 hydrolysis reaction can induce the formation of PLA2-binding domains at lipid bilayer interface and found that the formation was significantly influenced by the fluidity of the lipid bilayer. We prepared supported lipid bilayers (SLBs) with various molar ratios of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) to adjust the reactivity and fluidity of the lipid bilayers. A significant amount of the PLA2-induced domains was observed in mixtures of DPPC and DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) but not in either pure DPPC or pure DOPC bilayer, which might be the reason that previous studies rarely observed these domains in lipid bilayer systems. The fluorescently labeled PLA2 experiment showed that newly formed domains acted as binding templates for PLA2. The AFM result showed that the induced domain has stepwise plateau structure, suggesting that PLA2 hydrolysis products may align as bilayers and accumulate layer by layer on the support, and the hydrophobic acyl chains at the side of the layer structure may be exposed to the outside aqueous environment. The introduced hydrophobic region could have hydrophobic interactions with proteins and therefore can attract the binding of not only PLA2 but also other types of proteins such as proteoglycans and streptavidin. The results suggest that the formation of PLA2-induced domains may convert part of a zwitterionic nonsticky lipid membrane to a site where biomolecules can nonspecifically bind.