Effects of surface pressure and internal friction on the dynamics of shear-driven supported lipid bilayers

Supported lipid bilayers (SLBs) are one of the most common model systems for cell membrane studies. We have previously found that when applying a bulk flow of liquid above an SLB the lipid bilayer and its constituents move in the direction of the bulk flow in a rolling type of motion, with the lower monolayer being essentially stationary. In this study, a theoretical platform is developed to model the dynamic behavior of a shear-driven SLB. In most regions of the moving SLB, the dynamics of the lipid bilayer is well explained by a balance between the hydrodynamic shear force arising from the bulk flow above the lipid bilayer and the friction between the upper and lower monolayers of the SLB. These two forces result in a drift velocity profile for the lipids in the upper monolayer of the SLB that is highest at the center of the channel and decreases to almost zero at the corners of the channel. However, near the front of an advancing SLB a very different flow behavior is observed, showing an almost constant drift velocity of the lipids over the entire bilayer front. In this region, the motion of the SLB is significantly influenced by gradients in the surface pressure as well as internal friction due to molecules that have accumulated at the front of the SLB. It is shown that even a modest surface fraction of accumulated molecules (～1%) can drastically affect the behavior of the SLB near the bilayer front, forcing the advancing lipids in the SLB away from the center of the channel out toward the sides.     

Structure and dynamics of crystalline protein layers bound to supported lipid bilayers

We study proteins at the surface of bilayer membranes using streptavidin and avidin bound to biotinylated lipids in a supported lipid bilayer (SLB) at the solid-liquid interface. Using X-ray reflectivity and simultaneous fluorescence microscopy, we characterize the structure and fluidity of protein layers with varied relative surface coverages of crystalline and noncrystalline protein. With continuous bleaching, we measure a 10-15% decrease in the fluidity of the SLB after the full protein layer is formed. We propose that this reduction in lipid mobility is due to a small fraction (0.04) of immobilized lipids bound to the protein layer that create obstacles to membrane diffusion. Our X-ray reflectivity data show a 40 A thick layer of protein, and we resolve an 8 A layer separating the protein layer from the bilayer. We suggest that the separation provided by this water layer allows the underlying lipid bilayer to retain its fluidity and stability.     

Formation and diffusivity characterization of supported lipid bilayers with complex lipid compositions

The moving edge of a hydrodynamically manipulated supported lipid bilayer (SLB) can be used to catalyze SLB formation of adsorbed lipid vesicles that do not undergo spontaneous SLB formation upon adsorption on SiO(2). By removing the lipid reservoir of an initially formed SLB, we show how a hydrodynamically moved SLB patch composed of POPC can be used to form isolated SLBs with compositions that to at least 95% represent that of the adsorbed lipid vesicles. The concept is used to investigate the diffusivity of lissamine rhodamine B 1,2-dihexadecanoyl-sn-glycero-3-phosphoethanolamine (rhodamine-DHPE) in SLBs made from complex lipid compositions, revealing a decrease in diffusivity by a factor of 2 when the cholesterol content was increased from 0% to 50%. We also demonstrate how the concept can be used to induce stationary domains in SLBs containing 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), and cholesterol (39:21:40 mol %, respectively). Because the method serves as a means to form SLBs with lipid compositions that hamper SLB formation via spontaneous rupture of adsorbed lipid vesicles, it opens up the possibility for new biophysical investigations of SLBs with more nativelike compositions.     

Creation of lipid partitions by deposition of amphipathic viral peptides

Phospholipid vesicles exhibit a natural characteristic to fuse and reform into a continuous single bilayer membrane on hydrophilic solid substrates such as glass, mica, and silica. The resulting solid-supported bilayer mimics physiological tendencies such as lipid flip-flop and lateral mobility. The lateral mobility of fluorescently labeled lipids fused into solid-supported bilayers is found to change upon deposition on the membrane surface of an amphipathic alpha-helical peptide (AH) derived from the hepatitis C virus (HCV) NS5A protein. The binding of the AH peptide to a phospholipid bilayer, with the helical axis parallel to the bilayer, leads to immobilization of the bilayer. We used AFM to better understand the mechanistic details of this specific interaction, and determined that the diminished fluidity of the bilayer is due to membrane thinning. Utilizing this specific interaction between AH peptides and lipid molecules, we demonstrate a novel process for the creation of lipid partition by employing AH peptides as agents to immobilize lipid molecules, thus creating a patterned solid support with partition-defined areas of freely mobile lipid bilayers. This architecture could have a wide range of applications in novel sensing, biotechnology, high-throughput screening, and biomimetic strategies.     

Properties and behaviour of tetracyclic allopsoralen derivatives inside a DPPC lipid bilayer model

Allopsoralens are angular psoralen derivatives presenting advantages over the parent compound because of monofunctional DNA-photobinding and consequent lower toxicity. Allopsoralen molecules with three different substituents and different protonation states were studied using the molecular dynamics technique. The location of these molecules when inside the lipid bilayer is of major importance because their photochemical properties can change with the environment. Also, the ability of psoralens to form photoadducts with unsaturated phospholipids depends on the preference of the molecules to locate themselves closer to the bilayer middle were the double bond functionality can be found. Herein we show that the allopsoralens tend to accumulate inside the lipid bilayer closer to the water interface when protonated or closer to the interface middle otherwise. Allopsoralens containing one amine terminated carbon chain tend to have different rotational and orientational behaviour and an orientation preference close to the ones shown by the lipids. The size and chemical nature of the substituent also affect the molecular mobility and capacity to interact with water molecules and the nitrogen or phosphorus atoms of the lipids.     

Practical Labeling Methodology for Choline‐Derived Lipids and Applications in Live Cell Fluorescence Imaging

Lipids of the plasma membrane participate in a variety of biological processes, and methods to probe their function and cellular location are essential to understanding biochemical mechanisms. Previous reports have established that phosphocholine‐containing lipids can be labeled by alkyne groups through metabolic incorporation. Herein, we have tested alkyne, azide and ketone‐containing derivatives of choline as metabolic labels of choline‐containing lipids in cells. We also show that 17‐octadecynoic acid can be used as a complementary metabolic label for lipid acyl chains. We provide methods for the synthesis of cyanine‐based dyes that are reactive with alkyne, azide and ketone metabolic labels. Using an improved method for fluorophore conjugation to azide or alkyne‐modified lipids by Cu(I)‐catalyzed azide‐alkyne cycloaddition (CuAAC), we apply this methodology in cells. Lipid‐labeled cell membranes were then interrogated using flow cytometry and fluorescence microscopy. Furthermore, we explored the utility of this labeling strategy for use in live cell experiments. We demonstrate measurements of lipid dynamics (lateral mobility) by fluorescence photobleaching recovery (FPR). In addition, we show that adhesion of cells to specific surfaces can be accomplished by chemically linking membrane lipids to a functionalized surface. The strategies described provide robust methods for introducing bioorthogonal labels into native lipids.     

Surface-supported bilayers with transmembrane proteins: role of the polymer cushion revisited

Protein lateral mobility in surface-supported bilayers is often much lower than the mobility of the lipids. In the present study we explore whether the incorporation of a PEG cushion between the bilayer and the substrate increases the lateral mobility of transmembrane proteins in bilayers produced via directed assembly, a method based on Langmuir-Blodgett deposition techniques. In our experiments, the PEG cushions were incorporated by adding PEG lipids to the protein/lipid monolayer at the air/water interface, at the first step of bilayer assembly. The protein and lipid mobilities in 160 different bilayers, with various PEG molecular weights and PEG lipid concentrations, were measured and compared. We found that the measured diffusion coefficients do not depend on the PEG molecular weight or the PEG lipid concentration and are very similar to the values measured in the absence of PEG. Therefore, contrary to our expectations, we found that a PEG cushion does not necessarily increase protein mobility, suggesting that the low protein mobility is not a consequence of protein-substrate interactions. Furthermore, we showed that the low protein mobility is not due to protein aggregation. The major determinant of protein mobility in surface-supported bilayer systems appears to be the method of bilayer assembly. While proteins were always mobile if the bilayers were prepared using the directed assembly method, in the presence and absence of a PEG cushion, other bilayer assembly protocols resulted in complete lack of protein mobility.     

Dual polarization interferometric and capillary electrophoretic analysis of supported lipid bilayer constructed on silica-based surface: Evaluation of its anti-protein adsorption effect

Supported lipid bilayer (SLB) has been demonstrated as a model of cell membranes with prospective bioanalytical or biotechnological applications. In this study, the formation of SLB and their potential biofunctionality against protein adsorption were investigated by Dual Polarization Interferometry (DPI) and Capillary Electrophoresis (CE). DPI studies on different formulations of double-chained, zwitterionic phospholipidlipids, allow the process of bilayer formation to be followed in situ and in real time. Furthermore the anti-protein adsorption effect provided by the various formulated SLBs was examined by DPI. In addition, the SLB coatings of the same lipid formulations were subsequently employed in CE experiments as a pseudo-stationary phase for demonstrating more efficient separation of alkaline protein standard mixtures. SLB-assisted CE was found to be capable of separating 4 alkaline proteins (protonated at neutral pH). This study demonstrates the applicability of DPI to monitor the process of SLB formation; and our findings, obtained by both DPI and CE, confirm that the presence of the SLB reduced drastically the problematic interactions between cationic, alkaline proteins and the negatively charged silica capillary wall, leading to better recovery and efficient separation of the proteins under investigation.     

Fluorescent lipids: functional parts of fusogenic liposomes and tools for cell membrane labeling and visualization

In this paper a rapid and highly efficient method for controlled incorporation of fluorescent lipids into living mammalian cells is introduced. Here, the fluorescent molecules have two consecutive functions: First, they trigger rapid membrane fusion between cellular plasma membranes and the lipid bilayers of their carrier particles, so called fusogenic liposomes, and second, after insertion into cellular membranes these molecules enable fluorescence imaging of cell membranes and membrane traffic processes. We tested the fluorescent derivatives of the following essential membrane lipids for membrane fusion: Ceramide, sphingomyelin, phosphocholine, phosphatidylinositol-bisphosphate, ganglioside, cholesterol, and cholesteryl ester. Our results show that all probed lipids could more efficiently be incorporated into the plasma membrane of living cells than by using other methods. Moreover, labeling occurred in a gentle manner under classical cell culture conditions reducing cellular stress responses. Staining procedures were monitored by fluorescence microscopy and it was observed that sphingolipids and cholesterol containing free hydroxyl groups exhibit a decreased distribution velocity as well as a longer persistence in the plasma membrane compared to lipids without hydroxyl groups like phospholipids or other artificial lipid analogs. After membrane staining, the fluorescent molecules were sorted into membranes of cell organelles according to their chemical properties and biological functions without any influence of the delivery system.     

Asymmetry of lipid bilayers induced by monovalent salt: atomistic molecular-dynamics study

Interactions between salt ions and lipid components of biological membranes are essential for the structure, stability, and functions of the membranes. The specific ionic composition of aqueous buffers inside and outside of the cell is known to differ considerably. To model such a situation we perform atomistic molecular-dynamics (MD) simulations of a single-component phosphatidylcholine lipid bilayer which separates two aqueous reservoirs with and without NaCl salt. To implement the difference in electrolyte composition near two membrane sides, a double bilayer setup (i.e., two bilayers in a simulation box) is employed. It turns out that monovalent salt, being in contact with one leaflet only, induces a pronounced asymmetry in the structural, electrostatic, and dynamical properties of bilayer leaflets after 50 ns of MD simulations. Binding of sodium ions to the carbonyl region of the leaflet which is in contact with salt results in the formation of "Na-lipids" complexes and, correspondingly, reduces mobility of lipids of this leaflet. In turn, attractive interactions of chloride ions (mainly located in the aqueous phase close to the water-lipid interface) with choline lipid groups lead to a substantial (more vertical) reorientation of postphatidylcholine headgroups of the leaflet adjoined to salt. The difference in headgroup orientation on two sides of a bilayer, being coupled with salt-induced reorientation of water dipoles, leads to a notable asymmetry in the charge-density profiles and electrostatic potentials of bilayer constitutes of the two leaflets. Although the overall charge density of the bilayer is found to be almost insensitive to the presence of salt, a slight asymmetry in the charge distribution between the two bilayer leaflets results in a nonzero potential difference of about 85 mV between the two water phases. Thus, a transmembrane potential of the order of the membrane potential in a cell can arise without ionic charge imbalance between two aqueous compartments.     

Sterols associated with small unilamellar vesicles (SUVs): intrinsic mobility role for 1H NMR detection

Small unilamellar vesicles (SUVs) of phospholipids are often used as a membrane model system for studying the interaction of molecules. When using NMR under the standard liquid‐state conditions, SUV phospholipid proton spectra can be recorded, exhibiting sharp signals. This is not only because of the fast vesicular tumbling but also because of the combination of this tumbling with the individual motion of the lipids inside the bilayer. This appears evident because addition of cholesterol is responsible of broader resonances because of the slowing down of the lipid motion. On the other hand, no ¹H signal is detected for cholesterol in the bilayer. This lack of detection of the inserted molecules explains why generally SUVs are not considered as a good model for NMR studies under the standard liquid‐state conditions. Here, we use two other sterols in order to demonstrate that an increase of the molecular mobility inside the bilayer could allow the detection of their proton resonances. For desmosterol and lanosterol, which show higher mobility inside the bilayer, with increasing lateral diffusion rates, ¹H sterol signals are detected in contrast to cholesterol. For the fast diffusing lanosterol, no significant improvement in detection is observed using deuterated lipids, demonstrating that homonuclear dipolar coupling is fully averaged out. Furthermore, in the case of low mobility such as for cholesterol, the use of a fast magic angle spinning probe is shown to be efficient to recover the full proton spectrum. Copyright © 2014 John Wiley & Sons, Ltd.     

A Rhizavidin Monomer with Nearly Multimeric Avidin‐Like Binding Stability Against Biotin Conjugates

Developing a monomeric form of an avidin‐like protein with highly stable biotin binding properties has been a major challenge in biotin‐avidin linking technology. Here we report a monomeric avidin‐like protein—enhanced monoavidin—with off‐rates almost comparable to those of multimeric avidin proteins against various biotin conjugates. Enhanced monoavidin (eMA) was developed from naturally dimeric rhizavidin by optimally maintaining protein rigidity during monomerization and additionally shielding the bound biotin by diverse engineering of the surface residues. eMA allowed the monovalent and nonperturbing labeling of head‐group‐biotinylated lipids in bilayer membranes. In addition, we fabricated an unprecedented 24‐meric avidin probe by fusing eMA to a multimeric cage protein. The 24‐meric avidin and eMA were utilized to demonstrate how artificial clustering of cell‐surface proteins greatly enhances the internalization rates of assembled proteins on live cells.     

Chemoenzymatic reversible immobilization and labeling of proteins without prior purification

Site-specific chemical modification of proteins is important for many applications in biology and biotechnology. Recently, our laboratory and others have exploited the high specificity of the enzyme protein farnesyltransferase (PFTase) to site-specifically modify proteins through the use of alternative substrates that incorporate bioorthogonal functionality including azides and alkynes. In this study, we evaluate two aldehyde-containing molecules as substrates for PFTase and as reactants in both oxime and hydrazone formation. Using green fluorescent protein (GFP) as a model system, we demonstrate that the purified protein can be enzymatically modified with either analogue to yield aldehyde-functionalized proteins. Oxime or hydrazone formation was then employed to immobilize, fluorescently label, or PEGylate the resulting aldehyde-containing proteins. Immobilization via hydrazone formation was also shown to be reversible via transoximization with a fluorescent alkoxyamine. After characterizing this labeling strategy using pure protein, the specificity of the enzymatic process was used to selectively label GFP present in crude E. coli extract followed by capture of the aldehyde-modified protein using hydrazide-agarose. Subsequent incubation of the immobilized protein using a fluorescently labeled or PEGylated alkoxyamine resulted in the release of pure GFP containing the desired site-specific covalent modifications. This procedure was also employed to produce PEGylated glucose-dependent insulinotropic polypeptide (GIP), a protein with potential therapeutic activity for diabetes. Given the specificity of the PFTase-catalyzed reaction coupled with the ability to introduce a CAAX-box recognition sequence onto almost any protein, this method shows great potential as a general approach for selective immobilization and labeling of recombinant proteins present in crude cellular extract without prior purification. Beyond generating site-specifically modified proteins, this approach for polypeptide modification could be particularly useful for large-scale production of protein conjugates for therapeutic or industrial applications.     

Substrate-supported lipid nanotube arrays

This Communication describes the self-assembly of phospholipids into lipid nanotubes inside nanoporous anodic aluminum oxide substrate. Orientations of the lipid molecules in such lipid nanoscale structures were verified by high-resolution spin labeling EPR at 95 GHz. The static order parameter of lipids in such nanotube arrays was determined from low-temperature EPR spectra and was found to be exceptionally high, Sstatic approximately 0.9. We propose that substrate-supported lipid nanotube arrays have potential for building robust biochips and biosensors in which rigid nanoporous substrates protect the bilayer surface from contamination. The total bilayer surface in the lipid nanotube arrays is much greater than that in the planar substrate-supported membranes. The lipid nanotube arrays seem to be suitable for developing patterned lipid deposition and could be potentially used for patterning of membrane-associated molecules.     

Simulations of lipid transfer between a supported lipid bilayer and adsorbing vesicles

Recent experiments demonstrate transfer of lipid molecules between a charged, supported lipid membrane (SLB) and vesicles of opposite charge when the latter adsorb on the SLB. A simple phenomenological bead model has been developed to simulate this process. Beads were defined to be of three types, ‘n’, ‘p’, and ‘0’, representing POPS (negatively charged), POEPC (positively charged), and POPC (neutral but zwitterionic) lipids, respectively. Phenomenological bead–bead interaction potentials and lipid transfer rate constants were used to account for the overall interaction and transfer kinetics. Using different bead mixtures in both the adsorbing vesicle and in the SLB (representing differently composed/charged vesicles and SLBs as in the reported experiments), we clarify under which circumstances a vesicle adsorbs to the SLB, and whether it, after lipid transfer and changed composition of the SLB and vesicle, desorbs back to the bulk again or not. With this model we can reproduce and provide a conceptual picture for the experimental findings.     

Investigating the interactions of the first 17 amino acid residues of Huntingtin with lipid vesicles using mass spectrometry and molecular dynamics

The first 17 amino acid residues of Huntingtin protein (Nt17 of htt) are thought to play an important role in the protein's function; Nt17 is one of two membrane binding domains in htt. In this study the binding ability of Nt17 peptide with vesicles comprised of two subclasses of phospholipids is studied using electrospray ionization ‐ mass spectrometry (ESI‐MS) and molecular dynamics (MD) simulations. Overall, the peptide is shown to have a greater propensity to interact with vesicles of phosphatidylcholine (PC) rather than phosphatidylethanolamine (PE) lipids. Mass spectra show an increase in lipid‐bound peptide adducts where the ordering of the number of such specie is 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) > 1‐palmitoyl‐2‐oleoyl‐glycero‐3‐phosphocholine (POPC) > 1‐palmitoyl‐2‐oleoyl‐sn‐glycero‐3 phosphoethanolamine (POPE). MD simulations suggest that the compactness of the bilayer plays a role in governing peptide interactions. The peptide shows greater disruption of the DOPC bilayer order at the surface and interacts with the hydrophobic tails of lipid molecules via hydrophobic residues. Conversely, the POPE vesicle remains ordered and lipids display transient interactions with the peptide through the formation of hydrogen bonds with hydrophilic residues. The POPC system displays intermediate behavior with regard to the degree of peptide‐membrane interaction. Finally, the simulations suggest a helix stabilizing effect resulting from the interactions between hydrophobic residues and the lipid tails of the DOPC bilayer.     

Selective High‐Resolution Detection of Membrane Protein–Ligand Interaction in Native Membranes Using Trityl–Nitroxide PELDOR

The orchestrated interaction of transmembrane proteins with other molecules mediates several crucial biological processes. Detergent solubilization may significantly alter or even abolish such hetero‐oligomeric interactions, which makes observing them at high resolution in their native environment technically challenging. Dipolar electron paramagnetic resonance (EPR) techniques such as pulsed electro–electron double resonance (PELDOR) can provide very precise distances within biomolecules. To concurrently determine the inter‐subunit interaction and the intra‐subunit conformational changes in hetero‐oligomeric complexes, a combination of different spin labels is required. Orthogonal spin labeling using a triarylmethyl (TAM) label in combination with a nitroxide label is used to detect protein–ligand interactions in native lipid bilayers. This approach provides a higher sensitivity and total selectivity and will greatly facilitate the investigation of multimeric transmembrane complexes employing different spin labels in the native lipid environment.     

Soft lithographic patterning of supported lipid bilayers onto a surface and inside microfluidic channels

We present simple soft lithographic methods for patterning supported lipid bilayer (SLB) membranes onto a surface and inside microfluidic channels. Micropatterns of polyethylene glycol (PEG)-based polymers were fabricated on glass substrates by microcontact printing or capillary moulding. The patterned PEG surfaces have shown 97 +/- 0.5% reduction in lipid adsorption onto two dimensional surfaces and 95 +/- 1.2% reduction inside microfluidic channels in comparison to glass control. Atomic force microscopy measurements indicated that the deposition of lipid vesicles led to the formation of SLB membranes by vesicle fusion due to hydrophilic interactions with the exposed substrate. Furthermore, the functionality of the patterned SLBs was tested by measuring the binding interactions between biotin (ligand)-labeled lipid bilayer and streptavidin (receptor). SLB arrays were fabricated with spatial resolution down to approximately 500 nm on flat substrate and approximately 1 microm inside microfluidic channels, respectively.     

Lateral Diffusion of Lipids and Diffusion of Water through Lipid Bilayers in the Presence of (1,1-Dimethyl-3-Oxobutyl)Phosphonates

The influence of some amphiphilic (diethyl, dipropyl, and dibutyl) esters of (1,1-dimethyl-3-oxobutyl)phosphonic acid with the regularly changing number of CH₂ groups in the hydrocarbon (hydrophobic) moiety on the lateral diffusion of dioleoyl phosphatidylcholine lipid and transmembrane diffusion of water in the oriented multibilayer system was studied by ¹H pulsed field gradient NMR at phosphonate concentrations up to 30 mol %. The shape of the ³¹P NMR spectra and the dependence of the shape of the ¹H NMR spectra on the bilayer orientation suggest that the presence of phosphonates does not affect the phase state of the system. The lamellar liquid crystalline phase remains unchanged, and phosphonate molecules become incorporated into the bilayer and have the same orientation as phospholipid molecules. The presence of phosphonates in the lipid bilayer increases the coefficients of lipid lateral diffusion and water diffusion through bilayers. This effect depends monotonically on the number of CH₂ groups in the phosphonate molecule. The most probable place for the incorporation of amphiphilic phosphonate molecules is the hydrophilic/hydrophobic interphase region of the bilayer. The molecules incorporated into the interphase disorder the bilayer and increase lateral diffusion of lipids and bilayer permeability compared with the ester-free bilayer. When the number of CH₂ groups in the ester molecule increases from diethyl to dibutyl phosphonate, the arrangement of lipid hydrocarbon tails becomes more ordered. This decreases the lipid lateral diffusion coefficient and bilayer permeability to water molecules.     

Measuring the partitioning kinetics of membrane biomolecules using patterned two-phase coexistant lipid bilayers

We report a new method for measuring the partitioning kinetics of membrane biomolecules to different lipid phases using a patterned supported lipid bilayer (SLB) platform composed of liquid-ordered (lipid raft) and liquid-disordered (unsaturated lipid-rich) coexistent phases. This new approach removes the challenges in measuring partitioning kinetics using current in vitro methods due to their lack of spatial and temporal control of where phase separation occurs and when target biomolecules meet those phases. The laminar flow configuration inside a microfluidic channel allows us to pattern SLBs with coexistent phases in predetermined locations and thus eliminates the need for additional components to label the phases. Using a hydrodynamic force provided by the bulk flow in the microchannel, target membrane-bound species to be assayed can be transported in the bilayers. The predefined location of stably coexistent phases, in addition to the controllable movement of the target species, allows us to control and monitor when and where the target molecules approach or leave different lipid phases. Using this approach with appropriate experimental designs, we obtain the association and dissociation kinetic parameters for three membrane-bound species, including the glycolipid G(M1), an important cell signaling molecule. We examine two different versions of G(M1) and conclude that structural differences between them impact the kinetics of association of these molecules to raft-like phases. We also discuss the possibilities and limitations for this method. One possible extension is measuring the partitioning kinetics of other glycolipids or lipid-linked proteins with posttranslational modifications to provide insight into how structural factors, membrane compositions, and environmental factors influence dynamic partitioning.