The covalent bioconjugate of multiwalled carbon nanotube and amino‐modified linearized plasmid DNA for gene delivery

Carbon nanotubes (CNTs) are allotropes of carbon, which have unique physical, mechanical, and electronic properties. Among various biomedical applications, CNTs also attract interest as nonviral gene delivery systems. Functionalization of CNTs with cationic groups enables delivery of negatively charged DNA into cells. In contrast to this well‐known strategy for DNA delivery, our approach included the covalent attachment of linearized plasmid DNA to carboxylated multiwalled CNTs (MWCNTs). Carboxyl groups were introduced onto MWCNTs by oxidative treatment, and then the carboxyl groups were activated by 1‐ethyl‐3‐(3‐dimethylaminopropyl)carbodiimide (EDC). The whole pQE‐70 vector including the gene encoding green fluorescent protein (GFP) was subjected to polymerase chain reaction (PCR) using the modified nucleotide N6‐(6‐Amino)hexyl‐2′‐deoxyadenosine‐5′‐triphosphate. Hence, free amino groups were introduced onto the linearized plasmid. Covalent bonding between the amino‐modified plasmid DNA and the carboxylated MWCNTs was achieved via EDC chemistry. The resulting bioconjugate was successfully transformed into chemically competent Escherichia coli cells, without necessity of a heat‐shock step at 42°C. The presence of Ca²⁺ in transformation medium was required to neutralize the electrostatic repulsion between DNA and negatively charged outer layer of E. coli. The transformants, which were able to express GFP were inspected manually on ampicillin agar plates. Our study represents a novelty with respect to other noncovalent CNT gene delivery systems. Considering the interest for delivery of linear DNA fragments, our study could give insights into further studies. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 30:224–232, 2014     

Facile surface functionalization of multiwalled carbon nanotubes by soft dielectric barrier discharge plasma: Generate compatible interface for lipase immobilization

To create compatible interface for enzyme immobilization, the surface of multi-walled carbon nanotubes (MWCNTs) was functionalized using soft technique dielectric barrier discharge plasma (DBDP) for carboxylation and amination; followed by further amidation of carboxyl group with alkylamine. Successful functionalization and enzyme immobilization were structurally confirmed using spectroscopic analysis Fourier-Transform Infrared Spectroscopy (FTIR) and X-ray Photoelectron Spectroscopy (XPS). The immobilization of Candida rugosa lipase (CRL) on functionalized MWCNTs was evidenced by clearly viewing with Transmission Electron Microscopy (TEM) and Atomic Force Microscopy (AFM) imaging. CRL showed more Freundlich equilibrium behavior upon immobilization on annealed and octadecylamidated MWCNTs, which suggested a multilayer adsorption; while upon physical adsorption on aminated and carboxylated MWCNTs, CRL, to more extent, demonstrated a Langmuir equilibrium property, producing an enzyme monolayer. It was proven that DBDP-mediated surface-functionalization could create compatible microenvironments for enzyme immobilization, resulted in improved specific activity and thermostability. The immobilized CRL on octadecylamidated MWCNTs displayed excellent reusability and operation stability, indicating its potential for industrial application.     

Molecular dynamics simulation of doxorubicin adsorption on a bundle of functionalized CNT

In this study, molecular dynamics simulation is used to investigate the adsorption of an anticancer drug, doxorubicin, on bundles of functionalized single-walled carbon nanotubes (SWNTs) in an aqueous solution. Carboxylic group has been selected as the functional group. Molecular dynamics (MD) simulations are performed for both separated systems containing a SWNT bundle and a functionalized carbon nanotube bundle, and results are compared with existing experimental data. MD results show that doxorubicin can be adsorbed on CNTs using different methods such as entrapment within CNT bundle, attachment to the side wall of the CNT, and adsorption on the CNT inner cavity. For functionalized CNT, the adsorption of drugs on the functional groups is essential for predicting the enhancement of drug loading on the functionalized nanotubes. Furthermore, the adsorption behavior of doxorubicin on CNTs is fitted with Langmuir and Freundlich isotherm models. The results show that Langmuir model can predict the adsorption behavior of doxorubicin on CNTs more accurately than Freundlich model does. As predicted by this isotherm model, the adsorption process of doxorubicin on CNTs is relatively difficult, but it can be improved by increasing the functional groups on the CNTs surface.     

Covalent immobilization of proteins on carbon nanotubes using the cross-linker 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide--a critical assessment

Functionalization of carbon nanotubes (CNTs) with proteins is often a key step in their biological applications, particularly in biosensing. One popular method has used the cross-linker 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) to covalently conjugate proteins onto carboxylated CNTs. In this article, we critically assess the evidence presented in these conjugation studies in the literature. As CNTs have a natural affinity for diverse proteins through hydrophobic and electrostatic interactions, it is therefore important to differentiate protein covalent attachment from adsorption in the immobilization mechanism. Unfortunately, many studies of conjugating proteins onto CNTs using EDC lacked essential controls to eliminate the possibility of protein adsorption. In studies where the attachment was claimed to be covalent, discrepancies existed and the observed immobilization appeared to be due to adsorption. So far, bond analysis has been lacking to ascertain the nature of the attachment using EDC. We recommend that this approach of covalent immobilization of proteins on CNTs be re-evaluated and treated with caution.     

Buckling analysis of defective cross-linked functionalized single- and double-walled carbon nanotubes with polyethylene chains using molecular dynamics simulations

Functionalized carbon nanotubes (CNTs) can be used for improving the mechanical properties and load transfer in nanocomposites. In this research, the buckling behavior of perfect and defective cross-linked functionalized CNTs with polyethylene (PE) chains is studied employing molecular dynamics (MD) simulations. Two different configurations with the consideration of vacancy defects, namely mapped and wrapped, are selected. According to the results, critical buckling force of cross-linked functionalized CNTs with PE chains increases as compared to pure CNTs, especially in the case of double-walled carbon nanotubes (DWCNTs). By contrast, it is demonstrated that critical strain of cross-linked functionalized CNTs decreases as compared to that of pristine CNTs. Also, it is observed that increasing the weight percentage leads to the higher increase and the decrease in critical buckling force and strain of cross-linked functionalized CNTs, respectively. Moreover, the presence of defect considerably reduces both critical buckling force and strain of cross-linked functionalized CNTs. Finally, it is shown that the critical buckling strain is more sensitive to the presence of defects as compared to critical buckling force.     

A two‐enzyme immobilization approach using carbon nanotubes/silica as support

Multiple enzyme mixtures are attractive for the production of many compounds at an industrial level. We report a practical and novel approach for coimmobilization of two enzymes. The system consists of a silica microsphere core coated with two layers of individually immobilized enzymes. The model enzymes α‐amylase (AA) and glucoamylase (GluA) were individually immobilized on carbon nanotubes (CNTs). A CNT‐GluA layer was formed by adsorbing CNT‐GluA onto silica microsphere. A sol‐gel layer with entrapped CNT‐AA was then formed outside the CNT‐GluA/silica microsphere conjugate. The coimmobilized α‐amylase and glucoamylase exhibited 95.1% of the activity of the mixture of free α‐amylase and glucoamylase. The consecutive use exhibited a good stability of the coimmobilized enzymes. The developed approach demonstrates advantages, including controlling the ratio of coimmobilized enzymes in an easy way, facilitating diffusion of small molecules in and out of the matrix, and preventing the leaching of enzymes. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:42–47, 2015     

Inulinase immobilization on polyethylene glycol/polypyrrole multiwall carbon nanotubes producing a catalyst with enhanced thermal and operational stability

This paper describes the development of a simple method for mixed non‐covalent and covalent bonding of partially purified inulinase on functionalized multiwall carbon nanotubes (f‐MWCNTs) with polypyrrole (PPy). The pyrrole (Py) was electrochemically polymerized on MWCNTs in order to fabricate MWCNTs/PPy nanocomposite. Two multiple forms of enzyme were bound to N‐H functional groups from PPy and ‐COO^? from activated MWCNTs to yield a stable MWCNTs/PPy/PEG immobilized preparation with increased thermal stability. Fourier transform infrared (FTIR) spectroscopy and scanning electron microscopy (SEM) were used to confirm functionalization of nanoparticles and immobilization of the enzyme. The immobilization yield of 85% and optimal enzyme load of 345 μg protein onto MWCNTs was obtained. The optimum reaction conditions and kinetic parameters were established using the UV‐Vis analytical assay. The best functional performance for prepared heterogeneous catalyst has been observed at pH 3.6 and 10, and at the temperatures of 60 and 80ºC. The half‐life (t_1/2) of the immobilized inulinase at 60 and 80ºC was found to be 231 and 99 min, respectively. The reusability of the immobilized formulation was evaluated based on a method in which the enzyme retained 50% of its initial activity, which occurred after the eighteenth operation cycle.     

Carbon nanotubes and glucose oxidase bionanocomposite bridged by ionic liquid-like unit: preparation and electrochemical properties

For their biocompatibility and potential bionanoelectronic applications, integration of carbon nanotubes (CNTs) with biomolecules such as redox enzyme is highly anticipated. Therein, CNTs are expected to act not only as an electron transfer promoter, but also as immobilizing substrate for biomolecules. In this report, a novel method for immobilization of biomolecules on CNTs was proposed based on ionic interaction, which is of universality and widespread use in biological system. As illustrated, glucose oxidase (GOD) and single-walled carbon nanotubes (SWNTs) were integrated into a unitary bionanocomposite by means of ionic liquid-like unit on functionalized SWNTs. The resulted bionanocomposite illustrated better redox response of immobilized GOD in comparison of that prepared by weak physical absorption without ionic interaction. As a potential application of concept, the electrochemical detection of glucose was exemplified based on this novel bionanocomposite.     

Effects of interactions with micellar interfaces on the activity and structure of different lipolytic isoenzymes from Candida rugosa

The conformational and functional changes of cholesterol esterase (CE) and isolipase (CRL) from Candida rugosa after exposure to a micellar interface and subsequent extraction to a fresh buffer were studied. These two enzymes were activated by interaction with the micellar interface of a sulphosuccinic acid bis[2-ethylhexyl] ester/n-heptane/water system. For the hydrolysis of p-nitrophenyl butyrate ester in water, the catalytic efficiencies of CE and CRL were both improved because on activation their k_cat values increased from 378 to 465 and from 250 to 680 s⁻¹, respectively, while their K_m values decreased from 5.08 × 10⁻⁵ to 3.23 × 10⁻⁵ and from 2.28 × 10⁻⁴ to 1.14 × 10⁻⁴ M, respectively. After exposure to the micelles, CE showed a marked increase in its -helical content from 28 to 49%, but only limited changes were detected when CRL was exposed. These proteins exhibit similar capacities for increasing their -helical content in a helicogenic medium. In acetonitrile/water mixtures, CRL exhibits a partial decrease in the extent of its secondary structure, while CE exhibits an increase in its -helical content. The fact that this medium of reduced polarity permits one to simulate the effect of the AOT reverse micelles on the conformation of CE (increased helicity) but not their effect on the structure of CRL (decreased helicity) supports the hypothesis that only CE interacts to a significant extent with the apolar side of the micellar interface. After exposure to micelles of octyl-β-glucopyranoside, CE (but not CRL) showed a 10% increase in its -helical content.     

PLGA-Carbon Nanotube Conjugates for Intercellular Delivery of Caspase-3 into Osteosarcoma Cells

Cancer has arisen to be of the most prominent health care issues across the world in recent years. Doctors have used physiological intervention as well as chemical and radioactive therapeutics to treat cancer thus far. As an alternative to current methods, gene delivery systems with high efficiency, specificity, and safety that can reduce side effects such as necrosis of tissue are under development. Although viral vectors are highly efficient, concerns have arisen from the fact that viral vectors are sourced from lethal diseases. With this in mind, rod shaped nano-materials such as carbon nanotubes (CNTs) have become an attractive option for drug delivery due to the enhanced permeability and retention effect in tumors as well as the ability to penetrate the cell membrane. Here, we successfully engineered poly (lactic-co-glycolic) (PLGA) functionalized CNTs to reduce toxicity concerns, provide attachment sites for pro-apoptotic protein caspase-3 (CP3), and tune the temporal release profile of CP3 within bone cancer cells. Our results showed that CP3 was able to attach to functionalized CNTs, forming CNT-PLGA-CP3 conjugates. We show this conjugate can efficiently transduce cells at dosages as low as 0.05 μg/ml and suppress cell proliferation up to a week with no further treatments. These results are essential to showing the capabilities of PLGA functionalized CNTs as a non-viral vector gene delivery technique to tune cell fate.     

Immobilization of Candida rugosa lipase on poly(3-hydroxybutyrate-co-hydroxyvalerate): a new eco-friendly support

The overall objective of this study is to evaluate the morphological [scanning electron microscopy (SEM)], physicochemical [differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), chemical composition analysis, Fourier-transform infrared spectroscopy (FTIR), nuclear magnetic resonance (NMR)], and biochemical properties of Candida rugosa lipase (CRL) immobilized on a natural biopolymer poly(3-hydroxybutyrate-co-hydroxyvalerate) (PHBV) in aqueous solution. CRL was immobilized by physical adsorption with efficiency of 30%. Compared with free CRL enzyme, there were slight changes in immobilized CRL activity as a function of temperature (from 37°C to 45°C), but a similar optimal pH value of 7.0. Inactivation rate constants for immobilized CRL enzyme were 0.009 and 0.334 h⁻¹, and half-lives were 77 and 2 h at 40°C and 60°C, respectively. Kinetic parameters obtained for immobilized CRL include the Michaelis–Menten constant of K _m = 213.18 mM and maximum reaction velocity of V _max = 318.62 U/g. The operational stability of immobilized CRL was tested repeatedly, and after 12 cycles of reuse, the enzyme retained 50% activity. Based on our results, we propose that PHBV-immobilized CRL could serve as a promising biocatalyst in several industrial applications.     

Biochemical and cellular effects of inhibiting Nedd8 conjugation

The conjugation of proteins with the ubiquitin-like protein Nedd8 is an essential cellular process and an important anti-cancer therapeutic target. The major known role of Nedd8 is the attachment to and activation of Cullin RING E3 ubiquitin ligases (CRL). The attachment of Nedd8 to its substrates occurs via a process analogous to ubiquitin transfer, involving a Nedd8 E1 activating enzyme and a Nedd8 E2 conjugating enzyme, Ubc12, which transfers Nedd8 onto lysine residues of target proteins. In this study, we utilize dominant-negative Ubc12 (dnUbc12) and the Nedd8 E1 inhibitor MLN4924 to inhibit cellular neddylation. We demonstrate that dnUbc12 functions by depleting cellular Nedd8 concentrations. Inhibition of cellular neddylation leads to rapid accumulation of CRL substrates and an enlarged and flattened morphology in HEK293 cells. Inhibiting Nedd8 conjugation also causes abnormalities in the actin cytoskeleton. This is likely at least partially mediated via accumulation of the small GTPase RhoA, a recently identified CRL substrate. We indeed found that siRNA mediated knockdown of RhoA can reverse the morphological changes observed upon inhibition of cellular neddylation. In conclusion, the Nedd8 pathway plays an important role in regulating the actin cytoskeleton and cellular morphology. Dysfunction of the actin cytoskeleton may contribute to the anti-cancer effect of Nedd8 inhibition.     

Cytotoxicity of doxrubicin loaded single-walled carbon nanotubes

Carbon nanotube (CNTs) is a new alternative for efficient drug delivery and it has a great potential to change drug delivery system profile in pharmaceutical industry. One of the important advantage of CNTs is their needle-like, cylindrical shape. This shape provides a high surface area for multiple connections and adsorption onto for millions of therapeutic molecules. CNTs can be internalized by cells via endocytosis, passive diffusion and phagocytosis and release the drug with different effects like pH and temperature. The acidic nature of cancer cells and the susceptibility of CNTs to release the drug in the acidic environment have made it a promising area of research in cancer drug delivery. In this research, we investigated cell viability, cytotoxicity and drug delivery in breast cancer cell line by designing non-covalent single walled carbon nanotubes (SWNT)–doxorubicin (DOX) supramolecular complex that can be developed for cancer therapy. Applied high concentrations of DOX loaded SWNTs changed the actin structure of the cells and prevented the proliferation of the cells. It was showed that doxorubicin loaded SWNTs were more effective than free doxorubicin at relatively small concentrations. Once we applied same procedure for short and long (short: 1–1.3 µm; long: 2.5–4 µm) SWNTs and compared the results, more disrupted cell structure and reduction in cell proliferation were observed for long CNTs. DOX is bounded more to nanotubes in basic medium, less bound in acidic environment. Cancer cells were also examined for concentration at which they were effective by applying DOX and it was seen that 3.68 µM doxorubicin kills more than 55% of the cells.     

Understanding and modeling alternating tangential flow filtration for perfusion cell culture

Alternating tangential flow (ATF) filtration has been used with success in the Biopharmaceutical industry as a lower shear technology for cell retention with perfusion cultures. The ATF system is different than tangential flow filtration; however, in that reverse flow is used once per cycle as a means to minimize fouling. Few studies have been reported in the literature that evaluates ATF and how key system variables affect the rate at which ATF filters foul. In this study, an experimental setup was devised that allowed for determination of the time it took for fouling to occur for given mammalian (PER.C6) cell culture cell densities and viabilities as permeate flow rate and antifoam concentration was varied. The experimental results indicate, in accordance with D'Arcy's law, that the average resistance to permeate flow (across a cycle of operation) increases as biological material deposits on the membrane. Scanning electron microscope images of the post‐run filtration surface indicated that both cells and antifoam micelles deposit on the membrane. A unique mathematical model, based on the assumption that fouling was due to pore blockage from the cells and micelles in combination, was devised that allowed for estimation of sticking factors for the cells and the micelles on the membrane. This model was then used to accurately predict the increase in transmembane pressure during constant flux operation for an ATF cartridge used for perfusion cell culture. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1291–1300, 2014     

Synthesis of calix[n]arene-based silica polymers for lipase immobilization

The objective of this study was to prepare new calix[n]arene-based silica polymers for immobilization of Candida rugosa lipase. The amino functionalized calix[4]arene (C4P), calix[6]arene (C6P) and calix[8]arene (C8P)-based silica polymers were used for the covalent attachment of C. rugosa lipase using glutaraldehyde as a coupling agent. The characterization of synthesized CnP polymers and immobilized lipases were made by Fourier transform infrared spectroscopy (FTIR), thermal gravimetric analysis (TGA) and scanning electron microscope (SEM) techniques. The hydrolytic activities of immobilized lipases (CnP-L) were evaluated and compared with the free enzyme. The activity recovery of immobilized CRL (C. rugosa lipase) based on the carrier C4P, C6P and C8P reaches 74.6%, 68.5% and 51.4%, respectively. The optimal pH and temperature region of the immobilized lipases for the hydrolysis of p-NPP were 7.0 and 50 °C. Nevertheless, the immobilized lipase has good stability, adaptability and reusability in comparison with the free enzyme.     

Comparative prediction of binding affinity of Hydroxyurea anti-cancer to boron nitride and carbon nanotubes as smart targeted drug delivery vehicles

Abstract

In this study, the adsorption of Hydroxyurea (HU) onto the inner and outer surfaces of boron nitride and carbon nanotubes (CNTs) was investigated using the density functional theory calculations and molecular dynamics (MDs) simulations in aqueous solution. The values of the adsorption energy show that HU molecule is preferentially adsorbed inside of boron nitride and CNTs with the molecular axis parallel to the tubes axis, which means that the cavity of nanotubes is favorable for encapsulation of this drug. Also, it was found that the HU/boron nitride nanotube (BNNT) system is more stable than the HU/CNT system. The stability of the complexes of HU/ BNNT attributed to the formation of the intermolecular hydrogen bonds between the H atoms of HU molecule and the N atoms of BNNT, which is confirmed by Bader’s quantum theory of atoms in molecules. The natural bond orbital analysis shows the charge transfers occur from HU molecule to nanotubes in all complexes. Moreover, the adsorption of HU molecule on the surfaces of the nanotubes was investigated by explicit water models. Also, the adsorption behavior of HU on the functionalized boron nitride and CNTs is investigated to design and develop new nanocarriers for biomedical applications. Furthermore, MDs simulations are examined in the presence of one and two drug molecules. The obtained results illustrate that the lowest value of Lennard–Jones (L–J) energy between drug and nanotubes exist in the simulation system with two drug molecules.     

On the vibrational behavior of single- and double-walled carbon nanotubes under the physical adsorption of biomolecules in the aqueous environment: a molecular dynamics study

The adsorption of biomolecules on the walls of carbon nanotubes (CNTs) in an aqueous environment is of great importance in the field of nanobiotechnology. In this study, molecular dynamics (MD) simulations were performed to understand the mechanical vibrational behavior of single- and double-walled carbon nanotubes (SWCNTs and DWCNTs) under the physical adsorption of four important biomolecules (L-alanine, guanine, thymine, and uracil) in vacuum and an aqueous environment. It was observed that the natural frequencies of these CNTs in vacuum reduce under the physical adsorption of biomolecules. In the aqueous environment, the natural frequency of each pure CNT decreased as compared to its natural frequency in vacuum. It was also found that the frequency shift for functionalized CNTs as compared to pure CNTs in the aqueous environment was dependent on the radius and the number of walls of the CNT, and could be positive or negative.     

The influence of prolactin (PRL) on progesterone secretion by porcine luteal cells in vitro

Porcine luteal cells were obtained from corpora lutea on the 5th, 13th and 17th days of the estrous cycle. The cells were suspended at a concentration of 5 × 10⁴ cells/ml in Eagle's medium with 2% human serum albumin. These cells were incubated with or without 0.01, 0.1, 1 or 10 μg/ml porcine prolactin. The amount of progesterone in cultures was estimated by a radio-immunological method after 30 min, 3 h and 6 h of culturing.Luteal cells obtained on the 5th day of the estrous cycle and incubated without prolactin secreted 71.24 ± 21.91 ng progesterone/ml of medium, whereas under the influence of prolactin at 0.01, 0.1, 1 and 10 μg/ml, 39.06 ± 13.33, 44.31 ± 12.69, 44.88 ± 16.85 and 51.62 ± 15.01 ng progesterone/ml (P<0.01) were secreted. Luteal cells from the 13th day of the estrous cycle incubated without prolactin secreted on average 70.72 ± 9.21 ng progesterone/ml of medium, whereas under the influence of different prolactin doses 50.75 ± 8.52, 46.54 ± 7.13, 43.30 ± 6.78 and 41.68 ± 7.21 ng progesterone/ml (P<0.01) were secreted.Prolactin did not change progesterone secretion by luteal cells obtained on the 17th day of the estrous cycle. An influence of the incubation time on progesterone secretion by these cells was observed: after 30 min of incubation the cells secreted 8.83 ± 2.95 ng/ml, after 3 h 8.12 ± 2.57 ng/ml and after 6 h 6.86 ± 1.91 ng/ml, irrespective of the amount of PRL added.The results suggest that prolactin plays a role in the luteolysis of the corpus luteum.     

Mixed reverse micelles facilitated downstream processing of lipase involving water‐oil‐water liquid emulsion membrane

Our earlier work for the first time demonstrated that liquid emulsion membrane (LEM) containing reverse micelles could be successfully used for the downstream processing of lipase from Aspergillus niger. In the present work, we have attempted to increase the extraction and purification fold of lipase by using mixed reverse micelles (MRM) consisting of cationic and nonionic surfactants in LEM. It was basically prepared by addition of the internal aqueous phase solution to the organic phase followed by the redispersion of the emulsion in the feed phase containing enzyme, which resulted in globules of water‐oil‐water (WOW) emulsion for the extraction of lipase. The optimum conditions for maximum lipase recovery (100%) and purification fold (17.0‐fold) were CTAB concentration 0.075 M, Tween 80 concentration 0.012 M, at stirring speed of 500 rpm, contact time 15 min, internal aqueous phase pH 7, feed pH 9, KCl concentration 1 M, NaCl concentration 0.1 M, and ratio of membrane emulsion to feed volume 1:1. Incorporation of the nonionic surfactant (e.g., Tween 80) resulted in remarkable improvement in the purification fold (3.1–17.0) of the lipase. LEM containing a mixture of nonionic and cationic surfactants can be successfully used for the enhancement in the activity recovery and purification fold during downstream processing of enzymes/proteins. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1084–1092, 2014     

Distribution of attachment events relative to actin binding sites as evidenced in a bidirectional actomyosin interaction model

Optical trapping is one of the most evolving technologies that measures biophysical quantities and provides insights into some of the fundamental questions in the study of molecular motor proteins such as myosin. Several laboratories have successfully used this technique to observe and score nanometre-size displacements produced by myosin on interacting with actin. We have studied the distribution of attachment events for two myosin molecules with different orientations interacting with an actin filament within the framework of a Langevin-type bidirectional mathematical model. When myosin is detached from actin, our model predicts Brownian displacements centred at 0 ± 8 nm (mean ± SD, n = 251058). When attached, the time-averaged displacements of the actin filament system produced step sizes with peaks of 8 ± 6 nm (mean ± SD, n = 22174) (forward displacements) and −8 ± 6 nm (mean ± SD, n = 26769) (reverse displacements). We infer from our results that the population distribution of attachment events is strongly dependent on (i) the magnitude of the Brownian displacements, (ii) the location of the actin binding sites relative to the myosin molecules, (iii) the orientation of the myosin molcules, and (iv) the relative kinetics (rate constants) for the forward and reverse displacement events.