Discovery of a new motion mechanism of biomotors similar to the earth revolving around the sun without rotation

Revolving hexameric ATPases as asymmetric motors to translocate double-stranded DNA genome along one strand

DsDNA translocation through nanoscale pores is generally accomplished by ATPase biomotors. The discovery of the revolving dsDNA translocation mechanism, as opposed to rotation, in bacteriophage phi29 elucidated how ATPase motors move dsDNA. Revolution-driven, hexameric dsDNA motors have been reported in herpesvirus, bacterial FtsK, Streptomyces TraB, and T7 phage. This review explores the common relationship between their structure and mechanisms. Commonalities include moving along the 5'→3' strand, inchworm sequential action leading to an asymmetrical structure, channel chirality, channel size, and 3-step channel gating for controlling motion direction. The revolving mechanism and contact with one of the dsDNA strands addresses the historic controversy of dsDNA packaging using nicked, gapped, hybrid, or chemically modified DNA. These controversies surrounding dsDNA packaging activity using modified materials can be answered by whether the modification was introduced into the 3'→5' or 5'→3' strand. Perspectives concerning solutions to the controversy of motor structure and stoichiometry are also discussed.

Revolving ATPase motors as asymmetrical hexamers in translocating lengthy dsDNA via conformational changes and electrostatic interactions in phi29, T7, herpesvirus, mimivirus, E. coli, and Streptomyces

Investigations of the parallel architectures of biomotors in both prokaryotic and eukaryotic systems suggest a similar revolving mechanism in the use of ATP to drive translocation of the lengthy double-stranded (ds)DNA genomes. This mechanism is exemplified by the dsDNA packaging motor of bacteriophage phi29 that operates through revolving but not rotating dsDNA to "Push through a one-way valve". This unique and novel revolving mechanism discovered in phi29 DNA packaging motor was recently reported in other systems including the dsDNA packaging motor of herpesvirus, the dsDNA ejecting motor of bacteriophage T7, the plasmid conjugation machine TraB in Streptomyces, the dsDNA translocase FtsK of gram-negative bacteria, and the genome-packaging motor in mimivirus. These motors exhibit an asymmetrical hexameric structure for transporting the genome via an inch-worm sequential action. This review intends to delineate the revolving mechanism from a perspective of conformational changes and electrostatic interactions. In phi29, the positively charged residues Arg-Lys-Arg in the N-terminus of the connector bind the negatively charged interlocking domain of pRNA. ATP binding to an ATPase subunit induces the closed conformation of the ATPase. The ATPase associates with an adjacent subunit to form a dimer facilitated by the positively charged arginine finger. The ATP-binding induces a positive charging on its DNA binding surface via an allostery mechanism and thus the higher affinity for the negatively charged dsDNA. ATP hydrolysis induces an expanded conformation of the ATPase with a lower affinity for dsDNA due to the change of the surface charge, but the (ADP+Pi)-bound subunit in the dimer undergoes a conformational change that repels dsDNA. The positively charged lysine rings of the connector attract dsDNA stepwise and periodically to keep its revolving motion along the channel wall, thus maintaining the one-way translocation of dsDNA without reversal and sliding out. The finding of the presence of the asymmetrical hexameric architectures of many ATPases that use the revolving mechanism may provide insights into the understanding of translocation of the gigantic genomes including chromosomes in complicated systems without coiling and tangling to speed up dsDNA translocation and save energy.

Identification of Arginine Finger as the Starter of the Biomimetic Motor in Driving Double-Stranded DNA

Nanomotors in nanotechnology may be as important as cars in daily life. Biomotors are nanoscale machines ubiquitous in living systems to carry out ATP-driven activities such as walking, breathing, blinking, mitosis, replication, transcription, and trafficking. The sequential action in an asymmetrical hexamer by a revolving mechanism has been confirmed in dsDNA packaging motors of phi29, herpesviruses, bacterial dsDNA translocase FtsK, and Streptomyces TraB for conjugative dsDNA transfer. These elaborate, delicate, and exquisite ring structures have inspired scientists to design biomimetics in nanotechnology. Many multisubunit ATPase rings generate force via sequential action of multiple modules, such as the Walker A, Walker B, P-loop, arginine finger, sensors, and lid. The chemical to mechanical energy conversion usually takes place in sequential order. It is commonly believed that ATP binding triggers such conversion, but how the multimodule motor starts the sequential process has not been explicitly investigated. Identification of the starter is of great significance for biomimetic motor fabrication. Here, we report that the arginine finger is the starter of the motor. Only one amino acid residue change in the arginine finger led to the impediment and elimination of all following steps. Without the arginine finger, the motor failed to assemble, bind ATP, recruit DNA, or hydrolyze ATP and was eventually unable to package DNA. However, the loss of ATPase activity due to an inactive arginine finger can be rescued by an arginine finger from the adjacent subunit of Walker A mutant through trans-complementation. Taken together, we demonstrate that the formation of dimers triggered by the arginine finger initiates the motor action rather than the general belief of initiation by ATP binding.

Architecture of the herpesvirus genome-packaging complex and implications for DNA translocation

Genome packaging is a fundamental process in a viral life cycle and a prime target of antiviral drugs. Herpesviruses use an ATP-driven packaging motor/terminase complex to translocate and cleave concatemeric dsDNA into procapsids but its molecular architecture and mechanism are unknown. We report atomic structures of a herpesvirus hexameric terminase complex in both the apo and ADP•BeF3-bound states. Each subunit of the hexameric ring comprises three components-the ATPase/terminase pUL15 and two regulator/fixer proteins, pUL28 and pUL33-unlike bacteriophage terminases. Distal to the nuclease domains, six ATPase domains form a central channel with conserved basic-patches conducive to DNA binding and trans-acting arginine fingers are essential to ATP hydrolysis and sequential DNA translocation. Rearrangement of the nuclease domains mediated by regulatory domains converts DNA translocation mode to cleavage mode. Our structures favor a sequential revolution model for DNA translocation and suggest mechanisms for concerted domain rearrangements leading to DNA cleavage.

Controlling the Revolving and Rotating Motion Direction of Asymmetric Hexameric Nanomotor by Arginine Finger and Channel Chirality

Nanomotors in nanotechnology are as important as engines in daily life. Many ATPases are nanoscale biomotors classified into three categories based on the motion mechanisms in transporting substrates: linear, rotating, and the recently discovered revolving motion. Most biomotors adopt a multisubunit ring-shaped structure that hydrolyzes ATP to generate force. How these biomotors control the motion direction and regulate the sequential action of their multiple subunits is intriguing. Many ATPases are hexameric with each monomer containing a conserved arginine finger. This review focuses on recent findings on how the arginine finger controls motion direction and coordinates adjacent subunit interactions in both revolving and rotating biomotors. Mechanisms of intersubunit interactions and sequential movements of individual subunits are evidenced by the asymmetrical appearance of one dimer and four monomers in high-resolution structural complexes. The arginine finger is situated at the interface of two subunits and extends into the ATP binding pocket of the downstream subunit. An arginine finger mutation results in deficiency in ATP binding/hydrolysis, substrate binding, and transport, highlighting the importance of the arginine finger in regulating energy transduction and motor function. Additionally, the roles of channel chirality and channel size are discussed as related to controlling one-way trafficking and differentiating the revolving and rotating mechanisms. Finally, the review concludes by discussing the conformational changes and entropy conversion triggered by ATP binding/hydrolysis, offering a view different from the traditional concept of ATP-mediated mechanochemical energy coupling. The elucidation of the motion mechanism and direction control in ATPases could facilitate nanomotor fabrication in nanotechnology.

Breaking Symmetry in Viral Icosahedral Capsids as Seen through the Lenses of X-ray Crystallography and Cryo-Electron Microscopy

The majority of viruses on Earth form capsids built by multiple copies of one or more types of a coat protein arranged with 532 symmetry, generating an icosahedral shell. This highly repetitive structure is ideal to closely pack identical protein subunits and to enclose the nucleic acid genomes. However, the icosahedral capsid is not merely a passive cage but undergoes dynamic events to promote packaging, maturation and the transfer of the viral genome into the host. These essential processes are often mediated by proteinaceous complexes that interrupt the shell’s icosahedral symmetry, providing a gateway through the capsid. In this review, we take an inventory of molecular structures observed either internally, or at the 5-fold vertices of icosahedral DNA viruses that infect bacteria, archea and eukaryotes. Taking advantage of the recent revolution in cryo-electron microscopy (cryo-EM) and building upon a wealth of crystallographic structures of individual components, we review the design principles of non-icosahedral structural components that interrupt icosahedral symmetry and discuss how these macromolecules play vital roles in genome packaging, ejection and host receptor-binding.

An Arginine Finger Regulates the Sequential Action of Asymmetrical Hexameric ATPase in the Double-Stranded DNA Translocation Motor

Biological motors are ubiquitous in living systems. Currently, how the motor components coordinate the unidirectional motion is elusive in most cases. Here, we report that the sequential action of the ATPase ring in the DNA packaging motor of bacteriophage ϕ29 is regulated by an arginine finger that extends from one ATPase subunit to the adjacent unit to promote noncovalent dimer formation. Mutation of the arginine finger resulted in the interruption of ATPase oligomerization, ATP binding/hydrolysis, and DNA translocation. Dimer formation reappeared when arginine mutants were mixed with other ATPase subunits that can offer the arginine to promote their interaction. Ultracentrifugation and virion assembly assays indicated that the ATPase was presenting as monomers and dimer mixtures. The isolated dimer alone was inactive in DNA translocation, but the addition of monomer could restore the activity, suggesting that the hexameric ATPase ring contained both dimer and monomers. Moreover, ATP binding or hydrolysis resulted in conformation and entropy changes of the ATPase with high or low DNA affinity. Taking these observations together, we concluded that the arginine finger regulates sequential action of the motor ATPase subunit by promoting the formation of the dimer inside the hexamer. The finding of asymmetrical hexameric organization is supported by structural evidence of many other ATPase systems showing the presence of one noncovalent dimer and four monomer subunits. All of these provide clues for why the asymmetrical hexameric ATPase gp16 of ϕ29 was previously reported as a pentameric configuration by cryo-electron microscopy (cryo-EM) since the contact by the arginine finger renders two adjacent ATPase subunits closer than other subunits. Thus, the asymmetrical hexamer would appear as a pentamer by cryo-EM, a technology that acquires the average of many images.

New approach to develop ultra-high inhibitory drug using the power function of the stoichiometry of the targeted nanomachine or biocomplex

AIMS

To find methods for potent drug development by targeting to biocomplex with high copy number.

METHODS

Phi29 DNA packaging motor components with different stoichiometries were used as model to assay virion assembly with Yang Hui's Triangle [Formula: see text], where Z = stoichiometry, M = drugged subunits per biocomplex, p and q are the fraction of drugged and undrugged subunits in the population.

RESULTS

Inhibition efficiency follows a power function. When number of drugged subunits to block the function of the complex K = 1, the uninhibited biocomplex equals q(z), demonstrating the multiplicative effect of stoichiometry on inhibition with stoichiometry 1000 > 6 > 1. Complete inhibition of virus replication was found when Z = 6.

CONCLUSION

Drug inhibition potency depends on the stoichiometry of the targeted components of the biocomplex or nanomachine. The inhibition effect follows a power function of the stoichiometry of the target biocomplex.

Structural and Molecular Basis for Coordination in a Viral DNA Packaging Motor

Ring NTPases are a class of ubiquitous molecular motors involved in basic biological partitioning processes. dsDNA viruses encode ring ATPases that translocate their genomes to near-crystalline densities within pre-assembled viral capsids. Here, X-ray crystallography, cryoEM, and biochemical analyses of the dsDNA packaging motor in bacteriophage phi29 show how individual subunits are arranged in a pentameric ATPase ring and suggest how their activities are coordinated to translocate dsDNA. The resulting pseudo-atomic structure of the motor and accompanying functional analyses show how ATP is bound in the ATPase active site; identify two DNA contacts, including a potential DNA translocating loop; demonstrate that a trans-acting arginine finger is involved in coordinating hydrolysis around the ring; and suggest a functional coupling between the arginine finger and the DNA translocating loop. The ability to visualize the motor in action illuminates how the different motor components interact with each other and with their DNA substrate.

Biological Nanomotors with a Revolution, Linear, or Rotation Motion Mechanism

The ubiquitous biological nanomotors were classified into two categories in the past: linear and rotation motors. In 2013, a third type of biomotor, revolution without rotation (http://rnanano.osu.edu/movie.html), was discovered and found to be widespread among bacteria, eukaryotic viruses, and double-stranded DNA (dsDNA) bacteriophages. This review focuses on recent findings about various aspects of motors, including chirality, stoichiometry, channel size, entropy, conformational change, and energy usage rate, in a variety of well-studied motors, including FoF1 ATPase, helicases, viral dsDNA-packaging motors, bacterial chromosome translocases, myosin, kinesin, and dynein. In particular, dsDNA translocases are used to illustrate how these features relate to the motion mechanism and how nature elegantly evolved a revolution mechanism to avoid coiling and tangling during lengthy dsDNA genome transportation in cell division. Motor chirality and channel size are two factors that distinguish rotation motors from revolution motors. Rotation motors use right-handed channels to drive the right-handed dsDNA, similar to the way a nut drives the bolt with threads in same orientation; revolution motors use left-handed motor channels to revolve the right-handed dsDNA. Rotation motors use small channels (<2 nm in diameter) for the close contact of the channel wall with single-stranded DNA (ssDNA) or the 2-nm dsDNA bolt; revolution motors use larger channels (>3 nm) with room for the bolt to revolve. Binding and hydrolysis of ATP are linked to different conformational entropy changes in the motor that lead to altered affinity for the substrate and allow work to be done, for example, helicase unwinding of DNA or translocase directional movement of DNA.

RNA as a stable polymer to build controllable and defined nanostructures for material and biomedical applications

The value of polymers is manifested in their vital use as building blocks in material and life sciences. Ribonucleic acid (RNA) is a polynucleic acid, but its polymeric nature in materials and technological applications is often overlooked due to an impression that RNA is seemingly unstable. Recent findings that certain modifications can make RNA resistant to RNase degradation while retaining its authentic folding property and biological function, and the discovery of ultra-thermostable RNA motifs have adequately addressed the concerns of RNA unstability. RNA can serve as a unique polymeric material to build varieties of nanostructures including nanoparticles, polygons, arrays, bundles, membrane, and microsponges that have potential applications in biomedical and material sciences. Since 2005, more than a thousand publications on RNA nanostructures have been published in diverse fields, indicating a remarkable increase of interest in the emerging field of RNA nanotechnology. In this review, we aim to: delineate the physical and chemical properties of polymers that can be applied to RNA; introduce the unique properties of RNA as a polymer; review the current methods for the construction of RNA nanostructures; describe its applications in material, biomedical and computer sciences; and, discuss the challenges and future prospects in this field.

Discovery of a new method for potent drug development using power function of stoichiometry of homomeric biocomplexes or biological nanomotors

INTRODUCTION

Multidrug resistance and the appearance of incurable diseases inspire the quest for potent therapeutics.

AREAS COVERED

We review a new methodology in designing potent drugs by targeting multi-subunit homomeric biological motors, machines or complexes with Z > 1 and K = 1, where Z is the stoichiometry of the target, and K is the number of drugged subunits required to block the function of the complex. The condition is similar to a series electrical circuit of Christmas decorations: failure of one light bulb causes the entire lighting system to lose power. In most multi-subunit, homomeric biological systems, a sequential coordination or cooperative action mechanism is utilized, thus K equals 1. Drug inhibition depends on the ratio of drugged to non-drugged complexes. When K = 1, and Z > 1, the inhibition effect follows a power law with respect to Z, leading to enhanced drug potency. The hypothesis that the potency of drug inhibition depends on the stoichiometry of the targeted biological complexes was recently quantified by Yang-Hui's Triangle (or binomial distribution), and proved using a highly sensitive in vitro phi29 viral DNA packaging system. Examples of targeting homomeric bio-complexes with high stoichiometry for potent drug discovery are discussed.

EXPERT OPINION

Biomotors with multiple subunits are widespread in viruses, bacteria and cells, making this approach generally applicable in the development of inhibition drugs with high efficiency.

Single pore translocation of folded, double-stranded, and tetra-stranded DNA through channel of bacteriophage phi29 DNA packaging motor

The elegant architecture of the channel of bacteriophage phi29 DNA packaging motor has inspired the development of biomimetics for biophysical and nanobiomedical applications. The reengineered channel inserted into a lipid membrane exhibits robust electrophysiological properties ideal for precise sensing and fingerprinting of dsDNA at the single-molecule level. Herein, we used single channel conduction assays to quantitatively evaluate the translocation dynamics of dsDNA as a function of the length and conformation of dsDNA. We extracted the speed of dsDNA translocation from the dwell time distribution and estimated the various forces involved in the translocation process. A ∼35-fold slower speed of translocation per base-pair was observed for long dsDNA, a significant contrast to the speed of dsDNA crossing synthetic pores. It was found that the channel could translocate both dsDNA with ∼32% of channel current blockage and with ∼64% for tetra-stranded DNA (two parallel dsDNA). The calculation of both cross-sectional areas of the dsDNA and tetra-stranded DNA suggested that the blockage was purely proportional to the physical space of the channel lumen and the size of the DNA substrate. Folded dsDNA configuration was clearly reflected in their characteristic current signatures. The finding of translocation of tetra-stranded DNA with 64% blockage is in consent with the recently elucidated mechanism of viral DNA packaging via a revolution mode that requires a channel larger than the dsDNA diameter of 2 nm to provide room for viral DNA revolving without rotation. The understanding of the dynamics of dsDNA translocation in the phi29 system will enable us to design more sophisticated single pore DNA translocation devices for future applications in nanotechnology and personal medicine.

Common mechanisms of DNA translocation motors in bacteria and viruses using one-way revolution mechanism without rotation

Biomotors were once described into two categories: linear motor and rotation motor. Recently, a third type of biomotor with revolution mechanism without rotation has been discovered. By analogy, rotation resembles the Earth rotating on its axis in a complete cycle every 24h, while revolution resembles the Earth revolving around the Sun one circle per 365 days (see animations http://nanobio.uky.edu/movie.html). The action of revolution that enables a motor free of coiling and torque has solved many puzzles and debates that have occurred throughout the history of viral DNA packaging motor studies. It also settles the discrepancies concerning the structure, stoichiometry, and functioning of DNA translocation motors. This review uses bacteriophages Phi29, HK97, SPP1, P22, T4, and T7 as well as bacterial DNA translocase FtsK and SpoIIIE or the large eukaryotic dsDNA viruses such as mimivirus and vaccinia virus as examples to elucidate the puzzles. These motors use ATPase, some of which have been confirmed to be a hexamer, to revolve around the dsDNA sequentially. ATP binding induces conformational change and possibly an entropy alteration in ATPase to a high affinity toward dsDNA; but ATP hydrolysis triggers another entropic and conformational change in ATPase to a low affinity for DNA, by which dsDNA is pushed toward an adjacent ATPase subunit. The rotation and revolution mechanisms can be distinguished by the size of channel: the channels of rotation motors are equal to or smaller than 2 nm, that is the size of dsDNA, whereas channels of revolution motors are larger than 3 nm. Rotation motors use parallel threads to operate with a right-handed channel, while revolution motors use a left-handed channel to drive the right-handed DNA in an anti-chiral arrangement. Coordination of several vector factors in the same direction makes viral DNA-packaging motors unusually powerful and effective. Revolution mechanism that avoids DNA coiling in translocating the lengthy genomic dsDNA helix could be advantageous for cell replication such as bacterial binary fission and cell mitosis without the need for topoisomerase or helicase to consume additional energy.

Adenosine triphosphatases of thermophilic archaeal double-stranded DNA viruses

Adenosine triphosphatases (ATPases) of double-stranded (ds) DNA archaeal viruses are structurally related to the AAA+ hexameric helicases and translocases. These ATPases have been implicated in viral life cycle functions such as DNA entry into the host, and viral genome packaging into preformed procapsids. We summarize bioinformatical analyses of a wide range of archaeal ATPases, and review the biochemical and structural properties of those archaeal ATPases that have measurable ATPase activity. We discuss their potential roles in genome delivery into the host, virus assembly and genome packaging in comparison to hexameric helicases and packaging motors from bacteriophages.

Viral and cellular SOS-regulated motor proteins: dsDNA translocation mechanisms with divergent functions

DNA damage attacks on bacterial cells have been known to activate the SOS response, a transcriptional response affecting chromosome replication, DNA recombination and repair, cell division and prophage induction. All these functions require double-stranded (ds) DNA translocation by ASCE hexameric motors. This review seeks to delineate the structural and functional characteristics of the SOS response and the SOS-regulated DNA translocases FtsK and RuvB with the phi29 bacteriophage packaging motor gp16 ATPase as a prototype to study bacterial motors. While gp16 ATPase, cellular FtsK and RuvB are similarly comprised of hexameric rings encircling dsDNA and functioning as ATP-driven DNA translocases, they utilize different mechanisms to accomplish separate functions, suggesting a convergent evolution of these motors. The gp16 ATPase and FtsK use a novel revolution mechanism, generating a power stroke between subunits through an entropy-DNA affinity switch and pushing dsDNA inward without rotation of DNA and the motor, whereas RuvB seems to employ a rotation mechanism that remains to be further characterized. While FtsK and RuvB perform essential tasks during the SOS response, their roles may be far more significant as SOS response is involved in antibiotic-inducible bacterial vesiculation and biofilm formation as well as the perspective of the bacteria-cancer evolutionary interaction.

Finding of widespread viral and bacterial revolution dsDNA translocation motors distinct from rotation motors by channel chirality and size

Background

Double-stranded DNA translocation is ubiquitous in living systems. Cell mitosis, bacterial binary fission, DNA replication or repair, homologous recombination, Holliday junction resolution, viral genome packaging and cell entry all involve biomotor-driven dsDNA translocation. Previously, biomotors have been primarily classified into linear and rotational motors. We recently discovered a third class of dsDNA translocation motors in Phi29 utilizing revolution mechanism without rotation. Analogically, the Earth rotates around its own axis every 24 hours, but revolves around the Sun every 365 days.

Results

Single-channel DNA translocation conductance assay combined with structure inspections of motor channels on bacteriophages P22, SPP1, HK97, T7, T4, Phi29, and other dsDNA translocation motors such as bacterial FtsK and eukaryotic mimiviruses or vaccinia viruses showed that revolution motor is widespread. The force generation mechanism for revolution motors is elucidated. Revolution motors can be differentiated from rotation motors by their channel size and chirality. Crystal structure inspection revealed that revolution motors commonly exhibit channel diameters larger than 3 nm, while rotation motors that rotate around one of the two separated DNA strands feature a diameter smaller than 2 nm. Phi29 revolution motor translocated double- and tetra-stranded DNA that occupied 32% and 64% of the narrowest channel cross-section, respectively, evidencing that revolution motors exhibit channel diameters significantly wider than the dsDNA. Left-handed oriented channels found in revolution motors drive the right-handed dsDNA via anti-chiral interaction, while right-handed channels observed in rotation motors drive the right-handed dsDNA via parallel threads. Tethering both the motor and the dsDNA distal-end of the revolution motor does not block DNA packaging, indicating that no rotation is required for motors of dsDNA phages, while a small-angle left-handed twist of dsDNA that is aligned with the channel could occur due to the conformational change of the phage motor channels from a left-handed configuration for DNA entry to a right-handed configuration for DNA ejection for host cell infection.

Conclusions

The revolution motor is widespread among biological systems, and can be distinguished from rotation motors by channel size and chirality. The revolution mechanism renders dsDNA void of coiling and torque during translocation of the lengthy helical chromosome, thus resulting in more efficient motor energy conversion.

Entropy-driven one-step formation of Phi29 pRNA 3WJ from three RNA fragments

The emerging field of RNA nanotechnology necessitates creation of functional RNA nanoparticles but has been limited by particle instability. It has been shown that the three-way junction of bacteriophage phi29 motor pRNA has unusual stability and can self-assemble from three fragments with high efficiency. It is generally believed that RNA and DNA folding is energy landscape-dependent, and the folding of RNA is driven by enthalpy. Here we examine the thermodynamic characteristics of the 3WJ components as 2′-fluoro RNA, DNA, and RNA. It was seen that the three fragments existed either in 3WJ complex or as monomers, with the intermediate of dimers almost undetectable. It seems that the three fragments can lead to the formation of the 3WJ complex efficiently within a rapid time. A low dissociation constant (apparent K_D) of 11.4 nM was determined for RNA, inclusion of 2′-F pyrimidines strengthened the K_D to 4.5 nM, and substitution of DNA weakened it to 47.7 nM. The ΔG°₃₇, were −36, −28, and −15 kcal/mol for 3WJ_2′-F, 3WJ_RNA, and 3WJ_DNA, respectively. It is found that the formation of the three-component complex was governed by entropy, instead of enthalpy, as usually found in RNA complexes.

Binomial distribution for quantification of protein subunits in biological nanoassemblies and functional nanomachines

Living systems produce ordered structures and nanomachines that inspire the development of biomimetic nanodevices such as chips, MEMS, actuators, sensors, sorters, and apparatuses for single-pore DNA sequencing, disease diagnosis, drug or therapeutic RNA delivery. Determination of the copy numbers of subunits that build these machines is challenging due to small size. Here we report a simple mathematical method to determine the stoichiometry, using phi29 DNA-packaging nanomotor as a model to elucidate the application of a formula ∑M=0(Z)((Z)M)p(Z-M)q(M), where p and q are the percentage of wild-type and inactive mutant in the empirical assay; M is the copy numbers of mutant and Z is the stoichiometry in question. Variable ratios of mutants and wild-type were mixed to inhibit motor function. Empirical data were plotted over the theoretical curves to determine the stoichiometry and the value of K, which is the number of mutant needed in each machine to block the function, all based on the condition that wild-type and mutant are equal in binding affinity. Both Z and K from 1-12 were investigated. The data precisely confirmed that phi29 motor contains six copies (Z) of the motor ATPase gp16, and K=1. From the clinical editor: To determine copy numbers of subunits that form nanomachines in living organisms is a daunting task due to the complexities and the inherently small sizes associated with such systems. In this paper, a simple mathematical method is described how to determine the stoichiometry of copies in biomimetic nanodevices, using phi29 DNA-packaging nanomotor as a model.