A nucleotide binding rectification Brownian ratchet model for translocation of Y-family DNA polymerases

Background

Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.

Methods

In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing C. elegans during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.

Results and conclusion

The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.     

The brownian ratchet and power stroke models for posttranslational protein translocation into the endoplasmic reticulum

A quantitative analysis of experimental data for posttranslational translocation into the endoplasmic reticulum is performed. This analysis reveals that translocation involves a single rate-limiting step, which is postulated to be the release of the signal sequence from the translocation channel. Next, the Brownian ratchet and power stroke models of translocation are compared against the data. The data sets are simultaneously fit using a least-squares criterion, and both models are found to accurately reproduce the experimental results. A likelihood-ratio test reveals that the optimal fit of the Brownian ratchet model, which contains one fewer free parameter, does not differ significantly from that of the power stroke model. Therefore, the data considered here cannot be used to reject this import mechanism. The models are further analyzed using the estimated parameters to make experimentally testable predictions.     

Coarse-grained Brownian ratchet model of membrane protrusion on cellular scale

Membrane protrusion is a mechanochemical process of active membrane deformation driven by actin polymerization. Previously, Brownian ratchet (BR) was modeled on the basis of the underlying molecular mechanism. However, because the BR requires a priori load that cannot be determined without information of the cell shape, it cannot be effective in studies in which resultant shapes are to be solved. Other cellular-scale models describing the protrusion have also been suggested for modeling a whole cell; however, these models were not developed on the basis of coarse-grained physics representing the underlying molecular mechanism. Therefore, to express the membrane protrusion on the cellular scale, we propose a novel mathematical model, the coarse-grained BR (CBR), which is derived on the basis of nonequilibrium thermodynamics theory. The CBR can reproduce the BR within the limit of the quasistatic process of membrane protrusion and can estimate the protrusion velocity consistently with an effective elastic constant that represents the state of the energy of the membrane. Finally, to demonstrate the applicability of the CBR, we attempt to perform a cellular-scale simulation of migrating keratocyte in which the proposed CBR is used for the membrane protrusion model on the cellular scale. The results show that the experimentally observed shapes of the leading edge are well reproduced by the simulation. In addition, The trend of dependences of the protrusion velocity on the curvature of the leading edge, the temperature, and the substrate stiffness also agreed with the other experimental results. Thus, the CBR can be considered an appropriate cellular-scale model to express the membrane protrusion on the basis of its underlying molecular mechanism.     

The protein import motor of mitochondria: a targeted molecular ratchet driving unfolding and translocation

Unfolding and import of preproteins into mitochondria are facilitated by a molecular motor in which heat shock protein 70 (Hsp70) in the matrix plays an essential role. Here we present two different experimental approaches to analyze mechanisms underlying this function of Hsp70. First, preproteins containing stretches of glutamic acid (polyE) or glycine (polyG) repeats in front of folded domains were imported into mitochondria. This occurred although Hsp70 cannot pull on these stretches to unfold the folded domains, since it does not bind to polyE and polyG. Secondly, preproteins containing titin immunoglobulin (Ig)-like domains were imported into mitochondria, despite the fact that forces of >200 pN are required to mechanically unfold these domains. Since molecular motors generate forces of approximately 5 pN, Hsp70 could not promote unfolding of the Ig-like domains by mechanical pulling. Our observations suggest that Hsp70 acts as an element of a Brownian ratchet, which mediates unfolding and translocation of preproteins across the mitochondrial membranes.     

Ribosome binding to and dissociation from translocation sites of the endoplasmic reticulum membrane

We have addressed how ribosome-nascent chain complexes (RNCs), associated with the signal recognition particle (SRP), can be targeted to Sec61 translocation channels of the endoplasmic reticulum (ER) membrane when all binding sites are occupied by nontranslating ribosomes. These competing ribosomes are known to be bound with high affinity to tetramers of the Sec61 complex. We found that the membrane binding of RNC-SRP complexes does not require or cause the dissociation of prebound nontranslating ribosomes, a process that is extremely slow. SRP and its receptor target RNCs to a free population of Sec61 complex, which associates with nontranslating ribosomes only weakly and is conformationally different from the population of ribosome-bound Sec61 complex. Taking into account recent structural data, we propose a model in which SRP and its receptor target RNCs to a Sec61 subpopulation of monomeric or dimeric state. This could explain how RNC-SRP complexes can overcome the competition by nontranslating ribosomes.     

Step-size analyses of the mitochondrial Hsp70 import motor reveal the Brownian ratchet in operation

Newly synthesized mitochondrial precursor proteins have to become unfolded by the mitochondrial Hsp70 (mtHsp70) import motor to cross the mitochondrial membranes. To assess the mechanism of unfolding of precursor proteins by mtHsp70, we designed a system to measure step sizes of the mtHsp70 import motor, which are distances at which the motor system moves along polypeptide chains during a single turnover of ATP. We made a series of fusion proteins consisting of a mitochondrial presequence containing the first mtHsp70 binding site, a spacer sequence containing an Hsp70 avoidance segment followed by the second mtHsp70 binding site, and different folded mature domains. Analyses of the dependence of the import rates of those fusion proteins on the lengths of Hsp70 avoidance segments allowed us to estimate the step sizes, which differ for different mature domains and different lengths of the spacers. These results suggest that the mtHsp70 import motor functions at least as a molecular Brownian ratchet to unfold mitochondrial precursor proteins.     

A critical intramolecular interaction for protein kinase Cepsilon translocation

Disruption of intramolecular interactions, translocation from one intracellular compartment to another, and binding to isozyme-specific anchoring proteins termed RACKs, accompany protein kinase C (PKC) activation. We hypothesized that in inactive epsilonPKC, the RACK-binding site is engaged in an intramolecular interaction with a sequence resembling its RACK, termed psiepsilonRACK. An amino acid difference between the psiepsilonRACK sequence in epsilonPKC and its homologous sequence in epsilonRACK constitutes a change from a polar non-charged amino acid (asparagine) in epsilonRACK to a polar charged amino acid (aspartate) in epsilonPKC. Here we show that mutating the aspartate to asparagine in epsilonPKC increased intramolecular interaction as indicated by increased resistance to proteolysis, and slower hormone- or PMA-induced translocation in cells. Substituting aspartate for a non-polar amino acid (alanine) resulted in binding to epsilonRACK without activators, in vitro, and increased translocation rate upon activation in cells. Mathematical modeling suggests that translocation is at least a two-step process. Together our data suggest that intramolecular interaction between the psiepsilonRACK site and RACK-binding site within epsilonPKC is critical and rate limiting in the process of PKC translocation.     

A Brownian motor mechanism of translocation and strand separation by hepatitis C virus helicase

Helicases translocate along their nucleic acid substrates using the energy of ATP hydrolysis and by changing conformations of their nucleic acid-binding sites. Our goal is to characterize the conformational changes of hepatitis C virus (HCV) helicase at different stages of ATPase cycle and to determine how they lead to translocation. We have reported that ATP binding reduces HCV helicase affinity for nucleic acid. Now we identify the stage of the ATPase cycle responsible for translocation and unwinding. We show that a rapid directional movement occurs upon helicase binding to DNA in the absence of ATP, resulting in opening of several base pairs. We propose that HCV helicase translocates as a Brownian motor with a simple two-stroke cycle. The directional movement step is fueled by single-stranded DNA binding energy while ATP binding allows for a brief period of random movement that prepares the helicase for the next cycle.     

A chemically driven fluctuating ratchet model for actomyosin interaction

With reference to the experimental observations by Yanagida and his co-workers on actomyosin interaction, a Brownian motor of fluctuating ratchet kind is designed with the aim to describe the interaction between a Myosin II head and a neighboring actin filament. Our motor combines the dynamics of the myosin head with a chemical external system related to the ATP cycle, whose role is to provide the energy supply necessary to bias the motion. Analytical expressions for the duration of the ATP cycle, for the Gibbs free energy and for the net displacement of the myosin head are obtained. Finally, by exploiting a method due to Sekimoto [J. Phys. Soc. Jpn. 66 (1997) 1234], a formula is worked out for the amount of energy consumed during the ATP cycle.     

A stochastic model for a single click of Muller's ratchet

This work presents a new approach to Muller's ratchet, where Haigh's model is approximately mapped into a simpler model that describes the behaviour of a population after a click of the ratchet, i.e., after loss of what was the fittest class. This new model predicts the distribution of times to the next click of the ratchet and is equivalent to a Wright-Fisher model for a population of haploid asexual individuals with one locus and two alleles. Within this model, the fittest members of a population correspond to carriers of one allele, while all other individuals have suboptimal fitness and are represented as carriers of the other allele. In this way, all suboptimal fitness individuals are amalgamated into a single “mutant” class.The approach presented here has some limitations and the potential for improvement. However, it does lead to results for the rate of the ratchet that, over a wide range of parameters, are accurate within one order of magnitude of simulation results. This contrasts with existing approaches, which are designed for only one or other of the two different parameter regimes known for the ratchet and are more accurate only in the parameter regime they were designed for.Numerical results are presented for the mean time between clicks of the ratchet for (i) the Wright-Fisher model, (ii) a diffusion approximation of this model and (iii) individually based simulations of a full model. The diffusion approximation is validated over a wide range of parameters by its close agreement with the Wright-Fisher model.The present work predicts that: (a) the time between clicks of the ratchet is insensitive to the value of the selection coefficient when the genomic mutation rate is large compared with the selection coefficient against a deleterious mutation, (b) the time interval between clicks of the ratchet has, approximately, an exponential distribution (or its discrete analogue). It is thus possible to determine the variance in times between clicks, given the expected time between clicks. Evidence for both (a) and (b) is seen in simulations.     

A platform for compartmentalized protein synthesis: protein translation and translocation in the ER

Recent advances in the study of protein translocation across the membrane of the endoplasmic reticulum include insights into the mechanism of signal-sequence function. Biochemical and genetic studies have provided further evidence that lumenal proteins perform direct roles in secretory protein translocation and in the regulation of protein-conducting-channel permeability during membrane protein integration. A hypothesis identifying the endoplasmic reticulum as a site of mRNA localization and compartmentalized protein synthesis has been suggested.     

Weighted-ensemble Brownian dynamics simulations for protein association reactions.

A new method, weighted-ensemble Brownian dynamics, is proposed for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. The method has been applied to the Northrup and Erickson (1992) model of docking-type diffusion-limited reactions and yields reaction rate constants in agreement with those obtained by direct Brownian simulation, but at a fraction of the CPU time (10(-4) to 10(-3), depending on the model). Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics, in conjunction with biophysical force models, can be applied to a large class of association reactions of interest to the biophysics community.     

Peroxin 5: A cycling receptor for protein translocation into peroxisomes

Peroxins are proteins that regulate the biogenesis of peroxisomes—small vesicular subcellular organelles essential for human life and health. A key peroxin – to date the best studied – is peroxin 5. Structurally, peroxin 5 is a bi-domain protein of about 70 kDa containing both globular and non-globular segments and displaying conformational flexibility. Functionally, it is a cycling receptor for importing essential enzymes into the peroxisome lumen, facilitated by highly promiscuous interactions with numerous proteins and possibly lipids. Peroxin 5 has medical significance in that (i) congenital defects can lead to fatal peroxisome biogenesis disorders, (ii) inefficient peroxisome targeting is linked to disease and aging and (iii) differences between human peroxin 5 and homologues in pathogens may be exploited in the development of therapeutics.     

Translocation arrest by reversible folding of a precursor protein imported into mitochondria. A means to quantitate translocation contact sites

Passage of precursor proteins through translocation contact sites of mitochondria was investigated by studying the import of a fusion protein consisting of the NH2-terminal 167 amino acids of yeast cytochrome b2 precursor and the complete mouse dihydrofolate reductase. Isolated mitochondria of Neurospora crassa readily imported the fusion protein. In the presence of methotrexate import was halted and a stable intermediate spanning both mitochondrial membranes at translocation contact sites accumulated. The complete dihydrofolate reductase moiety in this intermediate was external to the outer membrane, and the 136 amino acid residues of the cytochrome b2 moiety remaining after cleavage by the matrix processing peptidase spanned both outer and inner membranes. Removal of methotrexate led to import of the intermediate retained at the contact site into the matrix. Thus unfolding at the surface of the outer mitochondrial membrane is a prerequisite for passage through translocation contact sites. The membrane-spanning intermediate was used to estimate the number of translocation sites. Saturation was reached at 70 pmol intermediate per milligram of mitochondrial protein. This amount of translocation intermediates was calculated to occupy approximately 1% of the total surface of the outer membrane. The morphometrically determined area of close contact between outer and inner membranes corresponded to approximately 7% of the total outer membrane surface. Accumulation of the intermediate inhibited the import of other precursor proteins suggesting that different precursor proteins are using common translocation contact sites. We conclude that the machinery for protein translocation into mitochondria is present at contact sites in limited number.     

A chromosomal translocation causing multiple abnormalities including open eyelids at birth and glomerulonephritis

We have characterized the phenotype of a mouse with a t(2;13) reciprocal translocation induced by chlorambucil. It results in abnormal eyelid formation as well as a series of neurological, physiological, and immunological abnormalities. This mutant has been termed T(2;13)1Fla/+. T(2;13)1Fla/+ mice exhibit open eyelids at birth, a dilute coat color, hyperactivity, and occasional circling and stargazing activity. At 1-6 months, T(2;13)1Fla/+ mice show signs of immune complex-mediated glomerulonephritis and die prematurely. Additionally, double-stranded DNA autoantibodies have been found in sera of T(2;13)1Fla/+ mice. Cytogenetic analysis situated the translocation breakpoint at the proximal end of Chromosome (chr) 2 at band A2, and on Chr 13 at band A4. The mutant phenotype completely correlated with the presence of the translocation. Additional genetic studies have mapped the mutation and translocation breakpoint to Chr 13 between D13Mit16 and D13Mit64, and to Chr 2 proximal to D2Mit5. By fluorescent in situ hybridization (FISH), the position of this mutation/translocation on Chr 13 has been mapped to a region less than 1cM from D13Mit61.     

Dual binding sites for translocation catalysis by Escherichia coli glutathionylspermidine synthetase

Most organisms use glutathione to regulate intracellular thiol redox balance and protect against oxidative stress; protozoa, however, utilize trypanothione for this purpose. Trypanothione biosynthesis requires ATP-dependent conjugation of glutathione (GSH) to the two terminal amino groups of spermidine by glutathionylspermidine synthetase (GspS) and trypanothione synthetase (TryS), which are considered as drug targets. GspS catalyzes the penultimate step of the biosynthesis-amide bond formation between spermidine and the glycine carboxylate of GSH. We report herein five crystal structures of Escherichia coli GspS in complex with substrate, product or inhibitor. The C-terminal of GspS belongs to the ATP-grasp superfamily with a similar fold to the human glutathione synthetase. GSH is likely phosphorylated at one of two GSH-binding sites to form an acylphosphate intermediate that then translocates to the other site for subsequent nucleophilic addition of spermidine. We also identify essential amino acids involved in the catalysis. Our results constitute the first structural information on the biochemical features of parasite homologs (including TryS) that underlie their broad specificity for polyamines.