Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Thermodynamics and Kinetics of Molecular Motors

Molecular motors are first and foremost molecules, governed by the laws of chemistry rather than of mechanics. The dynamical behavior of motors based on chemical principles can be described as a random walk on a network of states. A key insight is that any molecular motor in solution explores all possible motions and configurations at thermodynamic equilibrium. By using input energy and chemical design to prevent motion that is not wanted, what is left behind is the motion that is desired. This review is focused on two-headed motors such as kinesin and Myosin V that move on a polymeric track. By use of microscopic reversibility, it is shown that the ratio between the number of forward steps and the number of backward steps in any sufficiently long time period does not directly depend on the mechanical properties of the linker between the two heads. Instead, this ratio is governed by the relative chemical specificity of the heads in the front-versus-rear position for the fuel, adenosine triphosphate and its products, adenosine diphosphate and inorganic phosphate. These insights have been key factors in the design of biologically inspired synthetic molecular walkers constructed out of DNA or out of small organic molecules.     

Extracting the Stepping Dynamics of Molecular Motors in Living Cells from Trajectories of Single Particles

Molecular motors are responsible of transporting a wide variety of cargos in the cytoplasm. Current efforts are oriented to characterize the biophysical properties of motors in cells with the aim of elucidating the mechanisms of these nanomachines in the complex cellular environment. In this study, we present an algorithm designed to extract motor step sizes and dwell times between steps from trajectories of motors or cargoes driven by motors in cells. The algorithm is based on finding patterns in the trajectory compatible with the behavior expected for a motor step, i.e., a region of confined motion followed by a jump in the position to another region of confined motion with similar characteristics to the previous one. We show that this algorithm allows the analysis of 2D trajectories even if they present complex motion patterns such as active transport interspersed with diffusion and does not require the assumption of a given step size or dwell period. The confidence on the step detection can be easily obtained and allows the evaluation of the confidence of the dwell and step size distributions. To illustrate the possible applications of this algorithm, we analyzed trajectories of myosin-V driven organelles in living cells.     

Mechanical Operation and Intersubunit Coordination of Ring-Shaped Molecular Motors: Insights from Single-Molecule Studies

Ring NTPases represent a large and diverse group of proteins that couple their nucleotide hydrolysis activity to a mechanical task involving force generation and some type of transport process in the cell. Because of their shape, these enzymes often operate as gates that separate distinct cellular compartments to control and regulate the passage of chemical species across them. In this manner, ions and small molecules are moved across membranes, biopolymer substrates are segregated between cells or moved into confined spaces, double-stranded nucleic acids are separated into single strands to provide access to the genetic information, and polypeptides are unfolded and processed for recycling. Here we review the recent advances in the characterization of these motors using single-molecule manipulation and detection approaches. We describe the various mechanisms by which ring motors convert chemical energy to mechanical force or torque and coordinate the activities of individual subunits that constitute the ring. We also examine how single-molecule studies have contributed to a better understanding of the structural elements involved in motor-substrate interaction, mechanochemical coupling, and intersubunit coordination. Finally, we discuss how these molecular motors tailor their operation—often through regulation by other cofactors—to suit their unique biological functions.     

Mechanical Operation and Intersubunit Coordination of Ring-Shaped Molecular Motors: Insights from Single-Molecule Studies

Ring NTPases represent a large and diverse group of proteins that couple their nucleotide hydrolysis activity to a mechanical task involving force generation and some type of transport process in the cell. Because of their shape, these enzymes often operate as gates that separate distinct cellular compartments to control and regulate the passage of chemical species across them. In this manner, ions and small molecules are moved across membranes, biopolymer substrates are segregated between cells or moved into confined spaces, double-stranded nucleic acids are separated into single strands to provide access to the genetic information, and polypeptides are unfolded and processed for recycling. Here we review the recent advances in the characterization of these motors using single-molecule manipulation and detection approaches. We describe the various mechanisms by which ring motors convert chemical energy to mechanical force or torque and coordinate the activities of individual subunits that constitute the ring. We also examine how single-molecule studies have contributed to a better understanding of the structural elements involved in motor-substrate interaction, mechanochemical coupling, and intersubunit coordination. Finally, we discuss how these molecular motors tailor their operation—often through regulation by other cofactors—to suit their unique biological functions.     

The Stability of Cellulose: A Statistical Perspective from a Coarse-Grained Model of Hydrogen-Bond Networks

A critical roadblock to the production of biofuels from lignocellulosic biomass is the efficient degradation of crystalline microfibrils of cellulose to glucose. A microscopic understanding of how different physical conditions affect the overall stability of the crystalline structure of microfibrils could facilitate the design of more effective protocols for their degradation. One of the essential physical interactions that stabilizes microfibrils is a network of hydrogen (H) bonds: both intrachain H-bonds between neighboring monomers of a single cellulose polymer chain and interchain H-bonds between adjacent chains. We construct a statistical mechanical model of cellulose assembly at the resolution of explicit hydrogen-bond networks. Using the transfer matrix method, the partition function and the subsequent statistical properties are evaluated. With the help of this lattice-based model, we capture the plasticity of the H-bond network in cellulose due to frustration and redundancy in the placement of H-bonds. This plasticity is responsible for the stability of cellulose over a wide range of temperatures. Stable intrachain and interchain H-bonds are identified as a function of temperature that could possibly be manipulated toward rational destruction of crystalline cellulose.     

Bidirectional Transport by Molecular Motors: Enhanced Processivity and Response to External Forces

Intracellular transport along cytoskeletal filaments is often mediated by two teams of molecular motors that pull on the same cargo and move in opposite directions along the filaments. We have recently shown theoretically that this bidirectional transport can be understood as a stochastic tug-of-war between the two motor teams. Here, we further develop our theory to investigate the experimentally accessible dynamic behavior of cargos transported by strong motors such as kinesin-1 or cytoplasmic dynein. By studying the run and binding times of such a cargo, we show that the properties of biological motors, such as the large ratio of stall/detachment force and the small ratio of superstall backward/forward velocity, are favorable for bidirectional cargo transport, leading to fast motion and enhanced diffusion. In addition, cargo processivity is shown to be strongly enhanced by transport via several molecular motors even if these motors are engaged in a tug-of-war. Finally, we study the motility of a bidirectional cargo under force. Frictional forces arising, e.g., from the viscous cytoplasm, lead to peaks in the velocity distribution, while external forces as exerted, e.g., by an optical trap, lead to hysteresis effects. Our results, in particular our explicit expressions for the cargo binding time and the distance of the peaks in the velocity relation under friction, are directly accessible to in vitro as well as in vivo experiments.     

Plasticity of Fitness and Diversification Process During an Experimental Molecular Evolution

A simplified experimental evolution encompassing the essence of natural one was designed in an attempt to understand the involved mechanism. In our system, molecular evolution was observed through three serial cycles of consecutive random mutagenesis of the glutamine synthetase gene and chemostat culture of the transformed Escherichia coli cells containing the mutated genes. Selection pressure was imposed solely on the glutamine synthetase gene when varieties of mutant genes compete in an unstructured environment of the chemostat. The molecular phylogeny and population dynamics were deduced from the nucleotide sequences of the genes isolated from each of the chemostat runs. An initial mutant population in each cycle, comprised of diversified closely-related genes, ended up with several varieties of mutants in a state of coexistence. Competition between two mutant genes in the final population of the first cycle ascertained that the observed coexisting state is not an incidental event and that cellular interaction via environmental nutrients is a possible mechanism of coexistence. In addition, the mutant gene once extinct in the previous passage was found to have the capacity to reinvade and constitute the gene pool of the later cycle of molecular evolution. These results, including the kinetic characteristics of the purified wild-type and mutant glutamine synthetases in the phylogenetic tree, revealed that the enzyme activity had diverged, rather than optimized, to a fittest value during the course of evolution. Here, we proposed that the plasticity of gene fitness in consequence of cellular interaction via the environment is an essential mechanism governing molecular evolution. Received: 29 August 2000 / Accepted: 25 January 2001     

Insight Derived from Molecular Dynamics Simulations into Molecular Motions,Thermodynamics and Kinetics of HIV-1 gp120

Although the crystal structures of the HIV-1 gp120 core bound and pre-bound by CD4 are known, the details of dynamics involved in conformational equilibrium and transition in relation to gp120 function have remained elusive. The homology models of gp120 comprising the N- and C-termini and loops V3 and V4 in the CD4-bound and CD4-unbound states were built and subjected to molecular dynamics (MD) simulations to investigate the differences in dynamic properties and molecular motions between them. The results indicate that the CD4-bound gp120 adopted a more compact and stable conformation than the unbound form during simulations. For both the unbound and bound gp120, the large concerted motions derived from essential dynamics (ED) analyses can influence the size/shape of the ligand-binding channel/cavity of gp120 and, therefore, were related to its functional properties. The differences in motion direction between certain structural components of these two forms of gp120 were related to the conformational interconversion between them. The free energy calculations based on the metadynamics simulations reveal a more rugged and complex free energy landscape (FEL) for the unbound than for the bound gp120, implying that gp120 has a richer conformational diversity in the unbound form. The estimated free energy difference of ∼−6.0 kJ/mol between the global minimum free energy states of the unbound and bound gp120 indicates that gp120 can transform spontaneously from the unbound to bound states, revealing that the bound state represents a high-probability “ground state” for gp120 and explaining why the unbound state resists crystallization. Our results provide insight into the dynamics-and-function relationship of gp120, and facilitate understandings of the thermodynamics, kinetics and conformational control mechanism of HIV-1 gp120.     

The Missing Medians: Exclusion of Ordinal Data from Meta-Analyses

Background

Meta-analyses are considered the gold standard of evidence-based health care, and are used to guide clinical decisions and health policy. A major limitation of current meta-analysis techniques is their inability to pool ordinal data. Our objectives were to determine the extent of this problem in the context of neurological rating scales and to provide a solution.

Methods

Using an existing database of clinical trials of oral neuroprotective therapies, we identified the 6 most commonly used clinical rating scales and recorded how data from these scales were reported and analysed. We then identified systematic reviews of studies that used these scales (via the Cochrane database) and recorded the meta-analytic techniques used. Finally, we identified a statistical technique for calculating a common language effect size measure for ordinal data.

Results

We identified 103 studies, with 128 instances of the 6 clinical scales being reported. The majority– 80%–reported means alone for central tendency, with only 13% reporting medians. In analysis, 40% of studies used parametric statistics alone, 34% of studies employed non-parametric analysis, and 26% did not include or specify analysis. Of the 60 systematic reviews identified that included meta-analysis, 88% used mean difference and 22% employed difference in proportions; none included rank-based analysis. We propose the use of a rank-based generalised odds ratio (WMW GenOR) as an assumption-free effect size measure that is easy to compute and can be readily combined in meta-analysis.

Conclusion

There is wide scope for improvement in the reporting and analysis of ordinal data in the literature. We hope that adoption of the WMW GenOR will have the dual effect of improving the reporting of data in individual studies while also increasing the inclusivity (and therefore validity) of meta-analyses.     

Kinetics of Single Cells: Observation and Modeling of a Stochastic Process

The successive generation times for single cells of Escherichia coli K-12 were measured as described by A. Elfwing, Y. LeMarc, J. Baranyi, and A. Ballagi (Appl. Environ. Microbiol. 70:675-678, 2004), and the histograms they generated were used as empirical distributions to simulate growth of the population as the result of the multiplication of its single cells. This way, a stochastic birth model in which the underlying distributions were measured experimentally was simulated. To validate the model, analogous bacterial growth curves were generated by the use of different inoculum levels. The agreement with the simulation was very good, proving that the growth of the population can be predicted accurately if the distribution of the first few division times for the single cells within that population is known. Two questions were investigated by the simulation. (i) To what extent can we say that the distribution of the detection time, i.e., the time by which a single-cell-generated subpopulation reaches a detectable level, can be identified with that of the lag time of the original single cell? (ii) For low inocula, how does the inoculum size affect the lag time of the population?     

Statistical Analysis of Lateral Diffusion and Multistate Kinetics in Single-Molecule Imaging

Single-molecule trajectories of molecules on the membrane of living cells have indicated the possibility that the lateral mobility of individual molecules is variable with time. Such temporal variation in mobility may indicate intrinsic kinetics of multiple molecular states. To clarify the mechanisms of signal processing on the membrane, quantitative characterizations of such temporal variations are necessary. Here we propose a method to analyze and characterize the multiple states in lateral mobility and their transition kinetics from single-molecule trajectories based on a displacement probability density function and an autocorrelation function of squared displacements. We performed our method for three cases: a molecule with a single diffusion coefficient (D), a mixture of molecules in two states with different D-values, and a molecule switching between two states with different D-values. Our analysis of numerically generated trajectories successfully distinguished the three cases and estimated the characteristic parameters for mobility and the kinetics of state transitions. This method is applicable to single-molecule tracking analysis of molecules in multiple functional states with different lateral mobility on the membrane of living cells.     

Fermentation Kinetics and Continuous Process of L-Asparaginase Production

For the purpose of obtaining L-asparaginase in quantities from Erwinia aroideae, cell growth and enzyme formation were investigated in both batch and continuous fermentation. Using yeast extract as a growth-limiting substrate, the relationship between specific growth rate and substrate concentration was found to fit the Monod equation. The optimum temperature for enzyme production was 24 C, although cell growth was higher at 28 C. The enzyme yield reached its maximum of 4 IU/ml during the negative acceleration growth phase which occurs just prior to stationary growth. Compared to batch fermentations, the continuous fermentation process gave a lower enzyme yield except when the fermentation was conducted at a dilution rate of 0.1 hr(-1). The graphical method frequently used for prediction of continuous fermentation does not apply to L-asparaginase production by E. aroideae. The optimum temperature for enzyme production in continuous process was 24 C, which was the same as in batch process. Increasing the temperature from 24 to 28 C resulted in a 20% loss of enzyme yield.     

Happiness and Social Exclusion of Indigenous Peoples in Taiwan - A Social Sustainability Perspective

IntroductionHappiness and social inclusion are important indicators of social sustainability, as recommended in the Sustainable Development Goals; however, little is known about the social sustainable development of ethnic minorities. To fill this knowledge gap, special attention is paid to understanding the issues of social exclusion and happiness in relation to the indigenous peoples in Taiwan.MethodsData used were drawn from a nationwide representativeness survey of the Taiwanese Indigenous People in 2007; it included 2,200 respondents. This study employed binary logistic regression to examine the effects of different domains of social exclusion on the likelihood of perceiving happiness; other exogenous factors, were controlled.ResultsThe results show that among the respondents, mountain indigenous peoples, females, the elderly and those who are healthier, wealthier, highly educated, possessing western beliefs, and are more likely to be happy, compared to their counterparts. As expected, the results reveal that the likelihood of being happy is higher for those who have received medical benefits, as well as those persons without housing problems or financial difficulties, compared to their excluded counterparts. However, no significant association is found between happiness and some social exclusion domains, such as child and youth benefits, and unemployment benefits.ConclusionsThe disengagement of the indigenous peoples in mainstream society, with respect to the accessibility of welfare provisions, is a crucial element in regard to social exclusion and happiness. Several policy implications for the social sustainability of indigenous peoples can be inferred from these findings. For example, providing a mobile clinical tour, on-site health counseling, or homecare service can contribute to the removal of institutional and geographic barriers to medical welfare provisions for the mountain indigenes. Moreover, the government may devote more welfare resources to assist indigenous families and tribal communities to develop their own social safety net, instead of the individual-oriented welfare provisions.     

Molecular characterization of an anther-preferential gene from rice

Expression levels of anther-expressed genes in rice were estimated by plaque hybridization. A total of 33 cDNAs, isolated randomly from an anther-enriched cDNA library, were used as probes to hybridize both anther and leaf cDNAs. The expression level of individual cDNA clones was then estimated by counting the number of plaques hybridized to each probe. Based on abundance patterns that appeared in both anther and leaf cDNA libraries, the clones were classified into three groups. This classification showed that the majority of the clones (one group) exhibited expression in both cDNA libraries at almost equal frequency. The other two groups showed either low or no expression in the leaf cDNA library. Among the cDNA clones,RA1003 (detected only in the anther cDNA library) was selected and further characterized at the molecular level. Consistent with the results of the plaque hybridization experiment, northern blot analysis also revealed no gene expression in vegetative organs, leaves, or roots. However, expression was high in the flowers, especially in the anthers. Detailed molecular studies of the gene are also described and discussed here.     

Molecular and cellular characterization of an AT-hook protein from Leishmania

AT-rich DNA, and the proteins that bind it (AT-hook proteins), modulate chromosome structure and function in most eukaryotes. Unlike other trypanosomatids, the genome of Leishmania species is unusually GC-rich, and the regulation of Leishmania chromosome structure, replication, partitioning is not fully understood. Because AT-hook proteins modulate these functions in other eukaryotes, we examined whether AT-hook proteins are encoded in the Leishmania genome, to test their potential functions. Several Leishmania ORFs predicted to be AT-hook proteins were identified using in silico approaches based on sequences shared between eukaryotic AT-hook proteins. We have used biochemical, molecular and cellular techniques to characterize the L. amazonensis ortholog of the L. major protein LmjF06.0720, a potential AT-hook protein that is highly conserved in Leishmania species. Using a novel fusion between the AT-hook domain encoded by LmjF06.0720 and a herpesviral protein, we have demonstrated that LmjF06.0720 functions as an AT-hook protein in mammalian cells. Further, as observed for mammalian and viral AT-hook proteins, the AT-hook domains of LmjF06.0720 bind specific regions of condensed mammalian metaphase chromosomes, and support the licensed replication of DNA in mammalian cells. LmjF06.0720 is nuclear in Leishmania, and this localization is disrupted upon exposure to drugs that displace AT-hook proteins from AT-rich DNA. Coincidentally, these drugs dramatically alter the cellular physiology of Leishmania promastigotes. Finally, we have devised a novel peptido-mimetic agent derived from the sequence of LmjF06.0720 that blocks the proliferation of Leishmania promastigotes, and lowers amastigote parasitic burden in infected macrophages. Our results indicate that AT-hook proteins are critical for the normal biology of Leishmania. In addition, we have described a simple technique to examine the function of Leishmania chromatin-binding proteins in a eukaryotic context amenable to studying chromosome structure and function. Lastly, we demonstrate the therapeutic potential of compounds directed against AT-hook proteins in Leishmania.