Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes

Kinesins are processive motor proteins that move along microtubules in a stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent experiments have investigated the coupling between the individual steps of single kinesin molecules and ATP hydrolysis, taking explicitly into account forward steps, backward steps and detachments. A theoretical study of mechanochemical coupling in kinesins, which extends the approach used successfully to describe the dynamics of conventional motor proteins, is presented. The possibility of irreversible detachments of kinesins from the microtubules is also explicitly taken into account. Using the method of first- passage times, experimental data on the mechanochemical coupling in kinesins are fully described using the simplest two-state model. It is shown that the dwell times for the kinesin to move one step forward or backward, or to dissociate irreversibly are the same, although the probabilities of these events are different. It is concluded that the current theoretical view, that only the forward motion of the motor protein molecule is coupled to ATP hydrolysis, is consistent with all available experimental observations for kinesins.Comment: Submitted to Biophysical Journa

Plasticization and antiplasticization of polymer melts diluted by low molar mass species

An analysis of glass formation for polymer melts that are diluted by structured molecular additives is derived by using the generalized entropy theory, which involves a combination of the Adam-Gibbs model and the direct computation of the configurational entropy based on a lattice model of polymer melts that includes monomer structural effects. Antiplasticization is accompanied by a "toughening" of the glass mixture relative to the pure polymer, and this effect is found to occur when the diluents are small species with strongly attractive interactions with the polymer matrix. Plasticization leads to a decreased glass transition temperature T_g and a "softening" of the fragile host polymer in the glass state. Plasticization is prompted by small additives with weakly attractive interactions with the polymer matrix. The shifts in T_g of polystyrene diluted by fully flexible short oligomers are evaluated from the computations, along with the relative changes in the isothermal compressibility at T_g to characterize the extent to which the additives act as antiplasticizers or plasticizers. The theory predicts that a decreased fragility can accompany both antiplasticization and plasticization of the glass by molecular additives. The general reduction in the T_g and fragility of polymers by these molecular additives is rationalized by analyzing the influence of the diluent's properties (cohesive energy, chain length, and stiffness) on glass formation in diluted polymer melts. The description of glass formation at fixed temperature that is induced upon change the fluid composition directly implies the Angell equation for the structural relaxation time as function of the polymer concentration, and the computed "zero mobility concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure

Velocity and processivity of helicase unwinding of double-stranded nucleic acids

Helicases are molecular motors which unwind double-stranded nucleic acids (dsNA) in cells. Many helicases move with directional bias on single-stranded (ss) nucleic acids, and couple their directional translocation to strand separation. A model of the coupling between translocation and unwinding uses an interaction potential to represent passive and active helicase mechanisms. A passive helicase must wait for thermal fluctuations to open dsNA base pairs before it can advance and inhibit NA closing. An active helicase directly destabilizes dsNA base pairs, accelerating the opening rate. Here we extend this model to include helicase unbinding from the nucleic-acid strand. The helicase processivity depends on the form of the interaction potential. A passive helicase has a mean attachment time which does not change between ss translocation and ds unwinding, while an active helicase in general shows a decrease in attachment time during unwinding relative to ss translocation. In addition, we describe how helicase unwinding velocity and processivity vary if the base-pair binding free energy is changed.Comment: To appear in special issue on molecular motors, Journal of Physics - Condensed Matte

Rate Equations for Graphs

In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics. Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at https://rhz.github.io/fragger. We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.Comment: to be presented at the 18th International Conference on Computational Methods in Systems Biology (CMSB 2020

Synchronous Versus Metachronous Metastatic Disease: Impact of Time to Metastasis on Patient Outcome-Results from the International Metastatic Renal Cell Carcinoma Database Consortium

BACKGROUND: Patients with metastatic renal cell carcinoma (mRCC) may present with primary metastases (synchronous disease) or develop metastases during follow-up (metachronous disease). The impact of time to metastasis on patient outcome is poorly characterised. OBJECTIVE: To characterise overall survival (OS) and time to treatment failure (TTF) based on time to metastasis in mRCC patients treated with targeted therapy (tyrosine kinase inhibitors [TKIs]). DESIGN, SETTING, AND PARTICIPANTS: We used the International Metastatic Renal Cell Carcinoma Database Consortium (IMDC) to compare synchronous (metastases within ≤3 mo of initial diagnosis of cancer) versus metachronous disease (evaluated by >3-12 mo, >1-2 yr, >2-7 yr, and >7 yr intervals). OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: OS and TFF were assessed using Kaplan-Meier curves. Cox multivariable regressions analyses (MVAs) were adjusted for baseline factors. RESULTS AND LIMITATIONS: Of 7386 patients with mRCC treated with first-line TKIs, 3906 (53%) and 3480 (47%) had synchronous and metachronous metastasis, respectively. More patients with synchronous versus metachronous disease had higher T stage (T1-2: 19% vs 34%), N1 disease (21% vs 6%), presence of sarcomatoid differentiation (15.8% vs 7.9%), Karnofsky performance status <80 (25.9% vs 15.1%), anaemia (62.5% vs 42.3%), elevated neutrophils (18.9% vs 10.9%), elevated platelets (21.6% vs 11.4%), bone metastases (40.4% vs 29.8%), and IMDC poor risk (40.6% vs 11.3%). Synchronous versus metachronous disease by intervals >3-12 mo, >1-2 yr, >2-7 yr, and >7 yr correlated with poor TTF (5.6 mo vs 7.3, 8.0, 10.8, and 13.3 mo, p <  0.0001) and poor OS (median 16.7 mo vs 23.8, 30.2, 34.8, and 41.7 mo, p <  0.0001). In MVAs, the adjusted hazard ratios (95% confidence intervals) were 1.00 (reference), 0.98 (0.90-1.06), 0.81 (0.73-0.91), 0.74 (0.68-0.81), and 0.60 (0.54-0.67), respectively, for OS (p <  0.0001), and 1.00 (reference), 0.99 (0.92-1.06), 0.98 (0.90-1.07), 0.83 (0.77-0.89), and 0.66 (0.60-0.72), respectively, for TTF (p <  0.0001). Data were collected retrospectively. CONCLUSIONS: Timing of metastases after initial RCC diagnosis may impact the outcomes from targeted therapy in mRCC. PATIENT SUMMARY: We looked at the impact of the timing of metastatic outbreak on survival outcomes in kidney cancer patients treated with targeted therapy. We found that the longer time to metastatic development was associated with improved outcome

Rate Equations for Graphs

International audienceIn this paper, we combine ideas from two different scientifictraditions: 1) graph transformation systems (GTSs) stemming from thetheory of formal languages and concurrency, and 2) mean field approx-imations (MFAs), a collection of approximation techniques ubiquitousin the study of complex dynamics. Using existing tools from algebraicgraph rewriting, as well as new ones, we build a framework which gener-ates rate equations for stochastic GTSs and from which one can deriveMFAs of any order (no longer limited to the humanly computable). Theprocedure for deriving rate equations and their approximations can beautomated. An implementation and example models are available onlineat https://rhz.github.io/fragger. We apply our techniques and tools toderive an expression for the mean velocity of a two-legged walker proteinon DNA

A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations

We study mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we develop a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.Comment: 72 pages, 18 figures, Accepted to: Reports on Progress in Physic

Individual Actin Filaments in a Microfluidic Flow Reveal the Mechanism of ATP Hydrolysis and Give Insight Into the Properties of Profilin

A novel microfluidic approach allows the analysis of the dynamics of individual actin filaments, revealing both their local ADP/ADP-Pi-actin composition and that Pi release is a random mechanism