Detachment, Futile Cycling and Nucleotide Pocket Collapse in Myosin-V Stepping

Myosin-V is a highly processive dimeric protein that walks with 36nm steps along actin tracks, powered by coordinated ATP hydrolysis reactions in the two myosin heads. No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run-length with [ADP], [ATP] and external forcing. In particular, a result that has eluded all theoretical studies based upon rigorous physical chemistry is that run length decreases with both increasing [ADP] and [ATP]. We systematically analyse which mechanisms in existing models reproduce which experimental trends and use this information to guide the development of models that can reproduce them all. We formulate models as reaction networks between distinct mechanochemical states with energetically determined transition rates. For each network architecture, we compare predictions for velocity and run length to a subset of experimentally measured values, and fit unknown parameters using a bespoke MCSA optimization routine. Finally we determine which experimental trends are replicated by the best-fit model for each architecture. Only two models capture them all: one involving [ADP]-dependent mechanical detachment, and another including [ADP]-dependent futile cycling and nucleotide pocket collapse. Comparing model-predicted and experimentally observed kinetic transition rates favors the latter.Comment: 11 pages, 5 figures, 6 table

Synergistic Activation of RD29A Via Integration of Salinity Stress and Abscisic Acid in Arabidopsis thaliana.

Plants perceive information from the surroundings and elicit appropriate molecular responses. How plants dynamically respond to combinations of external inputs is yet to be revealed, despite the detailed current knowledge of intracellular signaling pathways. We measured dynamics of Response-to-Dehydration 29A (RD29A) expression induced by single or combined NaCl and ABA treatments in Arabidopsis thaliana. RD29A expression in response to a combination of NaCl and ABA leads to unique dynamic behavior that cannot be explained by the sum of responses to individual NaCl and ABA. To explore the potential mechanisms responsible for the observed synergistic response, we developed a mathematical model of the DREB2 and AREB pathways based on existing knowledge, where NaCl and ABA act as the cognate inputs, respectively, and examined various system structures with cross-input modulation, where non-cognate input affects expression of the genes involved in adjacent signaling pathways. The results from the analysis of system structures, combined with the insights from microarray expression profiles and model-guided experiments, predicted that synergistic activation of RD29A originates from enhancement of DREB2 activity by ABA. Our analysis of RD29A expression profiles demonstrates that a simple mathematical model can be used to extract information from temporal dynamics induced by combinatorial stimuli and produce experimentally testable hypotheses

Discrete Stochastic Models of Molecular Motor Stepping Cycles.

A molecular motor is the nano-scale combustion engine of the cell: it uses a chemical reaction to drive motion. These proteins are fundamental to many cellular processes such as intracellular transport or gene transcription and understanding their behaviour is vital in understanding how we all function. There exist many different types of molecular motor, in this work I am concerned with stepping motors that walk hand-over-hand along a track within a cell. Experiments imply how molecular motors function but in order to describe this precisely one uses the language of mathematics. As motors are small and difficult to observe there is controversy about their movement and thus many competing descriptions, or models, exist. This work focuses on creating and applying general methods to compare the fit to experimental data of different models of the motor myosin-V and its stepping cycles. A review of existing theoretical and experimental work on molecular motors is conducted with emphasis on one type: myosin-V (Chapter 1). Extensions of existing theoretical methods are discussed (Chapter 2) and a novel method for calculating experimentally measurable quantities of molecular motors is presented (Chapter 3). A framework to compare competing models of myosin-V is described in Chapter 4 that allows one to identify mechanisms that enable models to reproduce experimentally observed behaviour. In Chapter 5 a set of models for myosin-V is investigated to establish mechanisms compatible with experimental trends for the average velocity and run length against nucleotide concentration. Asymmetric gating, futile cycling (foot stomping) and a loss of chemical coordination within the molecule are shown to be suitable candidates. In Chapter 6 these ideas are extended to include myosin-V under external forcing. Here multiple substeps, the elastic properties of the motor and slippage along the track are demonstrated to be vital in reproducing important experimental trends

Discrete Stochastic Models of Molecular Motor Stepping Cycles.

A molecular motor is the nano-scale combustion engine of the cell: it uses a chemical reaction to drive motion. These proteins are fundamental to many cellular processes such as intracellular transport or gene transcription and understanding their behaviour is vital in understanding how we all function. There exist many different types of molecular motor, in this work I am concerned with stepping motors that walk hand-over-hand along a track within a cell. Experiments imply how molecular motors function but in order to describe this precisely one uses the language of mathematics. As motors are small and difficult to observe there is controversy about their movement and thus many competing descriptions, or models, exist. This work focuses on creating and applying general methods to compare the fit to experimental data of different models of the motor myosin-V and its stepping cycles. A review of existing theoretical and experimental work on molecular motors is conducted with emphasis on one type: myosin-V (Chapter 1). Extensions of existing theoretical methods are discussed (Chapter 2) and a novel method for calculating experimentally measurable quantities of molecular motors is presented (Chapter 3). A framework to compare competing models of myosin-V is described in Chapter 4 that allows one to identify mechanisms that enable models to reproduce experimentally observed behaviour. In Chapter 5 a set of models for myosin-V is investigated to establish mechanisms compatible with experimental trends for the average velocity and run length against nucleotide concentration. Asymmetric gating, futile cycling (foot stomping) and a loss of chemical coordination within the molecule are shown to be suitable candidates. In Chapter 6 these ideas are extended to include myosin-V under external forcing. Here multiple substeps, the elastic properties of the motor and slippage along the track are demonstrated to be vital in reproducing important experimental trends

In silico modeling of spore inhalation reveals fungal persistence following low dose exposure.

The human lung is constantly exposed to spores of the environmental mould Aspergillus fumigatus, a major opportunistic pathogen. The spectrum of resultant disease is the outcome of complex host-pathogen interactions, an integrated, quantitative understanding of which lies beyond the ethical and technical reach permitted by animal studies. Here we construct a mathematical model of spore inhalation and clearance by concerted actions of macrophages and neutrophils, and use it to derive a mechanistic understanding of pathogen clearance by the healthy, immunocompetent host. In particular, we investigated the impact of inoculum size upon outcomes of single-dose fungal exposure by simulated titrations of inoculation dose, from 10(6) to 10(2) spores. Simulated low-dose (10(2)) spore exposure, an everyday occurrence for humans, revealed a counter-intuitive prediction of fungal persistence (>3 days). The model predictions were reflected in the short-term dynamics of experimental murine exposure to fungal spores, thereby highlighting the potential of mathematical modelling for studying relevant behaviours in experimental models of fungal disease. Our model suggests that infectious outcomes can be highly dependent upon short-term dynamics of fungal exposure, which may govern occurrence of cyclic or persistent subclinical fungal colonisation of the lung following low dose spore inhalation in non-neutropenic hosts