There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Expression and tracking of fluorescent fusion proteins has revolutionized our understanding of basic concepts in cell biology. The protocol presented here has underpinned much of the in vivo results highlighting the dynamic nature of the plant secretory pathway. Transient transformation of tobacco leaf epidermal cells is a relatively fast technique to assess expression of genes of interest. These cells can be used to generate stable plant lines using a more time-consuming, cell culture technique. Transient expression takes from 2 to 4 days whereas stable lines are generated after approximately 2 to 4 months.

Rapid, transient expression of fluorescent fusion proteins in tobacco plants and generation of stably transformed plants.

The redox state of the chloroplast and mitochondria, the two main powerhouses of photosynthesizing eukaryotes, is maintained by a delicate balance between energy production and consumption, and affected by the need to avoid increased production of reactive oxygen species (ROS). These demands are especially critical during exposure to extreme environmental conditions, such as high light (HL) intensity, heat, drought or a combination of different environmental stresses. Under these conditions, ROS and redox cues, generated in the chloroplast and mitochondria, are essential for maintaining normal energy and metabolic fluxes, optimizing different cell functions, activating acclimation responses through retrograde signalling, and controlling whole-plant systemic signalling pathways. Regulation of the multiple redox and ROS signals in plants requires a high degree of coordination and balance between signalling and metabolic pathways in different cellular compartments. In this review, we provide an update on ROS and redox signalling in the context of abiotic stress responses, while addressing their role in retrograde regulation, systemic acquired acclimation and cellular coordination in plants.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-3040.2011.02336.x

ROS and redox signalling in the response of plants to abiotic stress

Physiological functions of mineral micronutrients (Cu, Zn, Mn, Fe, Ni, Mo, B, Cl).

Using a novel analytical tool, this study investigates the relative roles of actin, microtubules, myosin, and Golgi bodies on form and movement of the endoplasmic reticulum (ER) in tobacco (Nicotiana tabacum) leaf epidermal cells. Expression of a subset of truncated class XI myosins, which interfere with the activity of native class XI myosins, and drug-induced actin depolymerization produce a more persistent network of ER tubules and larger persistent cisternae. The treatments differentially affect two persistent size classes of cortical ER cisternae, those >0.3 μm2 and those smaller, called punctae. The punctae are not Golgi, and ER remodeling occurs in the absence of Golgi bodies. The treatments diminish the mobile fraction of ER membrane proteins but not the diffusive flow of mobile membrane proteins. The results support a model whereby ER network remodeling is coupled to the directionality but not the magnitude of membrane surface flow, and the punctae are network nodes that act as foci of actin polymerization, regulating network remodeling through exploratory tubule growth and myosin-mediated shrinkage.

Movement and Remodeling of the Endoplasmic Reticulum in Nondividing Cells of Tobacco Leaves

Gene families with multiple members are predicted to have individuals with overlapping functions. We examined all of the Arabidopsis (Arabidopsis thaliana) myosin family members for their involvement in Golgi and other organelle motility. Truncated fragments of all 17 annotated Arabidopsis myosins containing either the IQ tail or tail domains only were fused to fluorescent markers and coexpressed with a Golgi marker in two different plants. We tracked and calculated Golgi body displacement rate in the presence of all myosin truncations and found that tail fragments of myosins MYA1, MYA2, XI-C, XI-E, XI-I, and XI-K were the best inhibitors of Golgi body movement in the two plants. Tail fragments of myosins XI-B, XI-F, XI-H, and ATM1 had an inhibitory effect on Golgi bodies only in Nicotiana tabacum, while tail fragments of myosins XI-G and ATM2 had a slight effect on Golgi body motility only in Nicotiana benthamiana. The best myosin inhibitors of Golgi body motility were able to arrest mitochondrial movement too. No exclusive colocalization was found between these myosins and Golgi bodies in our system, although the excess of cytosolic signal observed could mask myosin molecules bound to the surface of the organelle. From the preserved actin filaments found in the presence of enhanced green fluorescent protein fusions of truncated myosins and the motility of myosin punctae, we conclude that global arrest of actomyosin-derived cytoplasmic streaming had not occurred. Taken together, our data suggest that the above myosins are involved, directly or indirectly, in the movement of Golgi and mitochondria in plant cells.

/pdf/a-comparative-study-of-the-involvement-of-17-arabidopsis-19tnjwujtt.pdf

A comparative study of the involvement of 17 Arabidopsis myosin family members on the motility of Golgi and other organelles.

https://radar.brookes.ac.uk/radar/file/cf691429-ea7a-488c-8725-b46cb0ef7ce9/1/Sparkes2014plant.pdf

The plant cytoskeleton, NET3C, and VAP27 mediate the link between the plasma membrane and endoplasmic reticulum

In many vacuolate plant cells, individual Golgi bodies appear to be attached to tubules of the pleiomorphic cortical endoplasmic reticulum (ER) network. Such observations culminated in the controversial mobile secretory unit hypothesis to explain transport of cargo from the ER to Golgi via Golgi attached export sites. This proposes that individual Golgi bodies and an attached-ER exit machinery move over or with the surface of the ER whilst collecting cargo for secretion. By the application of infrared laser optical traps to individual Golgi bodies within living leaf cells, we show that individual Golgi bodies can be micromanipulated to reveal their association with the ER. Golgi bodies are physically attached to ER tubules and lateral displacement of individual Golgi bodies results in the rapid growth of the attached ER tubule. Remarkably, the ER network can be remodelled in living cells simply by movement of laser trapped Golgi dragging new ER tubules through the cytoplasm and new ER anchor sites can be established. Finally, we show that trapped Golgi ripped off the ER are 'sticky' and can be docked on to and attached to ER tubules, which will again show rapid growth whilst pulled by moving Golgi.

Imogen Sparkes

Papers

Rapid, transient expression of fluorescent fusion proteins in tobacco plants and generation of stably transformed plants.

Movement and Remodeling of the Endoplasmic Reticulum in Nondividing Cells of Tobacco Leaves

A comparative study of the involvement of 17 Arabidopsis myosin family members on the motility of Golgi and other organelles.

The plant cytoskeleton, NET3C, and VAP27 mediate the link between the plasma membrane and endoplasmic reticulum

Grab a Golgi: laser trapping of Golgi bodies reveals in vivo interactions with the endoplasmic reticulum.