Thermodynamic limit of the Nekrasov-type formula for E-string theory

We give a proof of the Nekrasov-type formula proposed by one of the authors for the Seiberg-Witten prepotential for the E-string theory on R^4 x T^2. We take the thermodynamic limit of the Nekrasov-type formula following the example of Nekrasov-Okounkov and reproduce the Seiberg-Witten description of the prepotential. The Seiberg-Witten curve obtained directly from the Nekrasov-type formula is of genus greater than one. We find that this curve is transformed into the known elliptic curve by a simple map. We consider the cases in which the low energy theory has E_8, E_7+A_1 or E_6+A_2 as a global symmetry.Comment: 19 pages. v2: title and footnote 1 changed, typos corrected, version to appear in JHE

Distinct predictive performance of Rac1 and Cdc42 in cell migration.

We propose a new computation-based approach for elucidating how signaling molecules are decoded in cell migration. In this approach, we performed FRET time-lapse imaging of Rac1 and Cdc42, members of Rho GTPases which are responsible for cell motility, and quantitatively identified the response functions that describe the conversion from the molecular activities to the morphological changes. Based on the identified response functions, we clarified the profiles of how the morphology spatiotemporally changes in response to local and transient activation of Rac1 and Cdc42, and found that Rac1 and Cdc42 activation triggers laterally propagating membrane protrusion. The response functions were also endowed with property of differentiator, which is beneficial for maintaining sensitivity under adaptation to the mean level of input. Using the response function, we could predict the morphological change from molecular activity, and its predictive performance provides a new quantitative measure of how much the Rho GTPases participate in the cell migration. Interestingly, we discovered distinct predictive performance of Rac1 and Cdc42 depending on the migration modes, indicating that Rac1 and Cdc42 contribute to persistent and random migration, respectively. Thus, our proposed predictive approach enabled us to uncover the hidden information processing rules of Rho GTPases in the cell migration

Quantification of Local Morphodynamics and Local GTPase Activity by Edge Evolution Tracking

Advances in time-lapse fluorescence microscopy have enabled us to directly observe dynamic cellular phenomena. Although the techniques themselves have promoted the understanding of dynamic cellular functions, the vast number of images acquired has generated a need for automated processing tools to extract statistical information. A problem underlying the analysis of time-lapse cell images is the lack of rigorous methods to extract morphodynamic properties. Here, we propose an algorithm called edge evolution tracking (EET) to quantify the relationship between local morphological changes and local fluorescence intensities around a cell edge using time-lapse microscopy images. This algorithm enables us to trace the local edge extension and contraction by defining subdivided edges and their corresponding positions in successive frames. Thus, this algorithm enables the investigation of cross-correlations between local morphological changes and local intensity of fluorescent signals by considering the time shifts. By applying EET to fluorescence resonance energy transfer images of the Rho-family GTPases Rac1, Cdc42, and RhoA, we examined the cross-correlation between the local area difference and GTPase activity. The calculated correlations changed with time-shifts as expected, but surprisingly, the peak of the correlation coefficients appeared with a 6–8 min time shift of morphological changes and preceded the Rac1 or Cdc42 activities. Our method enables the quantification of the dynamics of local morphological change and local protein activity and statistical investigation of the relationship between them by considering time shifts in the relationship. Thus, this algorithm extends the value of time-lapse imaging data to better understand dynamics of cellular function

Inoculation with Arbuscular Mycorrhizal Fungi or Crop Rotation with Mycorrhizal Plants Improves the Growth of Maize in Limed Acid Sulfate Soil

Arbuscular mycorrhizal fungi (AMF) improve the uptake of immobile mineral nutrients such as phosphate, thereby improving plant growth. In acid sulfate soil (ASS), AMF spore density is generally low which impacts root colonization and phosphate uptake. Thus, inoculation may help increase AMF colonization of crops grown in ASS. AMF spore density decreases after cultivation of a non-host crop or bare fallow. In addition, preceding crops affect the growth and yield of subsequent crops. The production of AMF inocula requires AMF-compatible plants. The objective of the present study is to elucidate the effect of preceding crops on the persistence of inoculated AMF and growth of succeeding maize under an ASS condition with lime application. Spore density of AMF after cultivation of preceding crops (soybean or job’s tears) was maintained in comparison to fallow leading to higher AMF colonization of maize and improved plant growth. Thus, maintenance of AMF spore density, either through selection of preceding crops or application of AMF inoculum, may be a viable strategy to improve maize growth in limed ASS of Thailand

Inoculation with Arbuscular Mycorrhizal Fungi or Crop Rotation with Mycorrhizal Plants Improves the Growth of Maize in Limed Acid Sulfate Soil

Arbuscular mycorrhizal fungi (AMF) improve the uptake of immobile mineral nutrients such as phosphate, thereby improving plant growth. In acid sulfate soil (ASS), AMF spore density is generally low which impacts root colonization and phosphate uptake. Thus, inoculation may help increase AMF colonization of crops grown in ASS. AMF spore density decreases after cultivation of a non-host crop or bare fallow. In addition, preceding crops affect the growth and yield of subsequent crops. The production of AMF inocula requires AMF-compatible plants. The objective of the present study is to elucidate the effect of preceding crops on the persistence of inoculated AMF and growth of succeeding maize under an ASS condition with lime application. Spore density of AMF after cultivation of preceding crops (soybean or job’s tears) was maintained in comparison to fallow leading to higher AMF colonization of maize and improved plant growth. Thus, maintenance of AMF spore density, either through selection of preceding crops or application of AMF inoculum, may be a viable strategy to improve maize growth in limed ASS of Thailand