Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the thermodynamic cost as a key physical constraint in the morphogen profile formation in Drosophila development.

TOROPETSKY UEZD IN THE MIDDLE AGES IN RUSSIAN HISTORIOGRAPHY: FACTORS OF FORMATION OF TERRITORIAL-ADMINISTRATIVE DIVISION AND SETTLEMENT

Статья посвящена особенностям формирования территориально-административной структуры территории Торопецкого уезда в трудах отечественных историков. Пристальное внимание обращено на развитие Торопца в период его вхождения в состав Великого княжества Литовского. В этот период продолжали развиваться тенденции - налоговые, политические и промысловые - древнерусского периода. Среди факторов, оказавших влияние на формирование территориально-административного деления и поселенческой структуры, выделены периферийное положение Торопца, его статус господарского населенного пункта, прямой сбор налогов и одновременно сохранение относительной самостоятельности, что вызвало споры в отечественной историографии. В историографии отмечается также вовлеченность населения в промысловую деятельность, что повлияло на формирование особых территорий - перевар - в Торопецком уезде. Выявлена также специфическая организация поселенческой структуры в виде гнезд поселений. The article is devoted to the characteristic of the formation of the territorial-administrative structure of the territory of Toropetsky uezd in Russian historiography. Much attention is given to the development of Toropets as a part of Lithuania, it was continuing to develop the taxing, political and working tendencies of ancient Russia. Among the factors that have influenced on the formation of the territorial-administrative division and settlement structure, there are the boundary position of Toropets, its status as a Grand Duke’s settlement, direct tax collection and at the same time the preservation of relative independence, which caused controversy in Russian historiography. In historiography there is also the engagement of people in forest bee-keeping that have influenced on the formation of special territories - perevaras - in Toropetsky uezd. The specific organization of the settlement structure in the form of settlement nests is also revealed.

Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries growing into macroscopic structures through animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. To establish accurate boundaries, the morphogen concentration which thresholds the expression of target gene at the boundary should be precise enough, exhibiting large gradient and small fluctuations. Producing more morphogens would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-degradation model of morphogen profile formation, the morphogens synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise morphogen profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source, so that the boundary is formed at the position where the morphogen concentration is ~10% of the value at the source. Remarkably, we find that the well characterized morphogens that pattern the fruit fly embryo and wing imaginal disk form profiles with nearly optimal λ, which underscores the thermodynamic cost as a key physical constraint in the morphogen profile formation.

Reasons for the High Electrical Conductivity of Bismuth Ferrite and Ways to Minimize It

The reasons for the high electrical conductivity of bismuth ferrite due to its natural composite structure, structural non-stoichiometry, redox processes, and the boundary position in the perovskite family have been considered. It has been shown that it is possible to significantly (2–3 orders of magnitude) reduce the conductivity of BiFeO3 by introducing large-sized ions of rare-earth elements (REE: La, Pr, Nd, Sm, Eu, Gd with 0.94 ≤ R¯ ≤ 1.04 Å) in amounts of up to 10 mol %. An interpretation of the observed effects has been given. A consideration about the appropriateness of taking into account the presented results when developing devices using materials of the BiFeO3/REE type has been expressed.

A Simulation Study on Reducing the Grain Boundary Position Dependency in Tunneling Thin-Film Transistors Using a Wide Tunneling Area

In this paper, we confirmed the effect of the grain boundary position dependency on short channel poly-Si Tunneling TFTs using technology computer aided design (TCAD) simulation. The simulation results show that the grain boundary (GB) in the channel affects the tunneling barrier and thus, produces variations in the electrical characteristics of the device such as the Vth and off-current. In the case of tunneling TFTs, the characteristics of the entire device are determined by the band to band tunneling (BTBT) currents occurring in very limited regions. In this study, we proposed that a TFT device requires a wider BTBT region because this limited region worsens the variations in the electrical characteristics of the TFT device. Two additional methods were proposed, one using vertical BTBT over a wide area through an additional poly-Si layer deposition and one widening the BTBT area through tilting implantation without an additional deposition process. The simulation results show that the variation of Vth is reduced to 10% through the extension of the BTBT area.

Development of Scanning Line Tool Path Generation Algorithm Using Boundary Position Information of Approximate Polyhedron of Complex Molds

In the manufacturing industry, molds are required for mass production operations, and the industry’s recent small lot, multi-product production systems call for such molds to be made by NC machine tools in short periods of time. The tool path point coordinates of NC machine tools are derived by geometric computations, which are used in turn to derive the polyhedron-approximated mold surface and the contact positions of the tool. In the conventional method, however, placing surplus tool path points on the planar section makes it difficult to acquire the boundary position coordinate values in the vicinity of the boundaries of the polyhedrons that constitute the curved surface, resulting in errors in the path point coordinates for the polyhedron-approximated shape of the mold surface. In this study, therefore, we have developed CAM algorithms that can reduce the tool path errors and suppress the number of tool path points by not deriving the path point coordinates in the linearly approximated section. This is done by using the boundary information of the approximate polyhedrons that constitute the concave section of the mold model.