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The steepness range of the selected waves is 0.01~0.03, with regular and random signals.
For the current study, the selection of steepness range for particular chemotactic molecules was mostly made by referencing to the literature.
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Estimated from our simulation results, the horizontal diffusion of Sema3A in the SOURCE layer was estimated to give an input concentration ranging from 1 × 10−3 to 0.05 nM for different cylinder hydrogels after 12 h diffusion, effectively built up Sema3A gradient with a steepness ranging from 1 × 10-5 to 3.6 × 10-3 μm−1 (or 0.6 8.8%).
For example, NGF gradient steepnesses ranging from 0.1% to 0.4% has been reported to induce a differential response in DRG neurite outgrowth13,30.
The experiments were executed in the domain of dimensionless wave steepness that ranged between 0.01 and 0.07 while the measured dimensionless run-up varied between 1.26 and 2.24.
The attractive axonal guidance effects from NGF appeared to be steepness-independent for the tested steepness and concentration range (Fig. 3g); significant attractive guidance was still observed for neurites in cylinders containing an NGF gradient as smooth as 0.3 × 10−3 μm−1 (p < 0.05, paired Kruskal Wallis test).
Actually, molecular concentration, gradient steepness, and neuronal responsive range are inter-correlated elements, and it is easier to dissociate gradient steepness and absolute concentration variables under relatively shallow gradients13,30.
Of these, eleven exhibit concave-up river profiles with a mean concavity of 0.64 and normalized steepness indices in the range 47.5 219.0 m0.9.
The range and steepness of the distribution were chosen following common guidelines: the range from −4 to +4 is considerable comfortable for respondents considering the number of statements (n = 35); a steeper distribution is considered appropriate for topics of higher complexity [ 16].
Sema3A is a strong chemorepulsive cue for axonal growth, but works as a chemoattractant to promote neuronal migration over a large range of gradient steepness (~1% to 9% as quantified in fractional change).
The analysis is done for the S175 container ship and a chemical tanker in head seas for a range of wave steepness and Froude numbers.
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