Eukaryotic cells can detect the direction of a chemoattractant gradient precisely by generating intracellular gradients of signaling molecules that mirror the extracellular gradient ? an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in spatially-graded stimuli, the internal gradients of the signaling molecules at steady state reflect the relative steepness -- rather than the absolute concentration -- of the chemoattractant  along the cell body. Second, upon a spatially homogeneous temporal increase in the chemoattractant concentration, the signaling molecule is transiently activated such that the response magnitude is determined by the ratio of the change in the input stimuli before and after the increase . However, the underlying mechanisms that endow the system with these response properties remain elusive. Here, by adopting a widely used modeling framework of directional sensing, i.e., local excitation and global inhibition (LEGI), we propose the hypothesis that the two scaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model identify two different types of scale invariance , each of which is responsible for the two response properties. Our hypothesis leads to an experimentally testable prediction that a system with both types of invariance detects the relative steepness even in spatio-temporal gradient stimuli such as waves . Furthermore, we show that such behavior is independent of specific network topologies as long as the scale invariance holds, demonstrating the generic relationship between the scale invariance and the response properties .
Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient - an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness , rather than the absolute concentration , of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels . However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts , each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients . Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies .
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respond to
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precisely by generating
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mirror the extracellular gradient ?
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magnitude is determined by the ratio of the change in the input stimuli before and after the increase
magnitudes are dependent on fold changes of the stimulus, not on absolute levels
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mechanisms that endow
mechanism that endows
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identify two different types of scale invariance
reveal that the invariance can be divided into two parts
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both types of invariance detects the
the invariance detects
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spatio-temporal gradient stimuli such as waves
dynamic gradient stimuli as well as in static gradients
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such behavior is independent of specific network topologies as long as the scale invariance holds, demonstrating the generic relationship between the scale invariance and the response properties
the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies