Chemotaxis is frequently observed in microorganisms.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
In other words, the existence of memory in the internal state makes chemotaxis possible.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
However, this is true only for short-term behavior of chemotaxis.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
All simulations for other parameters show that the elements assemble in the region x ≥ 0, that is, the chemotaxis works well for τs <∼ τ ∗ <∼ τa .
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Now, ˜τs , the threshold beyond which the (renormalized) Oosawa condition ˜τs <∼ τ ∗ is satisﬁed, is expected to give a criterion for chemotaxis.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
By changing the internal timescales τs and τa , we have examined the validity of the Oosawa condition for chemotaxis.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Whether chemotaxis works eﬃciently is determined by the Oosawa condition for both the chemical concentration ﬁeld of a stepfunction and a constant slope, and both for short- and long-term behavior.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
The fraction 0.5 indicates the absence of chemotaxis in short-term behavior.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
In contrast, response of the tumbling frequency without adaptation causes the long-term behavior of cells to be represented by a random walk, so that chemotaxis is not possible.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Clark and Grant recently reported the conditions for the internal response function R(t) to show chemotaxis.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
In general, the conditions for short- and long-term chemotaxis differ, but by imposing some type of optimization to balance the two behaviors, they were able to obtain a certain condition for the response function, which implies the existence of a form of memory in the autocorrelation function.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Our work answers the question about why chemotaxis requires dynamics.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
By assuming a class of intracellular dynamics, we have shown that chemotaxis occurs in both short- and long-term behavior without requiring an optimization condition, provided that the Oosawa condition is satisﬁed.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Because short- and long-term chemotactic behaviors are satisﬁed simultaneously, one expects that cells can choose such internal adaptation dynamics that enable eﬃcient chemotaxis for a variety of external conditions.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
Here we have demonstrated chemotaxis in the two cases: with a constant slope and with a stepwise change.
On a Condition for Intracellular Adaptive Dynamics for Chemotaxis
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