Single line equilibria notation
...equilibria symbol which is one line rather than two with 'half arrows' at either end


I'm pretty confident you mean "⥋" arrow within the reaction scheme for enzyme $\ce{E}$ and inhibitor $\ce{I}$ which I tried to recreate from your description:

$$\ce{E + I ⥋ \underset{\rm loose\\bond}{EI} &lt;=&gt; \underset{\rm strong\\bond}{EI'}}$$

I've seen this arrow in literature before, and in general it's been also utilized to denote equilibrium. This notation is not officially supported by IUPAC standards. However, there is a couple of references tangentially mentioning it.

From the article "The Chemical Equation Part I: Simple Reactions" [1, p. 189] (emphasis mine):


  Sometimes reactants interact quickly, but the reaction never goes to completion because the reverse reaction is competing with the forward reaction, and the system ends up in a state of chemical equilibrium. A pair of arrows pointing in both directions indicates an equilibrium system, but the second arrow need not be there. Even when two arrows are used, the equation still cannot identify the point of equilibrium.


There is also a recent outstandingly well-written review with the title that speaks for itself: "Chemistry: A Panoply of Arrows" [2, p. 592], which pretty much says the same (emphasis mine):


  Van't Hoff's double arrow was modified in 1902 by Hugh Marshall,... who removed the inner barb of each arrow. This created the half-headed double arrows, ⇌, which have since been further simplified to ⥋. In justifying his proposal, he noted that single arrows were being used in organic chemistry
  “to indicate merely the stages and methods by which a substance can be produced from some other substance as a starting point. In such cases, as no attention is paid by the bye products (sic), there is nothing of the nature of an equation
  involved.” 


My humble opinion is that authors' intent was to visually separate those two processes, e.g. due to exceptional difference in rates, or maybe they wanted to denote conformational change aside from the chemical equilibrium.

Notes


"⥋" arrow belongs to the Supplemental Arrows-B Unicode block under the name "Left barb down right barb up harpoon" and is invoked via U+294B.  
This and many other symbols you are having troubles identifying can be recognized by services like Shapecatcher or Detexify.  
I also asked a question on Mathematics.SX hoping that someone could provide more definitive answer regarding the proper usage of this arrow (no answer yet).


References


Kolb, D. Journal of Chemical Education 1978, 55 (3), 184. DOI: 10.1021/ed055p184.  
Alvarez, S. Angewandte Chemie International Edition 2012, 51 (3), 590–600. DOI: 10.1002/anie.201101767.