The banking system doesn't really operate as described in this thread. It is much more bizarre than many think (at least what I thought)
A "bank" is strictly defined as an institution with access to the Fed and there are indeed reserve requirements which can be adjusted theoretically controlling lending.
However, the "actual" market mechanisms used to control banking are driven by other factors. For one thing, excess reserves at one institution are generally made available to other banks using overnight lending. This doesn't change the Fractional Reserve aggregate but its important when considering other system dynamics such as government spending.
Essentially, what happens (and this gets mind blowing pretty quickly) is the government spends money which credits bank accounts -> increases excess reserves which puts downward pressure on overnight rates (yup, you read that right, government spending decreases interest rates). When the rates fall below target, the Fed sells bonds and participates in other "open market" operations... which decreases liquidity (sops up excess reserves) and pushes rates up.
In short, reserves are available irrespective of private deposits at an institution given the overnight lending mechanism which is driven by excess reserves which is driven by government spending which is controlled by selling treasuries.
So, the auction of treasuries are in response to interest rate issues. From an external perspective, clearly, when the government spends in excess of revenue, its gonna need to sell bonds... but the actual dynamics are far more subtle and why things like "money supply" are also things which need to be controlled as opposed to simply dictating money multipliers through the bank reserve requirement.
All this relates to the "shadow banking" system as well. While non-banks don't have access to the Fed window, they certainly have access to credit. They can borrow at rates related to those available to regular banks (sometimes the same rate or marginally higher) and lend - invest.
In recent years, these shadow institutions have played a much larger role as lenders but the Fed has no direct control over these institutions through reserve requirements etc. Therefore, the control is indirect, again through debt issuance.
Where things get very tricky is during panics as the Fed can't intervene directly with the shadow banking system... information asymmetry causes a freeze in credit flows which can trigger cascading defaults even if there is no "actual" problem.
BTW, this is where the naked short sale game is played and how Bear and Lehman were taken down. Naked short selling is much more sinister than has been portrayed... but I digress.
(and I don't really understand the whole thing yet... but it sure ain't Fractional Banking like I thought it was)
-glenn