In the above image, I've drawn out a prototype (?) schematic for a photodiode amplifier. This is a departure from what would normally be used since I am intending on using only discrete transistors as the amplifying devices for this preamplifier stage. I would like to know how to calculate V_out/I_in given the values of R1 through R6. R1 and R3 could be changed as well.

I previously posted this in the "projects" section of this site but I believe it belongs here instead.

 

Assuming I_in is the photo-diode current, an LTspice sim gives dv/di as ~ 0.25V per uA with the component values shown :-

 

I would like to know what the relationship between I_in, V_out, and R1 thru R6 is.

 

The relationship would be quite complicated (unless you make simplifying assumptions), since the current gain of the transistors and circuit temperatue would play a role.