LED strip driver using Standalone atmega823 and MOSFETs
Your breadboard is missing basic components that are on the Uno.


Connect all the power and Gnd pins on the 328P.
Add 0.1uF caps from VCC, AVCC, and Aref (if making analog measurements).
Add a 10uF to 100uF cap from Vcc to Gnd on the incoming 5V power rail.
Add 10K pullup resistor from Reset pin to Vcc.
Make sure the crystal caps are 22pF cap (18, 20, 22, in that range). Folks have been known to use much larger, which keeps the crystal from oscillating.
Add current limit resistor to the LED cathode pins (unless it is just used to represent the LED strip in the drawing).
Add small current limit resistor between the 3 328 IO pins and the MOSFETs gate. I calculate it by treating the gate as a capacitor connected to Gnd that needs to be charged up, and you need to limit that charge current to a safe level. 5V/35mA = 142 ohm, so a 150 ohm resistor is good to protect the 328 pin. (and once high, to discharge a cap that has been charged to 5V, same math applies).
Make sure you have N-MOSFETs that will turn fully on with a 4.5 to 5V gate signal.  I was using AOI514 on my boards, but that package has been obsoleted, so now I use AOD514, in a SMD package. Very low Rds, 0.0085 ohm typical to  0.012 ohm max with Vgs 4.5V and up to 20A if properly heat-sinked, altho won't need much at low currents. P = I^2 x R, so at 2A and 12mOhm P = 48mW, which is the range I'm designing for a lot of times. Even at 4A, the Power dissipated by the MOSFET is just 192mW.