the running of the proteins is not by gravity. They run due to the negative charges they get when they are surrounded by SDS. In principle you can do it horizontally, but then you will have problems using different buffers for the stacking and separating cuvettes (if you do not want them to mix when they are horizontally.
the reason why we run SDS-PAGE in vertical position is due to gravity only in respect of sample loading and because preparation of separation and stacking gel is not possible in horizontal position. Another reason is that you want to run your electric current only through the gel, which is usually not the case for agarose gels, were the gels are simply submerged in your running buffer. Another important point, as you already metioned is that the gel is very thin gel compared to agarose DNA gels and in horizontal position you could only load tiny amounts of sample.
@Ahmet DNA is by usually far bigger than proteins a 100bp dsDNA has a appr. molecular weight of more than 60kDa!!! A common sized plasmid with 3000bp has a calculated molecular weight of 1.853.876 Da
the running of the proteins is not by gravity. They run due to the negative charges they get when they are surrounded by SDS. In principle you can do it horizontally, but then you will have problems using different buffers for the stacking and separating cuvettes (if you do not want them to mix when they are horizontally.
The principle of SDS-PAGE is just that the proteins are separated based on size. One can also run it horizontally, but, the standard gel equipments available in market are designed in such a way that it is run vertically. As some of the researchers have pointed out, one will face problems with buffers spillage and so on if you run it horizontally.
One can also design some horizontal SDS-PAGE, but, it would not have practical applications, as the current vertical ones give you the desired result.
Remember, research is all about arriving at the answer traversing the least distant path.
If you can load the samples horizontally, even upsite down vertically, into each well you can run the electrophoresis. The problem will be whether all your proteins will follow the order and enter into the gel. Straight vertical can at least guarantee most of the samples will enter into the gel.
Actually the only reason we do this is dictated by in house made gradient gels or gels using a stacking layer. On the commercial market are multiple miniaturized systems available (with and without stacking gel) that run SDS page horizontally.
It's purely for simplicity of loading and design of tanks. There are horizontal SDS rigs like the BioRAD Protean Plus dodeca cell, they're more awkward to set up but the pay off is running more gels in a run. Because the sample loading end of the gel and the far end of the gel need to be held at difference charges with the buffers kept separate, sealing the gels into the tank can be fiddly. So, in essence, horizontal is possible (electric charge drives the molecules) but fiddly (liquids like to flow down/across thanks to gravity).
I strongly agree with the above discussed points. But, I would like to add that main reason for running SDS-PAGE in vertical position is to avoid the oxidation process. Polymerization is initiated by ammonium persulfate and TEMED. TEMED accelerates the rate of formation of free radicals from persulfate and these in turn catalyze polymerization. The persulfate free radicals convert acrylamide monomers to free radicals which react with unactivated monomers to begin the polymerization chain reaction. The reaction may therefore be inhibited by any element or compound that serves as a free radical trap. Oxygen is such an inhibitor. Oxygen, present in the air, dissolved in gel solutions, or adsorbed to the surfaces of plastic, rubber, etc., will inhibit, and in extreme cases prevent, acrylamide polymerization.
It is true that oxygen can inhibit polymerization, but once the gel is polymerized, oxygen has little effect. Thus excluding oxygen is important for gel polymerization, but as long as oxygen is excluded, the gel can be successfully poured in a horizontal position. I once saw a graduate student pour a polyacrylamide gel horizontally on one plate as is done with agarose gels. He did the pouring in a deep tray that had liquid nitrogen in the bottom. The evaporating N2 excluded the air (and oxygen) and polymerization of the gel was successful. Also note that the polymerization arguments do not address why SDS-PAGE gels are RUN in the vertical position.