Why are Dose response curves, as well as most biological graphs shown in semi log graphs and not normal graphs? What is the advantage of semi log graphs over regular graphs? I still haven't gotten an intuitive sense of the answer, can someone explain, maybe with a diagram?
The reason is to make it easier to determine a suitable dose from the graph. Normally, using a arithmetic scale, the response curve is a hyperbolic, with most of the information squished together in a small section of the graph. By using the log the function usually becomes somewhat sigmoid, with a relatively linear section in the transition from low-high response. This means that this dynamics in this section can be studied more carefully.
See e.g. this example (with data from https://www.idbs.com/media/396649/dose-response-comparison-example-hr.jpg), where I have reversed the x and y-axes, and used a secondary y-scale to show the log dose (so the graph is flipped compared to a normal dose-response curve). Here, the orange line shows a semi-log dose-response curve, and the blue line shows the same data using a normal arithmetic scale. Note that the orange line (log dose) should be read against the right scale and the "normal" dose against the left scale):
Here it is obvious that the normal scale doesn't give any possibility to interpret the region where the dose is effective, while this is obvious in the log graph.
The statistical modelling of these data is to some extent a separate issue though, where probit model or logit models along with data transformations are often used to analyse the data. Note also that the "usefulness" of the semilog-plot only lies in the visual presentation, and whether it will add anything depends on the dose series used in an experiment. If the doses used are not exponential (as in this example), the semilog-plot will not add much. In the statistical test of an effect the log dose is also usually not important, and I suspect (as someone not working in pharmacology) that the semilog plot is to some extent a historical artifact from the time before computer analysis of results, when the appropriate dose was determined in a more manual way (e.g. linear analysis of the middle portion of the semilog graph).
dose (conc.) response 0.00001 0.993 0.0001 1.02 0.001 3.12 0.01 6.36 0.1 31.97 1 51.2 10 75.96 100 89 1000 97.932 10000 98.8