CURVAS DOSIS vs RESPUESTA
|Introducing dose-response curves |
|What is a dose-response curve? |
|Dose-response curves can be used to plot the results of many kinds of experiments. The X-axis plots concentration of a drug or |
|hormone. The Y-axis plots response, which could be almost anything. For example, the response might be enzyme activity, |
|accumulation of an intracellular second messenger, membrane potential, secretion of a hormone, heart rate or contraction of a |
|muscle. |
|The term 'dose' is often used loosely. The term 'dose' strictly only applies to experiments performed with animals or people, |
|where you administer various doses of drug. You don't know the actual concentration of drug -- you know the dose you administered.|
|However, the term 'dose-response curve' is also used more loosely to describe in vitro experiments where you apply known |
|concentrations of drugs. The term 'concentration-response curve' is a more precise label for the results of these experiments. The|

|term 'dose-response curve' is occasionally used even more loosely to refer to experiments where you vary levels of some other |
|variable, such as temperature or voltage. |
|An agonist is a drug that causes a response. If you administer various concentrations of an agonist, the dose-response curve will |
|go uphill as you go from left (low concentration) toright (high concentration). A full agonist is a drug that appears able to |
|produce the full tissue response.  A partial agonist is a drug that provokes a response, but the maximum response is less than the|
|maximum response to a full agonist. An antagonist is a drug that does not provoke a response itself, but blocks agonist-mediated |
|responses. If you vary the concentration of antagonist (in the presence of a fixed concentration of agonist), the dose-response |
|curve will run downhill. |
|The shape of dose-response curves |
|Many steps can occur between the binding of the agonist to a receptor and the production of the response. So depending on which |
|drug you use and which response you measure, dose-response curves can have almost any shape. However, in very many systems |
|dose-response curves follow a standard shape, shown below. [pic] |
|Dose-response experiments typically use 10-20 doses of agonist, approximately equally spaced on a logarithmic scale. For example |
|doses might be 1, 3, 10, 30, 100, 300, 1000, 3000, and 10000 nM. When converted to logarithms, these values are equally spaced: |
|0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0. |
|Note: The logarithm of 3 is actually 0.4771, not 0.50. The antilog of 0.5 is 3.1623. So to make the doses truly equally spaced on |
|a log scale, the concentrations ought to be 1.0, 3.1623, 10.0, 31.623 etc. |
|Since thelinkage between agonist binding and response can be very complex, any shape is possible. It seems surprising, therefore,|
|that so many dose-response curves have shapes identical to receptor binding curves. The simplest explanation is that the link |
|between receptor binding and response is direct, so response is proportional to receptor binding. However, in most systems one or |
|more second-messenger systems link receptor binding to response. For example, agonist binding activates adenylyl cyclase, which |
|creates the second-messenger cAMP. The second messenger can then bind to an effector (such as a protein kinase) and initiate a |
|response. |
|What do you expect a dose-response curve to look like if a second messenger mediates the response? If you assume that the |
|production of second messenger is proportional to receptor occupancy, the graph of agonist concentration vs. second messenger |
|concentration will have the same shape as receptor occupancy (a hyperbola if plotted on a linear scale, a sigmoid curve with a |
|slope factor of 1.0 if plotted as a semilog graph). If the second messenger works by binding to an effector, and that binding step|
|follows the law of mass action, then the graph of second messenger concentration vs. response will also have that same standard |
|shape. It isn't obvious, but Black and Leff (see The operational model of agonist action) have shown that the graph of agonist |
|concentration vs. response will also have that standard shape (provided that both binding steps follow the law of mass action). In|
|fact, it doesn't matter how many steps intervene between agonist binding and response. So longas each messenger binds to a single|
|binding site according to the law of mass action, the dose-response curve will follow the same hyperbolic/sigmoid shape as a |
|receptor binding curve. |
|The EC50 |
|A standard dose-response curve is defined by four parameters: the baseline response (Bottom), the maximum response (Top), the |
|slope, and the drug concentration that provokes a response halfway between baseline and maximum (EC50). |
|It is easy to misunderstand the definition of EC50. It is defined quite simply as the concentration of agonist that provokes a |
|response half way between the baseline (Bottom) and maximum response (Top).  It is impossible to define the EC50 until you first |
|define the baseline and maximum response. |
|Depending on how you have normalized your data, this may not be the same as the concentration that provokes a response of Y=50. |
|For example, in the example below, the data are normalized to percent of maximum response, without subtracting a baseline. The |
|baseline is about 20%, and the maximum is 100%, so the EC50 is the concentration of agonist that evokes a response of about 60% |
half way between 20% and 100%).  [pic] |
|Don't over interpret the EC50. It is simply the concentration of agonist required to provoke a response halfway between the |
|baseline and maximum responses. It is usuallynot the same as the Kd for the binding of agonist to its receptor. |
|The steepness of a dose-response curve |
|Many dose-response curves follow exactly the shape of a receptor binding curve. As shown below, 81 times more agonist is needed to|
|achieve 90% response than a 10% response. [pic] |
|Some dose-response curves however, are steeper or shallower than the standard curve. The steepness is quantified by the Hill |
|slope, also called a slope factor. A dose-response curve with a standard slope has a Hill slope of 1.0. A steeper curve has a |
|higher slope factor, and a shallower curve has a lower slope factor. If you use a single concentration of agonist and varying |
|concentrations of antagonist, the curve goes downhill and the slope factor is |

|negative pic] |
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|Fitting sigmoid dose-response curves with Prism |