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A second messenger is a small intracellular molecule or ion that relays a received signal to target proteins. Its production, release, removal or binding changes its availability after signal reception. For a cell-surface receptor, distinguish the extracellular ligand, often called the first messenger, from the intracellular second messenger. An activated relay protein is not thereby a second messenger: the term identifies small chemical mediators, rather than every downstream component of signal transduction. ^[ref]

Two examples clarify what changes. A biological cell can make cAMP from ATP; alternatively, release of stored calcium ions can raise the free calcium concentration in its cytoplasm. The latter need not increase the total calcium content of the biological cell. Availability to target proteins, not merely the total amount present, carries the message. Removal and sequestration help terminate such signals. ^{[ref] [ref]}

The experimental motivation is unusually tangible: can a hormone's effect be transferred to machinery that barely responds to the hormone itself? In Rall, Sutherland and Berthet's 1957 experiment, washed cat-liver particles were incubated with ATP and magnesium ions, with or without epinephrine and glucagon, two hormones. After five minutes at $30{}^{\circ }\mathrm{C}$, the mixtures were heated in boiling water for three minutes, chilled, and separated to remove insoluble material. Small samples of the clarified extracts were transferred to a separate soluble dog-liver preparation, again supplied with ATP and magnesium ions. The readout was the change in glycogen phosphorylase activity over five minutes, not the amount of newly synthesized protein. ^[ref]

The hormone-conditioned extract caused a larger increase in glycogen phosphorylase activity. Water, extract made without hormones, and hormones added directly to the soluble preparation produced smaller effects. These comparisons distinguish transferred activity from baseline activity, preparation effects and simple hormone carryover. ^[ref]

The inference is a transferable, heat-stable intermediary between the hormone-sensitive particles and the soluble machinery. This does not identify the intermediary merely from heat resistance, establish its direct target, or show that every hormone uses the same mechanism. Rall and Sutherland's 1958 paper reports the factor's identification as cAMP in accompanying chemical work, and follows its production from ATP. It also reports an important limit: washed heart and skeletal-muscle particles produced detectable cAMP with epinephrine under their test conditions, whereas brain particles produced similar amounts with and without it. Tissue and preparation matter. ^[ref]

The useful and beautiful separation is between recognition and execution: an extracellular ligand can control intracellular enzymes through a chemically different intermediary. Making many second messenger molecules can support signal amplification, while different target proteins give the same mediator different consequences. A second messenger identifies a mode of relaying information; its presence alone does not specify the size or direction of the response. ^[ref]

Signal amplification is an increase in a specified downstream response relative to an initiating signal. In a molecular-count description, one activated component can generate or activate many downstream molecules. Repeated catalysis by an enzyme supplies a mechanism: the enzyme remains available for another chemical reaction. Successive stages can multiply the response. For a biological example, Cooper describes the epinephrine-to-glycogen phosphorylase pathway, where production of many cAMP molecules and repeated downstream protein phosphorylation provide opportunities for signal amplification. This is an example, not a claim that every signal transduction pathway has the same stages or gain. ^[ref]

Here is a counting toy extending the example under signal transduction. Suppose $N_0$ activated receptors each activate $a=5$ distinct relay proteins during a first interval. During a subsequent interval, each relay activates $b=20$ distinct target proteins. Assume enough inactive relays and targets, no shared targets, and no loss of activity during the count. ThenFor $N_0=1$, this gives $N_1=5$ and $N_2=100$: the target-to-receptor count ratio is $100$. These are assumed integer counts, not measured rates or a universal physiological amplification factor. The intervals are sequential; the equations do not specify a time course.

Availability limits the multiplication. As a second toy assumption, let there be only $T=250$ initially inactive target proteins shared by all branches, and suppose the branches can activate distinct targets until this pool is exhausted. ThenTwo activated receptors give $200$ active targets, whereas three give $250$, not $300$. At three activated receptors, the total count ratio is $250/3\simeq 83.3$; adding a fourth activates no additional targets. Thus total output per input and the increment caused by an extra input are different notions of gain. This finite-pool rule is an illustrative bound, not an enzyme kinetics law.

Signal amplification makes a small initiating signal capable of a larger response, but it does not supply the material or energy for downstream chemical reactions. In the second messenger transfer experiment, both stages still required added ATP and magnesium ions. Counts, changes in concentration, and changes in enzyme activity are different readouts; an amplification claim should name its input, output and observation interval. ^[ref]

Signal transduction converts a detected signal into a change inside a biological cell. For chemical signals, distinguish reception by a receptor, intracellular signal transduction, and the response: altered gene expression, enzyme activity or ion channel opening, for example. A cell-surface receptor can relay a ligand's presence across a cell membrane without the ligand entering the cytoplasm. Thus a hydrophilic signal need not cross the membrane to influence the interior. See Clark, Douglas and Choi, Biology 2e, 9.2: intracellular signal propagation.

For a computed example of possible signal amplification, suppose one activated receptor activates five relay proteins, and each relay activates twenty target proteins during a chosen interval. If the targets are distinct and available, $1\times 5\times 20=100$ targets are activated. Those assumed counts illustrate multiplication, not a measured pathway or a universal gain. Actual signal transduction can branch, saturate or inhibit activity. Changes in gene expression and changes in existing enzyme activity are different responses. See Clark, Douglas and Choi, Biology 2e, 9.3: cellular responses.

Signal amplification, signaling feedback and signaling adaptation are possible properties of signal transduction, rather than requirements of every cascade. Intracellular relays can use proteins or second messengers; different biological cells can interpret the same ligand differently because they contain different receptors and relay machinery. The useful and striking idea is that recognition and response are separable: an extracellular chemical message can control many internal tasks without itself performing those tasks. See General Principles of Cell Communication.

An original experimental route to this separation appears in T. W. Rall and Earl W. Sutherland's 1958 work on cAMP. They described a heat-stable factor formed from ATP in separated biological cell preparations; it affected enzyme activity in other preparations where the initiating chemical signals had no direct effect. This helped distinguish an initial signal from a molecule carrying its effect to another target. ^[ref]