I've read that the amoeba is capable of learning. Since these protists have no nervous system, it's safe to assume that even highly simplified learning mechanisms of the Aplysia are miles off in the evolutionary distance.
How does this species learn? I would presume that there is a complicated chain of receptor mediated transcription regulation, but what are the specifics? What types of receptors does an amoeba have to sense its environs?
I'd like to know what is the reference for amoebic learning. I cannot comment directly on this, but there is some evidence for "adaptive anticipation" in both prokaryotes and single-celled Eukaryotes which do not have a nervous system.
In the case of E. coli, it has been shown that the bacteria can anticipate the environment it is about to enter. E. coli in the digestive tracts of mammals will typically be exposed to initially a lactose, and then later to a maltose environment as the bacteria pass down through the animal tract. This suggests that upon encountering a lactose environment, maltose operons are induced. I.e., upon encountering lactose, maltose is anticipated. This suggests a "genetic memory" of the sequence of sugar types where lactose is always encountered before maltose.
Further cultures (500 generations) of E. coli in the absence of maltose but in the presence of lactose reduced the maltose operon activity to negligible levels, suggesting that this is an adaptive prediction of environmental changes.
Mitchell, A et al., Adaptive Prediction of environmental changes by microorganisms, 2009, 460, 1038
In addition to the excellent response up top (by Poshpaws), one can also imagine how these systems work by looking at recent synthetic examples of single-celled organism memory.
It is possible to design various bistable switches using protein pathways, RNAi, or other means that will latch a particular state. In that way, an organism could effectively "remember" one bit of data by querying the state of the toggle.
For a specific example, see the Gardner 2000 paper [1]. It's a transcription-level circuit, that in response to a certain stimulus can latch either high or low. While the synthetic version itself is not terribly robust, one could see how in nature a highly evolved / refined circuit could maintain state and effectively serve as "memory" for a single-celled organism.
[1] Gardner, et. al 2000 "Construction of a genetic toggle switch in Escherichia coli."
The authors of The omnistat: A flexible continuous‐culture system for prolonged experimental evolution report on an experiment where they evolved Lactococcus lactis to have an anticipatory response to their environment. A culture was set up in their bioreactor, and periodically one of two weak bases was introduced: either lactate or acetate, and then, depending on the base, fresh media of fructose or galactose was introduced. The simple idea is depicted below:
1. randomly choose either:
dose with dilute acetate -> fructose comes next
dose with dilute lactate -> galactose comes next
2. go back to step 1.
The culture is continually exposed to this treatment over many days or weeks (it's not clear from their paper), during which, there is an evolutionary pressure for the bacteria to engineer a response between the weak base and future energy source. That is, a bacterium that can shift its metabolism slightly towards processing fructose faster when acetate is present will have higher fitness, and likewise of lactate/galactose.
In the end, after many rounds, the bacteria have encoded the relationship into their genes - a type of "learning" that the other answers to this question also give examples of.
