I always wondered why gametes from two different species dont fuse together to form an offspring. eg a donkey (sperm) and a female dog (egg)
I know this is not possible but I'm just curious.
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Daniel's answer excellently explains the issue in an understandable fashion, though you may have been looking for a more cell biological approach.
According to Immunological aspects of sperm receptors on the zona pellucida of mammalian eggs, 1976, Dunbar & Shivers, the egg cell has a receptor construction which is necessary for the sperm to attach. If the receptor is too different from what the sperm is built for (which will be the case in different species), it will not be able to attach and fertilise the egg.
The biological environment in every cell and tissue of your body is an extremely complex, tightly controlled system. There are tens of thousands of genes in a typical eukaryotic genome, and depending on tissue types and environmental conditions, these genes are turned on and off in a very controlled manner. There is regulation at every point in the flow of genetic information: nucleosome disruption to expose DNA; RNA transcription from the DNA; protein translation from the RNA; and in some cases, additional modifications of proteins or intermediate mRNAs. At early stages in development, regulation of RNA and protein levels is even more crucial than, say, when an organism is fully developed and healthy.
All living organisms share some basic building blocks--DNA, RNA, and proteins work pretty much the same in all of life (there are a few rare variations of the genetic code but the basic premise is identical). However, the way that specific genes, transcripts, and proteins work together to sustain life varies widely between different organisms.
For a very rough analogy, imagine you want to bake a batch of cookies. Then consider the three following scenarios.
The first example we can relate to two individuals of the same species mating. Of course there is natural variation in the population, but this doesn't typically lead to lethality during development. The second example we can relate to individuals of two related species (such as a horse and a donkey). Sometimes these matings can produce viable offspring, although these offspring are often sterile. The third example we can relate to individuals of two very divergent species (such as donkey and dog in your original question). The biological systems inside donkeys are just so different from those inside dogs that this mating cannot produce a viable offspring.
Admittedly this is a rough analogy, but hopefully is sheds some light on the issue.
Often, they do fuse together but the chromosome pairing is not precise enough to guarantee faithful cell division without loss of genetic material. Consider for example a simple inversion of one large part of a chromosome. In a closely related species that does not have this inversion, either the inverted part pairs or the non-inverted ends pair, but never the whole chromosome. That leads to strand-breaks and loss of large amounts of genetic material. That's an easy event for speciation, since it does not disrupt much. Only the ends where the inverted piece joins has two disruption. So, maximally two genes might be broken, but the chromosomes modified in this way won't pair.
I can answer this for mammals. The mammalian oocyte (egg) is surrounded by a layer called the zona pellucida. There are three well-characterized proteins in this layer, called ZP1, ZP2 and ZP3 (not very imaginative, I know). I don't know much about ZP1 but ZP2 and ZP3 are involved in fertilization. The sperm's outer surface has receptors for ZP2 and ZP3. Part of the 'zona reaction') to prevent fertilization by more than one sperm) involves destruction of these sperm receptors. The ZP proteins are species-specific, meaning that ZP receptors on, say, human sperm, would not recognize ZP2, ZP3 on the zona of hamster eggs.
There is a test that was used in fertility assessments of human sperm, checking their ability to fertilize an egg. Human eggs are kind of difficult to come by, so they developed a test based on the ability of a human patient's sperm to fertilize a hamster egg. For that to work, they had to first remove the zona from the hamster egg, so sperm had direct access to the egg membrane.
This might not be freely available, but here is a link to an article: https://humrep.oxfordjournals.org/content/13/3/624.full.pdf
There is also a brief wikipedia page about this test.