At what point do scientists consider something sentient vs random and/or genetic?
if you have 300 neurons and 10 of them can put you in a depressed state, you are a sad eukariote.

To compare the logic gates of a worm and a mouse? which one is sentient? a slug literally has 10k neurons and a fly has 250k. that would make a slug 25 time sless sentient than a human, and a dog less sentient than a human, but a human is equally as sentient as a dog so numerically there may be now lower bounds. 

Logic Gates are electronic switches which provide routing for AND/OR/NOT/EQUALS of data types, or objects. They come into existence when you have the first cilia and sensory cells. 20 nerves are a signal routing engine, logic system.

A neuron can roughly represented by 4-8 transistors, and a logic gate is a simple transistor routing/instruction, so a worm has about 2000 logic gate equivalents. https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons   

A logic gate is digital, a brain is analogue, no software, , so you inadvertantly weave smoke and mirrors to clarify your question. 

The question evokes electrical sentience, synapses are electrochemical, slower than electricity and can varied in many ways chemically, and they are self organizing.

feeling, aware and knowing (reductionism of sentience) are much more debated topics in science. Relative to random and genetic logic gates for intelligence, that's unclear and you are discussing free will and decision (philosophy), intelligence has unclear relation to sentience/emotion.

Your question is confusing a vast range of scientific measures by using the term sentience, which is rarely used in science. Scientists write informally about sentience as an ethical issue based on their experience, but there's only fringe research on animal sentience. https://scholar.google.fr/scholar?hl=en&amp;as_sdt=0%2C5&amp;q=sentience+fish&amp;btnG=

Animal psychology is a scientific topic, and sentience is metaphysical, it means feeling, aware and knowing, it's incommensurate and imprecise.

So scientists don't consider there to be such a point of sentience. They measure certain markers of sentience, such as 

self awareness, 

stress response, 

emotional queues, 

counting, 

comparing,

memory, 

puzzle solving, 

social behaviour, 

hormones, that kind of thing. 

There are perhaps a 2 publications about sentience in fish, none about lizards or insects, and there are thousands of books and opinions about sentience in insects and other animals.

The brain increases in size from a dozens to billions of neurons. So the progression is in stages, so awareness is likely to be a complex series of steps.

A good animal psychologist can give you an entire book about the onsent of emotions and knowing in animals.