Do you feel that the demand of my supervisor is too much?
I work in theoretical mathematics. In that field, a requirement of four publications in journals of impact factor greater than 2 would stop more than 99% of students from getting a PhD thesis. (I got my PhD in 2003 and am now a tenured, "full" professor. If I'm not mistaken, I have zero publications in journals of impact factor greater than 2....but in my field we do not speak of impact factors when we talk about journal quality.)
The above paragraph is there only to tell you where I'm coming from. In fact I do not understand the logic behind such a requirement -- in particular, I don't see where the number four is coming from, and if I wanted to impose high standards on my students I would do it in terms of the quality of their work rather than the quantity. But I can't say that the demand is too much, since I am not in your field, am probably not in your country or university, and I am not working with your supervisor. Whether it is too much is mostly up to the two of you to decide, along with other members of your committee and subject to the rules of your program and university.
Is it even possible to produce 4 more journal paper in the next 3 years?
It is certainly possible for someone. I would be willing to bet at any reasonable odds that there are students in computational biology who have this many publications in this amount of time. I urge you to look in the literature of your field and see when, where and how often this occurs.
Perhaps you mean to ask whether it is possible for you. That's a really good question, though of course we are not in a position to answer it.
Is it possible to bargain the count of paper down to 3 instead of 4? If so, how should I do it?
The language of "bargaining" is not very apt, but: yes, you should certainly discuss the situation with your advisor sooner rather than later. Your advisor is setting what I think we can agree is an unusually high bar -- you mention that other students in your institute have gotten their PhD with a single paper, and he is asking for four papers. Note though that you said that that's what he wants. Many thesis advisors have high expectations for their students and try to push them to do their best work. (And the others are not very good advisors, in my opinion.) However, (i) what you want your student to do, (ii) the least they need to do to graduate and (iii) what they actually end up doing are three different things: wildly different, sometimes. Here you seem to be assuming (i) and (ii) are the same. I think that they probably are not, but they could be in your situation. The only way to find out is to ask.
Here are my specific recommendations:
Step 1: Do your research. Find out the publication records of students in your area. In particular, look at all the students who have gotten PhDs in computational biology in your institute and under your advisor. Then pick a few other institutions for comparison, including at least one that would be regarded as better. How often is it that students have four publications in IF > 2 journals before they graduate? If this happens only a small percentage of the time and/or if it almost never happens at your institute or with other students of your advisor, that's a strong clue that the constraints you've been given are aspirational...or ought to be.
Step 2: Have a serious conversation with your advisor. Show him the research you've done in Step 1 -- not confrontationally, but so that both of you will be working with the same facts. Then show him a plan of the work that you will do and the papers that you will have published by a certain time. This plan should be serious but realistic: you should be able to defend the amount of time you'll spend at any stage. Your plan should include a specific time that you want to graduate. If your plan shows you with three papers for sure and very iffy on the fourth, bring that up explicitly with your advisor.
I think it is likely that you will find that your advisor is flexible on the requirements and appreciative of the thought you've put into your future. However, it is also possible that he is absolutely intransigent and insists on more papers than you think you can reasonably write in the allotted time. Well, if that is the case, far better to have that information now rather than three years later! If you have it now, you have plenty of time to figure out how to respond to it.