The first thing I notice about Marc Quinn is that he is much paler than I expected. It takes a moment to realise that that’s because the first, second and third times I saw his face, it was sculpted in his own blood. He has been making new versions of Self, the frozen-blood head which made his name in 1991, every five years, and each one takes nine or ten pints of blood to construct. The idea that an artist might need to sacrifice something for his art could hardly be more neatly illustrated.

The second thing I notice is that for a man who has shocked polite society with everything from a solid gold statue of Kate Moss with her ankles behind her ears to a set of sculptures of nude transsexuals and a pregnant man, he isn’t in the least shocking in person. He’s calm, thoughtful and so softly-spoken that when I listen back to the recording of our interview, I have to strain to hear him. If you had to guess what he did for a living, academic would seem much more likely than artist.

Perhaps that’s because, unlike the other Young British Artists, with whom he has been bracketed, he didn’t go to art college: he went to Cambridge and read History of Art instead. He resists the title of YBA, however, pointing out that he is now, if anything, a MABA – Middle-Aged British Artist. This self-deprecation is unexpected too. When we sit down, the first thing he talks about isn’t himself or his work. It’s his father’s new book, a history of measurement through the ages. So no wonder he is so keen on mixing science with art: it’s in his DNA.

He’s fascinated by science, but not in thrall to it. He likes to use it to make art, but doesn’t see it as a substitute for what art can offer us: ‘What’s interesting is that science and art are both about the fundamental question of who are we, what are we doing here, what’s the world, how do we relate to it, how do we relate to other people – all these kinds of questions. And the difference is that science tries to find concrete answers to all these questions, whereas art just poses the question in different ways. So that you hopefully create an object or something which makes you think about the question rather than giving you an answer.’ I ask him if that means he’s not looking for answers. He replies, ‘There are no answers. It’s the questions that don’t have answers that for me are the most interesting.’

And his studio is a vibrant mass of questions. Stretched over two floors, it’s packed with books and models of his earlier work. Tiny Kate Mosses stare across the room at huge bright flower paintings. Her yoga pose is alarmingly contorted (Moss did model for Quinn, though the yoga position was modelled by another, presumably bendier woman). There’s a sprayed-white model of a pot-plant, growing the flowers of an orchid alongside bananas and apples. A mobile of two planes, noses merged into each other, hangs suspended from the ceiling. Giant eyes look down at you from several walls. And dotted around his work are extraordinary antiquities, statues of Buddhist icons, which he collects. What inspired him to start buying this kind of art?

‘I always loved going to the British Museum, and then I realised you could actually buy it and have it around instead of having to go there. Living with something is completely different from going and looking at it. And everything I buy I end up being influenced by in some way.’ He has a particular passion for his Gandharan sculptures – Greco-Buddhist pieces from where East once met West on the Silk Road. ‘It’s an in-between style, it’s not really one thing or the other. So, for a long time, academically they didn’t know how to deal with it, because it wasn’t Greek or Roman, it wasn’t Indian. It was something slightly… in-between. When I was buying that, I was interested in the whole transsexual thing, people not being either one thing or the other.’

The place between two opposing states is something which infuses his work. There is the statue of Chelsea Charms, a woman with vast surgically-enhanced breasts. To give her a sense of context, her statue appeared in the same exhibition as a bronze of Pamela Anderson, and Anderson looked comparatively normal. And that’s before we get on to the bust of a man who’s has extensive plastic surgery to look like a cat. Or at least like one of the cast of Andrew Lloyd Webber’s Cats. It’s not the freakishness which attracted Quinn to these extremes, it’s the fact that they are impossible to categorise. The Catman looks like neither cat nor man, and Chelsea Charms is somewhere between an erotic figure and a disturbing one. Then there are the flowers frozen in silicon – beautiful, but dead. ‘They’re ironic as well,’ he points out. ‘These flowers are only preserved by destroying them.’

Paradoxes fascinate him, never more so than when he talks about his DNA portrait of John E Sulston. Sulston worked on the Human Genome Project, for which he received the Nobel Prize. Quinn’s portrait of his is made of bacteria, containing Sulston’s DNA, suspended in agar jelly. It’s the first abstract work to appear in the National Portrait Gallery – insofar as you could deduce nothing about Sulston’s appearance from the work - and yet as Quinn points out, it isn’t abstract at all. And the plotting of the human genome isn’t just a scientific discovery, it’s a historical milestone. ‘It’s an amazing moment in history. It’s the first time we can see the instructions to remake ourselves. And then when you see that as a real object, you can’t see him at all, it’s abstract, so there’s a paradox there as well. You have this small jar of agar jelly with dots in that’s John Sulston. And it’s completely abstract – you can’t see it. And yet it’s the most realistic portrait in there, because it contains the instructions to remake him.’

The paradoxes slide through into other parts of his life. He’s been designing much of the Elton John AIDS Foundation Winter Ball, which confusingly happens just before Halloween this year. Even the tabletops will look like giant eyeballs – after sculpting physical extremes for his last exhibition, Quinn’s new work is focussed on the more ordinary aspects of appearance: fingerprints and irises. He has even designed the cocktails which will be drunk on the night – no mean feat for a teetotaller. Quinn was an alcoholic during his twenties. He drank a bottle of wine before breakfast, before moving on to the spirits. He began suffering regular blackouts, and went into rehab in 1993, after realising that he either stopped drinking, or died. I suggest he might not be an expert on vodka now. ‘I remember it from a while ago,’ he laughs. ‘And I just got lots of people drunk. And I saw how they got drunk and decided which level of drunkenness was the most amusing and effective. So it’s more like a medical experiment, in which I was the mad doctor. So it was a bit like making art, really.’ Will there be an alcohol-free cocktail for him? ‘I only like water,’ he says, rather plaintively.

He doesn’t seem able to turn down work. I ask him if he thinks the fact that his studio, packed with current and previous projects, suggests that he has merely swapped one addiction for another. ‘Probably. But I don’t work all the time, I go home and have a family life as well.’ Does he think about work when he’s at home? ‘Yes, definitely. But it’s a positive addiction rather than a negative one.’

Certainly, his work has often been influenced by his family – he is married to the children’s author Georgia Byng, sister of Jamie Byng, the Canongate publisher. She and Quinn have two sons, Lucas, 9, and Sky, 5. The theme of pregnancy has run through Quinn’s more recent work, and his 2005 exhibition, Chemical Life Support, featured statues of chronically-ill people made from wax mixed with the drug which kept each of them alive. One of the figures, Innoscience, was based on Lucas, who had developed a severe milk allergy. The wax of his sculpture was combined with a chemically-produced milk substitute.

Quinn’s work has often commanded vast sums of money. In 2005, Charles Saatchi sold the first Self to an American collector for £1.5 million. The fourth Self – made in 2006 -was bought by the National Gallery for £300,000. And a series of nine sculptures which followed the progression of a developing foetus – made out of marble from the same quarry used by Michelangelo - was bought by a single collector. I wonder if that pressurises Quinn to create the kind of work that will sell for those amounts again. He seems appropriately sanguine: ‘No, I just do what I want and some of it sells and some of it doesn’t. But I can afford to make things… If I wasn’t successful, I wouldn’t be able to make the more extreme works. I can afford to make something and I don’t care if it sells.’

Quinn has clearly come a very long way since his first job, as an intern for the sculptor Barry Flanagan. Growing up in Englefield Green, near Egham, Quinn went to Millfield School, then spent his gap year working for Flanagan. He went from there to Robinson College, Cambridge, where he started producing art, and from there to a London squat. It wasn’t until 1991 that he created the first Self, which was bought by Charles Saatchi for £13,000. Now he has a team of people to help him realise his ideas – though he’s obviously very hands-on: when he is asked to pose for the photographs accompanying this piece, his work clothes are covered in paint. He points out that the idea of any sculptor working alone is a romantic fallacy: even Michelangelo had a studio of people to help him.

The marriage of art and commerce goes further. He has recently designed a range of iris t-shirts and temporary tattoos of flowers and praying skeletons for Selfridges (they’ll be instore from October 27^th). ‘I think it’s interesting to get images into the real world as well as in galleries and on walls.’ Given that he could presumably generate far more cash by casting another golden supermodel, it seems churlish to argue.

Since he can afford to make whatever he likes, pretty much – the raw materials alone for the Kate Moss sculpture cost over £1million - I ask him what his dream project would be. He doesn’t hesitate: ‘Well, hopefully it should be the next thing I’m doing, because I can do what I like all the time. Once you can do what you want, it’s about putting your energy in the right place and making sure that what you do is worth it.’