Sadly, the odds are against them succeeding. Neither is in the first flush of youth and when they were introduced last year, just before the breeding season, Bao Bao gave the female a savage mauling which left her missing a claw, part of an ear and with two infections. She needed surgery and antibiotics.
There is a lively debate within the zoo between scientists and keepers about whether to risk putting the two animals together again or to rely on artificial insemination (AI). But the 14-year- old female has already had six AIs in China and two at London; none produced a pregnancy.
This week London Zoo will unveil its pounds 20m strategy for the remainder of the century and insist the air of failure and uncertainty which has dogged it for the past two years has dispersed.
It will be 'repositioning' - putting much more emphasis on its work as a conservation centre, preserving extinction-threatened species. But in the absence of any government subsidy the zoo must maintain the numbers of visitors and ticket sales.
The pandas are not only in need of conservation but are also big crowd pullers. Huge queues formed when Ming Ming and Bao Bao arrived in Regent's Park at the end of 1991, ending three pandaless years at London Zoo.
Fewer than 1,500 wild pandas survive in the vanishing bamboo forests of Szechuan in China and about 100 are in zoos. There are 17 in western zoos at present, where eight cubs have been born.
Regent's Park has never had a baby though its scientists are renowned for their work on large mammal reproduction. The director, Dr Joe Gipps, is one of two keepers of the international panda studbook, which records all pandas in captivity, their relationships and offspring.
Dr Gipps is proud that Ming Ming was the first panda the Chinese sent to a foreign zoo to breed rather than as a political gift. However, she shows little promise of becoming a mother and may be infertile. Last year she failed to come into oestrus or 'heat' at the start of the breeding season in late February and had to be induced into that state with hormone injections.
The staff admit that the odds are against the ultimate crowd- pulling event - the birth of a baby panda. 'But of course it's worth the effort; if we don't try we certainly won't succeed,' Dr Gipps said. The keeper in charge, Mick Carman, said: 'She's not a Rolls-Royce panda - perhaps more of a Skoda.'
Bao Bao boasts an unusually high sperm count, 'The best panda sperm I've ever seen,' said Dr Bill Holt, a reproductive biologist at the zoo's Institute of Zoology. But the male's assault on Ming Ming last year was so fierce and prolonged that staff had to spray gas fire extinguishers to separate them. This time the two pandas are being exposed to each others' smells, as would happen in the wild. Faeces and urine are being swapped between dens, in the hope that the odours will help induce oestrus in Ming Ming and make Bao Bao less dangerous. They will swap dens, then encounter each other snout-to- snout with a mesh fence in between.
The zoo is monitoring the levels of oestrogen, a female hormone, in Ming Ming's urine; it should rise rapidly as she comes into oestrus. But this is difficult because she urinates rarely and tends to attack keepers who enter her cage. The keepers hope she will visibly come into oestrus, groaning and lifting her tail. Mr Carman hopes that if that happens the two pandas can be brought together to mate safely, with keepers on hand with fire extinguishers. 'I think a natural mating gives a better chance of conception,' he said.
But Dr Gipps fears the risks are too great and it is more likely she will be artificially inseminated. Bao Bao will have to be anaesthetised and an electronic probe inserted in his rectum in order to induce ejaculation.
Ming Ming will be anaesthetised to receive his sperm. She will probably have a laparoscopy at the same time, allowing her uterus, ovaries and fallopian tubes to be examined microscopically using keyhole surgery techniques and a fibre-optic cable to see if there are ova - eggs - or signs of infertility.
If the pandas fail to conceive they may leave London by the year's end. Both were loaned for an initial two-year period in order to breed. Berlin Zoo may want Bao Bao back. Chinese intentions are unknown but some American zoos are prepared to pay millions of dollars to have pandas on breeding loan.
It can be argued that the panda is a doomed species. Although it has clear carnivore origins it has specialised in eating one plant and reproduces at a painfully slow rate.
Dr Gipps said: 'Other things being equal, the giant panda was on the road to extinction, but it wasn't going to happen for a million years. We're talking about it being lost in decades because of our destruction of its habitat.'
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