If a single private key of the HD bitcoin account is compromised, is the whole HD account compromised?

If a single private key of the HD bitcoin account is compromised, is the whole HD account compromised?

The subject pretty much asks it all. I asked the same question on the Mycelium web site but did not get an answer. An HD account can have multiple private keys. If one of the previous private keys gets compromised (falls into hands of a hacker) and this private key has no bitcoins assigned to it. Would the hacker be able to re-create subsequent private keys based on this single one private key?

The question applies to Mycelium and all other HD accounts. Also, is there a standardized way how private keys are created or each wallet does it on its own?

This question is important to me since we see more and more bitcoin forks. To claim newly forked bitcoins I would need to import private key(s) into another wallet. Assuming the new wallet may be used to harvest my private keys and to spend bitcoins, I would like to move my bitcoins from my HD account from private_key1->public_key1->address1 to private_key2->public_key2->address2. If I now import private_key1 into a hacked wallet, the hacker can not spend my bitcoins directly. But should I worry that he will be able to re-create private_key2 and therefore still be able to spend my bitcoins?

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