Anxiety is a part of human nature, a survival mechanism that has evolved to protect us, and the problems it can bring, in themselves, reflect what it means to be human:-
* worrying (planning ahead)
* physical symptoms (eg. increased heartrate/breathing to prepare us for action)
* even obsessive compulsive behaviour (the need for order and control)
All are deeply ingrained in human make-up to help us survive.

However, when we talk about nature versus nurture in regard to anxiety problems we are usually referring to the cause of the problem: is it due to nature (a faulty gene, brain structure, chemical imbalance or disease) or nurture (the environment we live in, our experiences, learning and conditioning)?

The answer, of course, is both - but what role does each actually play?

Genetic information passed from parent to child could contain much more than we are aware of today, possibly even passing on hopes, fears and desires - such things being an integral part of a person's make up. Without doubt a parent that has lived a life 'surviving' with OCD (or depression or high anxiety etc.) will pass such 'survival' information to their offspring.
However, all such information can only be in the form of predispositions - ways to behave given the 'right' (although negative) conditions for the inherent information / potential behaviours to flourish. This must be the case, for adaption (survival) purposes - it would not be sensible to be born into an unknown environment with 'fixed' attitudes/behaviours. Eg. it would not be appropriate to be constantly fearful in an environment of love.

So - genetics is important in the form of predispositions: coded information from our ancestors to help us survive/ thrive in various environments, but it is the environment in which we live that controls whether these predispostions  flourish or wither and die.

Let's look at OCD, for example, being a major problem that current trends proffer 'nature' as the cause: OCD represents trying to get control over 'unseen' forces and dangers - through rituals (there is no other way to attempt to get control over powerful negative forces that control us other than by rituals), ordering (to have everything ordered, in control) etc.
Given the right (wrong) set of life circumstances, it is not surprising that many turn to ordering / rituals to try and get control over relentless, uncontrollable anxiety (It's not called an anxiety disorder for nothing).
But it's the environment and fears/anxieties that have been learned and conditioned that drive this need to get control (to assuage the fears). Genetic history may enhance this or not.

Note also that a parent with OCD not only promotes direct learning (as a role model) but often treats their children in such a way (over cautious, negatively due to their own problems etc.) that may promote fears and anxieties. A child with OCD from a parent with OCD does not confirm a genetic link as the cause.

Included in the 'nature' argument is the idea of physical brain differences being the cause of OCD - they are not, they are the result of it, and many books that proffer this cause go on to say that the brain can be changed by learning (to a non-OCD state) - yes it can, just as it is changed in the first place to an OCD state by learning and conditioning.
This change of brain state obviously involves changes in levels (usually deficiencies) of such things as neurotransmitters (generally Dopamine and Serotonin are the ones frequently mentioned), proteins AND EVEN GENES. [The  work of Barbara McClintock in the 1950's -originally ignored by her peers, later awarded the Nobel prize for her work showing that genes in plants change in stressful environmental conditions(whole sequences of DNA moving from one place to another). This is in plants - imagine what could be really happening in humans!]

And so, science may find brain structure changes, neurotransmitter level differences, protein diffrerences, genetic differences in those with OCD - BUT all these changes are, more logically, the result of the OCD not the cause.
Manipulating these factors can only (as the failure of modern medications as a cure already confirms) alleviate some symtoms for they never touch the cause.
The environment must be the overriding factor - these problems are psychological and the answer is psychological - reconditioning and relearning our attitudes, beliefs and fears ... in effect, re-changing our brain and probably in doing so, altering a part of our genetic make up.