I work in a hospital environment in the UK so frequently have email correspondence with persons with titles such as Doctor, or "Mr" (which denotes a consultant, senior to a doctor).
There does not seem to be a "rule" but I have developed a code of my own in this aspect. In a professional work environment I will always address a doctor as "Doctor" in spoken and written correspondence as long as the correspondence seems formal/work-related.
I don't trust email signatures as an indication of how someone wishes to be addressed because they can be preset, or even written in a hurry. I have also noted that some doctors use their first names to distinguish themselves from another doctor with the same surname, so again this doesn't indicate they want you to call them this.
Additionally, and I may be opening up a can of worms here, you should remember that it may not be your culture dictating what a person may want to be called, but their own. Again, from my experience, I may be in the UK but many of the doctors I mentioned are from overseas, and interestingly the majority of those who have invited me to call them by a particular name are not UK born. Another reason to avoid any hard and fast rule.
As you are concerned about it, the best course of action is to keep it formal. In my experience, this does not hinder the development of any professional relationships. If anything, it can build one of mutual respect. For example - when I was at school (again, in the UK) we all referred to our male teachers as "sir". Now, aged 42, I often see one of my old teachers in my town who always stops me to chat. He is friendly, asks about my family, asks about my work, and I would go as far as to say we have a friendship of sorts - but I still call him "sir", and he has never corrected me.