I always thought that a molecule of DNA was made of two polynucleotides each making up one strand of the molecule... Is that right?
The term molecule was coined by chemists to describe small entities in which the atoms are joined by covalent bonds. When one is talking about large biological entities involving non-covalent bonds (proteins, nucleic acids) the strict definition often conflicts with the way one conceptualizes these entities, and this has led to common usage that may strictly be regarded as incorrect. However the definition of a molecule is of no real concern to molecular biologists and few people care that the situation is ambiguous.
Definition of Molecule (Wikipedia)
A molecule is an electrically neutral group of two or more atoms held together by chemical bonds
By this definition double-stranded DNA consists of two molecules, and haemoglobin consists of four molecules (or perhaps eight, if one regards the haem as a separate molecule).
Use of Molecule to refer to multistrand Nucleic Acids and Proteins
Because we are often concerned with the functions of a double-stranded nucleic acid or a multi-subunit protein in its entirety, one finds them referred to as molecules by quite reputable sources. For example:
Each hemoglobin molecule is made up of four heme groups surrounding a globin group, forming a tetrahedral structure.
DNA is arguably one of the most beautiful molecules in living cells. Its graceful helix is pleasing to the eye. DNA is also one of the most familiar molecules, the central icon of molecular biology, easily recognized by everyone.
It would be better to spend one’s energies on more important and intellectually interesting topics concerning nucleic acids and proteins then whether only their individual strands or subunits are truly molecules.
In general, it is right since with the term DNA you commonly refer to the double-stranded DNA. However, you need to be aware that DNA may exist in different forms.
Single-stranded DNA (ssDNA), for example, is composed of only one strand of DNA, so one chain of nucleotides or one polynucleotide molecule.
Double-stranded DNA (dsDNA) is the common form of DNA found in cells and it is composed of two polynucleotide molecules.
Triple-stranded DNA (tsDNA ?) also exist, which of course, is composed of 3 polynucleotide molecules.
There are four ways to answer a question (Anguttara Nikaya); a counter-question is one of them.
When water changes its state from gas to liquid to ice does the number of water molecules in the system increase, decrease, or remain the same?
The answer is: The number of water molecules in the system remains the same. (Note: The three states of water differ by spatial arrangement of water molecules and by the number of "hydrogen bonds" between the molecules.)
Now, let's replace "water" with "deoxyribonucleic acid" (DNA) . . .
When DNA changes its state from dissociated to associated does the number of DNA molecules in the system increase, decrease, or remain the same?
The answer is: The number of DNA molecules in the system remains the same. (Note: The two states of DNA differ by spatial arrangement of DNA molecules and by the number of "hydrogen bonds" between the molecules---cf. water.)
The "water" analogy goes even further: The process of dissociation of DNA molecules is called "melting."
i melt DNA (computationally) for a living. Seriously. No kidding.