From the books "The Genetics of the Dog", by Dr. Marca Burns and "The Inheritance Of Coat Color in Dogs" by Clarence Little.

          The genetic code for coat color in Yorkshires is: at, B, C or cch, D, E, G, m, S, t - as defined by Clarence Little. For the purpose of discussing coat color for the Yorkshire Terrier, there are several excerpts which will be quoted here from both books about these "locations" of genes and their alleles, and how they bear on  color and its distribution in dogs in general as well as Yorkshire Terriers.

Burns:         "It can be said ... that the pigment is composed of chemical substances called melanins, and is usually deposited in the form of granules in the skin and hair. This process begins some weeks before the pup is born, but continues after birth. Under a microscope the pigment granules of 'black' hair appear very dark brown or black, whilst those of red or yellow (fawn) hair are smaller and appear yellow. In dogs two kinds of black pigment have been observed by the author: the commonest kind is deposited mostly in fairly large granules, although there is a wide range of granule size from small to large; in the second type all the granules are small and even in size. After bleaching with an oxidizing agent such as hydrogen peroxide, the pigment granules of black dogs appear the same as those of yellow dogs. This suggests that 'yellow' pigment may be formed from black pigment by a further chemical process. This is supported by the fact that yellow dogs usually have black pigment in their skin, eyes and nose, and the amount of tan on a black-and-tan dog continues to increase after birth." (Yorkshires are basically black and tan color, and this can also account for the "running gold" seen as some Yorkshires mature.)
         "The pigment is deposited in the hair as the hair grows, and not afterwards; therefore, if the pigment-forming process in the hair-root changes when a hair is partly grown, that hair will come out banded,  partly one color and partly another." (This can account for the horizontal stripes sometimes seen as the coat grows out.)

Little:          "Each chromosome has its own content of genes which belong to it and remain with it. Between different pairs of chromosomes there should and usually does exist complete independence. A gene in chromosome 1 will, therefore, show no relation to, or association with, a gene in chromosome 2 in the method of or during the process of inheritance. On the other hand, if two different genes are located in the same chromosome, there should and does exist a relationship, or linkage, between them in inheritance. The existence of such a linkage may be detected by a constant departure from the ratio of types expected by the normal independent recombination of Mendel's law."
          "The various forms of a gene which can occupy the same site (locus) in a chromosome are called alleles of one another. Allele is a contraction of a term formerly employed, allelomorph, which means "another form of." This terminology therefore retains the concept of basic similarity, but of different arrangement, of the component parts - in other words, a new form of a mutant gene compared with its original form."
          "When more than two alleles have been identified at a single locus, they are called multiple alleles. In the dog four loci for coat color have been identified which may contain any one of  four alleles, and six which contain two each. Whenever three or more alleles are found, they can usually be classified and arranged in the order in which they can mask, conceal, or cover the expression of the the other members ... the one of the pair which masks or conceals the other is called dominant, and the one which is masked, or concealed, recessive." (It is important to remember that such masking or dominance is seldom complete, and may produce a characteristic independent of either.)

at Locus   -  The at produces the bicolor varieties (black&tan, liver&tan, etc.) These form a series of patterns of different distributions of dark and light pigment. Two 'bicolours' (black and tans, liver and tans, or blue and tans) mated together should throw all tan marked pups. This is also proved by general experience in many breeds, but if any red or yellow pups occur the tan markings cannot as a rule be distinguished on them.
         Yorkshire puppies are born black with somewhat indistinct tan points. This indicates that the breed is atat in genetic type. As the dog ages and the hair lengthens, there are two changes in color pattern which occur gradually. First, the area covered by the dark pigment decreases gradually, somewhat as in Airedales, so that it becomes a very heavy saddle rather than a complete body coverage. (If the dark body coat  is affected by this gene, although the color lightens to blue, this may be where you see running gold or bronzing.)  It is, however, essential that dark pigment cover the nape and extend unbroken to the head. Second, the black pigment pales to a steel-blue, which suggests the action of the dilution factor G seen also in Bedlington Terriers.

Bb Locus  -  One gene about which all workers seem to agree is the one which makes the dog produce chocolate-coulored pigment instead of black. These genes were named B (black) and b (chocolate) by Little in 1914 and their relationship seems to be definite and simple, the gene b always behaving as a simple Mendelian recessive to B in every experiment that has been reported, in numerous breeds and their crosses. A dog which has the formula bb apparently cannot produce any black pigment anywhere in its body; ... which is why 'Standards' permit brown noses and lighter eyes with this coat color. All Yorkshires carry the gene B for Black and S for solid color, i.e., absence of white spotting (parti-color)." (my comment - although a white spot may be seen on chest or chin.)

C or cch Locus -   The cch locus is named "chinchilla" and it has a distinctly greater effect in reducing the red-yellow pigment than it does on the black pigment ... Schnauzers in which the dark pigment is still plentiful, but the yellow has been so reduced ... as to be almost absent (white) from the coat.

D Locus   -   There are only two other coat-color genes about which there seems to be no debate, one the 'merle' gene, which will be dealt with later, and the other the gene for 'blue dilution'. The latter gene was also named by Little (1919) and he gave it the symbol d as it is also a simple recessive to its allele D. In a dog which lacks D, i.e. has the genetic formula dd, the pigment granules are clumped into very distinctive agglomerations, larger and much more definite than those produced by the gene b. This clumping certainly affects black ... pigment, but there may be a yellow that is not affected. The affect on black pigment gives the familiar 'blue' of Greyhounds, and the 'silver' of Poodles. With chocolate pigment, it produces the rather pinkish shades known as 'liver' in Bedlington Terriers and 'apricot' in Poodles.
          Blue-dilution affects the pigment in the skin, eyes, etc., as well as in the hair. This  is the reason why 'blue'dogs have slaty noses and smoky eyes. Probably the shade of blue of dd dogs depends on the gene complex as a whole, as it does in mice and other rodents, but possibly D is not always fully dominant to d, so that the very dark 'blues' may be heterozygous Dd. (Which means that the much desired 'blue' body coat on the Yorkshire may be a "hybrid" color, and why it doesn't always breed true.)
          (Little) "The D locus contains another well-established pair of genes producing alternative characters. The dominant member, D, causes intense pigmentation, seen in deep rich-colored dogs such as Schipperkes and Irish Setters. The recessive member, d, resulting in blue or Maltese dilution, is seen in Great Danes, Greyhounds, Poodles and Weimaraners. (he makes the distinction of the that the G locus is responsible for a progressive graying from birth until old age or throughout life, and dominant over g which is found in normal dark-pigmented animals which show no progressive graying.)

          The other loci are related to black masks, merle coloring, parti-color and ticking, and not really relevant to a discussion of coat color in the Yorkshire.

         (I hope this has been of help, and if I've drawn the wrong conclusions from what I've read, I hope someone better versed than I in genetics can correct it.)
 

On the right is the human chromosome chart, with genes in the same position on each chromosome. The dog has 39 pairs of chromosomes. Each pair of genes (alleles) governs a particular trait or characteristic. Each parent contributes one gene of a pair, and while they both govern a particular trait, they may express different values, i.e., one for brown nose, and one for black nose. The nose (or trait) will be black in that case, as the gene for brown nose is recessive to black. The illustration on the left represents the well known double helix of a DNA strand, representing a chromosome and it's paired genes. There are infinite possible combinations, which is why it's difficult to pinpoint genetic problems.