This Kibbitzer is based on a summary by a Greek-speaking postgraduate student of Physiology:

As shown by citations 1 - 8, predominate is not a Transitive verb: it cannot be followed by an Object, but can be followed by a Prepositional Phrase constructed with among, in, over etc.

 1 ng intact and faithful to Peter. This version still predominates among Roman catholic laity in most 
 2 limax species, trees such as the dipterocarps which predominate in primary rainforest in Southeast A
 3 south, for example. Yet the colours and shapes that predominate in any one place seem to bear no rel
 4  have low levels of IgG, the class of antibody that predominates in blood. She made her measurements
 5  conservative concentration on the human figure: it predominates in each painting, a strong, solid v
 6 omadic and seminomadic to herdsman husbandry: goats predominated over sheep, donkeys were the main t
 7 H2 cells may take over. In essence, while TH1 cells predominate, a person may resist the virus with 
 8 o spread and on which strains of the bacterium will predominate. Fortunately, research into the micr

The verb dominate may be used intransitively, with a meaning close to predominate (see citations 9 - 12):

 9 would expect that only a few hybrid genotypes would dominate, as when hybrids reproduce parthenogeni
10 aused. It is the resulting harm (death) which still dominates, as is evident from the fact that man 
11 In other positions, one or two specific amino acids dominate, but not to the extent that they do in 
12 ic predictability suggest that internal variability dominates for periods less than 1O-20 days. It i

However, dominate is most often used transitively as in the following citations:

13 f how the political and business elites continue to dominate activity in the region. The Pilot plann
14 lutionary history. The pattern he found has come to dominate all debates about brain evolution.
15 Settinius, and others that no single airline should dominate American airline services, and favoured
16 ntention of their paper was that if Britain did not dominate an area, the Russians would. This gener
17 re between high- and low-tides. Their life-style is dominated by the tides rather than the sun and t
18  class structure of Northern Ireland is predictably dominated by protestants. Of course, with the do
19 natural forces meant that the concept of time which dominated Maya thought was purely astrological.
20 l realities. This tendency for academic thinking to dominate minds is strengthened by the fact that 
20            In a homogeneous early Universe, protons dominate the nuclear reactions, and little beryl
21                  The territory holders aggressively dominate the landless males, even if they are on
22 lso point out that even though greenhouse gases now dominate global warming, if part of the warming 

That raises the question: could not the transitive dominate be used in place of predominate in the student's text? Unfortunately there is a difference in meaning as shown by the citations:
      Predominate means something like 'is important because it outnumbers the others.
      Dominate means something lime 'is important because it controls the others.
Here there is no implication that the neurophils control the other phagocytes, so dominate is inappropriate.