What is the most likely mode of transmission for a trait that is not expressed in parents but is expressed by one half of the sons?

Rare X-linked recessive

Explanation:

In humans our biological sex-determination is based on a pair of sex chromosomes namely, XX in females, XY in males. The genes on our X chromosome are X-linked. and have special  patterns of inheritance due to their presence in contrasting numbers in males (XY, 1 X chromosome) and females (XX, 2 X chromosomes); thus they are more common in genetic males.

The observed trait is X-linked, and given that only half the sons are affected, the trait is recessive and carried by the heterozygous mother -heterozygous alleles are two variants of the allele at the same gene locus. The Y chromosome inherited from the father does not carry the gene, thus there is no normal copy available. The incidence for its inheritance is at 50% as the mother has two X hromosomes, one normal, and one carrying the trait.

transcription is a process in which information is rewritten. it is something our cells must do, in a more specialized and narrowly defined way. in biology, transcription is the process of copying out the dna sequence of a gene in the similar alphabet of rna. it needs to happen in the nucleus because that's where the dna is. dna is always inside the nucleus unless the cell is dividing.

transcription is the first step in gene expression, which involves copying a gene's dna sequence to make an rna molecule. transcription is performed by rna polymerases. it has three stages: initiation, elongation, and termination. rna molecules must be processed after transcription in eukaryotes.

explanation:

long version:

the protein synthesis consists two processes which are, transcription and translation. transcription takes place in the nucleus. it uses dna as a template to make an rna molecule. rna then leaves the nucleus and goes to a ribosome in the cytoplasm, where translation occurs. transcription is the first part of the central dogma of molecular biology: dna → rna. it is the transfer of genetic instructions in dna to messenger rna (mrna). during transcription, a strand of mrna is made that is complementary to a strand of dna.  

these three stages are:

  initiation: in which   is the beginning of transcription.occuring when the enzyme rna polymerase binds to a region of a gene called the promoter. this signals the dna to unwind so the enzyme can ‘‘read’’ the bases in one of the dna strands. the enzyme is now ready to make a strand of mrna with a complementary sequence of bases.

    elongation: in which is the addition of nucleotides to the mrna strand. rna polymerase reads the unwound dna strand and builds the mrna molecule, using complementary base pairs. there is a brief time during this process when the newly formed rna is bound to the unwound dna. during this process, an adenine (a) in the dna binds to an uracil (u) in the rna.

    termination: in which is the ending of transcription, and occurs when rna polymerase crosses a stop (termination) sequence in the gene. the mrna strand is complete, and it detaches from dna.