By looking at a chromosome fragment, is there a way to tell, how it is oriented in the chromosome? I wonder if the genomic sequence in chromosomes is directional, for example maybe one strand has more of the sense strand of genes than the other? Or some other signature?
As far as I know there is no such "signature" of direction in eukaryotic chromosomes. In many bacteria there is a very strong signal of the direction of replication on the circular chromosome and also often on larger plasmids. For one example, in the genomes of bacteria that are very A+T rich and G+C poor such as the Clostridia, more than 80% of the protein-coding regions are on the fast-replicating strand (facing away from the origin of replication) and not on the other strand which lags a bit behind in replication.
I am attaching a figure showing the genes on the chromosome and on a plasmid from one isolate of Clostridium botulinum. You can see that almost all the genes on one side of the circular chromosome are on one strand (and colored blue) while on the other side they are on the other strand (and colored red). The next to the innermost ring plot is the "GC skew" of the DNA and that is usually said to be correlated with the direction of replication, rather than the genes. But if you zoom in on chromosomal regions, or look at the plasmid plot (the plasmid is 148kb, the genome is 3.96 megabases in size) you can see that the GC skew is more correlated with the gene orientation, than the direction of replication.
Eukaryotic chromosomes have far more origins of replication, and many other differences from bacterial chromosomes. I have never heard of any signatures like this indicating which direction a region of DNA is facing with regard to being toward or away from the centromere.
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