The successful inheritance of genetic information across generations is a complex process requiring replication of the genome and its faithful segregation into two daughter cells. At each replication cycle there is a risk that new DNA strands incorporate genetic changes caused by miscopying of parental information. By contrast the parental strands retain the original information. This raises the intriguing possibility that specific cell lineages might inherit "immortal" parental DNA strands via non-random segregation. If so, this requires an understanding of the mechanisms of non-random segregation. Here, we review several aspects of asymmetry in the very symmetrical cell, Escherichia coli, in the interest of exploring the potential basis for non-random segregation of leading- and lagging-strand replicated chromosome arms. These considerations lead us to propose a model for DNA replication that integrates chromosome segregation and genomic localisation with non-random strand segregation. (C) 2013 Elsevier Ltd. All rights reserved.