Building a Mosaic Sentence

A set of mosaic proteins can be a better choice for a vaccine than a similar set of natural proteins, a concept we can illustrate by linking words together to form mosaic sentences.

A mosaic sentence is built using only the words found within an initial set of "natural" sentences, just as a mosaic protein is built from the small protein segments (epitopes) obtained by chopping up a set of natural proteins. Our initial set contains 10 sentences, and just for fun, each is a pangram (a sentence containing all 26 letters of the alphabet) derived from the ancestral pangram: The quick brown fox jumps over the lazy dog. The initial set is shown at right. There are 95 words in the set, but only 26 unique ones, as some words (such as "quick") appear many times. We define the coverage as the number of unique words in a set of sentences divided by the number of unique words in the initial set.

The goal is to construct a set of mosaic sentences that maximizes the coverage, where each mosaic is a pangram with words in a certain order (no dogs jumping over foxes), and each only uses words that appear more than once in the initial set. These rules are simplified versions of the criteria used to construct mosaic proteins. A mosaic protein should only contain epitopes found in the viruses one is trying to immunize against, it must resemble a natural protein to ensure a cell will process it properly, and the epitopes should be common to many viruses (not rare epitopes). The coverage is analogous to the breadth of the theoretical immune response.

A nearly optimal set of two mosaic sentences is shown, and the graph shows that it has much greater coverage (blue dot) compared to any set of two sentences from the initial set (orange dots). In this example, the 10 natural pangrams were deliberately constructed to lead to an impressively large difference. For HIV, a set of mosaic proteins has been found that should initiate a broader immune response than a similar set of natural proteins.

*Detailed information about mosaic proteins can be found in Fischer, W., et al., Nature Medicine 13(1):100, 2007.

Ancestral pangram:
The quick brown fox jumps over the lazy dog
Set of natural pangrams, aligned. Number of unique words = 26.
The quick brown fox jumped over the   lazy dogs
The quick brown fox jumped over these   lazy dogs
Then quick brown foxes jumped over this   lazy dog
That quick brownish fox jumped over this   lazy dog
The quick brown ox jumps over his fat lazy dog
The quick brownish ox jumps over this fat lazy dog
That quirky brown ox jumped over this flat crazy dog
That quirky brown ox jumped over his flaky crazy dog
That quirky town fox jumps over this black crazy dog
That queazy town fox jumps over his black   dog
 
Set of mosaic pangrams:
The quick brown ox jumped over this fat lazy dog
That quirky town fox jumps over his black crazy dogs

Chart

 

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