Error threshold (evolution) Totally Explained

Everything about Error Threshold Evolution totally explained

The error threshold is a concept in the study of evolutionary biology and population genetics and is concerned with the origins of life, in particular of very early life, before the advent of DNA. The first self-replicating molecules were probably small ribozyme-like RNA molecules. These molecules consist of strings of base pairs or "digits", and their order is a code that directs how the molecule interacts with its environment. All replication is subject to mutation error. During the replication process, each digit has a certain probability of being replaced by some other digit, which changes the way the molecule interacts with its environment, and may increase or decrease its fitness, or ability to reproduce, in that environment. It was noted by Manfred Eigen in his 1971 paper (Eigen 1971) that this mutation process places a limit on the number of digits a molecule may have. If a molecule exceeds this critical size, the effect of the mutations become overwhelming and a runaway mutation process will destroy the information in subsequent generations of the molecule. The error threshold is also controlled by the fitness landscape for the molecules. Molecules which differ only by a few mutations may be thought of as "close" to each other, while those which differ by many mutations are distant from each other. Molecules which are very fit, and likely to reproduce, have a "high" fitness, those less fit have "low" fitness. These ideas of proximity and height form the intuitive concept of the "fitness landscape". If a particular sequence and its neighbors have a high fitness, that'll form a quasispecies and will be able to support longer sequence lengths than a fit sequence with few fit neighbors, or a less fit neighborhood of sequences. Also, it was noted by Wilke (Wilke 2005) that the error threshold concept doesn't apply in portions of the landscape where there are lethal mutations, in which the induced mutation yields zero fitness and prohibits the molecule from reproducing.
The concept of this critical mutation rate, or "error threshold" is crucial to understanding "Eigen's paradox" which is discussed in the next section.

Eigen's Paradox

Eigen's paradox is one of the most intractable puzzles in the study of the origins of life. It is thought that the error threshold concept described above limits the size of self replicating molecules to perhaps a few hundred digits, yet almost all life on earth requires much longer molecules to encode their genetic information. This problem is handled in living cells by the presence of enzymes which repair mutations, allowing the encoding molecules to reach sizes on the order of millions of base pairs. These large molecules must, of course, encode the very enzymes that repair them, and herein lies Eigen's paradox, first put forth by Manfred Eigen in his 1971 paper (Eigen 1971). Simply stated, Eigen's paradox amounts to the following:

Without error correction enzymes, the maximum size of a replicating molecule is about 100 base pairs.
In order for a replicating molecule to encode error correction enzymes, it must be substantially larger than 100 bases.

This is a chicken-or-egg kind of a paradox, with an even more difficult solution. Which came first, the large genome or the error correction enzymes? A number of solutions to this paradox have been proposed:

Stochastic corrector model (Szathmáry & Smith, 1995). In this proposed solution, a number of primitive molecules of say, two different types, are associated with each other in some way, perhaps by a capsule or "cell wall". If their reproductive success is enhanced by having, say, equal numbers in each cell, and reproduction occurs by division in which each of various types of molecules are randomly distributed among the "children", the process of selection will promote such equal representation in the cells, even though one of the molecules may have a selective advantage over the other.

Relaxed error threshold (Kun et al., 2005) - Studies of actual ribozymes indicate that the mutation rate can be substantially less than first expected - on the order of 0.001 per base pair per replication. This may allow sequence lengths of the order of 7-8 thousand base pairs, sufficient to incorporate rudimentary error correction enzymes.

A simple mathematical model illustrating the error threshold

Consider a 3-digit molecule [A,B,C] where A, B, and C can take on the values 0 and 1. There are eight such sequences ([000], [001], [010], [011], [100], [101], [110], and [111]). Let's say that the [000] molecule is the most fit; upon each replication it produces an average of

a

copies, where

a>1

. This molecule is called the "master sequence". The other seven sequences are less fit; they each produce only 1 copy per replication. The replication of each of the three digits is done with a mutation rate of μ. In other words, at every replication of a digit of a sequence, there's a probability

mu

that it'll be erroneous; 0 will be replaced by 1 or vice versa. Let's ignore double mutations, and divide the eight molecules into three classes depending on their Hamming distance from the master sequence:
ť of the total population.

It can be seen that there's a sharp transition at a value of 1-Q just a bit larger than 0.05. For mutation rates above this value, the population of the master sequence drops to practically zero. Above this value, it dominates.
In the limit as L approaches infinity, the system does in fact have a phase transition at a critical value of Q:

Q_c=1/a.

. One could think of the overall mutation rate (1-Q) as a sort of "temperature", which "melts" the fidelity of the molecular sequences above the critical "temperature" of

1-Q_c

. In order for faithful replication to occur, the information must be "frozen" into the genome.

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