Why the "Lee peptide" Cannot Sustain Exponential Growth

 Why the "Lee peptide" Cannot Sustain Exponential Growth Even with a Continuous Supply of Substrates

***Under Construction***

(See, "Q's Response to Richard Carrier: About the Debate," for context)

(See also, "Q's Open Challenge to Richard Carrier", and "The 'Fatal Flaw' with Richard Carrier's '1 in 10^41' Argument for Abiogenesis")

The "Lee peptide" cannot sustain its own replication via exponential growth (even in the "right environment"), due to intrinsic deficiencies in its catalytic ability. It exhibits parabolic rate kinetics—not exponential—due to product inhibition. Richard would know this if he had carefully read and understood  his primary source citation. Specifically, when the "Lee peptide" makes a copy of itself, the resulting "Lee peptide" copy (i.e., product) fails to dissociate from the template strand (i.e., it tends to ‘stick’ or stay bound to the original "Lee peptide"). This means that with each successive round of self-replication, fewer and fewer "Lee peptide" copies are created. It is a case of diminishing returns (even in "a suitable environ") with progressively dwindling results until the autocatalytic cycle is effectively arrested. As such, the "Lee peptide" also does not meet the NASA definition of life that Richard appeals to, since it is not "a self-sustaining chemical system capable of Darwinian evolution."

Lee et al. (1996), report that the “self-replication process [of the "Lee peptide"] displays parabolic growth” instead of sustained exponential growth with “a square root profile” that “reflects catalyst (template) inhibition through aggregation.” (Lee et al. 1996).

(Figure 1, Lee et al. 1996)

Evolutionary biology can "in principle, be extended to...Darwinian evolution in chemical systems" when there is replication, mutation, and selection; beginning with the replication of a large number of copies of the replicator molecule. (p. 1190). Such replicators must first replicate at a rate that exceeds their rate of decomposition in order to survive, and then, at minimum "need to be able to grow exponentially in order to exhibit Darwinian evolution". (p. 1191) (Duim, H., & Otto, S. (2017). Towards open-ended evolution in self-replicating molecular systems. Beilstein journal of organic chemistry, 13(1), 1189-1203). By contrast, "A system in which product inhibition occurs, will not show exponential growth...but only sub exponential [i.e., parabolic] growth." (p. 1194) (Duim, H., & Otto, S. (2017). Towards open-ended evolution in self-replicating molecular systems. Beilstein journal of organic chemistry, 13(1), 1189-1203).

"A requirement for effective autocatalysis, however, is the dissociation of the [T∙T] complex into two individual template molecules. If this complex does not dissociate, the newly formed template molecule cannot lead to further enhancement of the reaction rate, effectively arresting the autocatalytic cycle. Such product inhibition is an important limiting factor in many synthetic replicator systems and prevents them from attaining exponential growth." (Duim, H., & Otto, S. (2017). Towards open-ended evolution in self-replicating molecular systems. Beilstein journal of organic chemistry, 13(1), 1189-1203).

"The inhibited growth regime for the doubling of well-mixed and resourceful autocatalytic and cross-catalytic macromolecules has its roots in a general self-capturing phenomenon termed 'strand inhibition'. Without external 'help', usually from enzymes, the unfolding of T:T double-strands....is difficult for intrinsic molecular reasons....Hence, in spite of plentiful resources, fully suppressed side reactions—no degradation or chain elongation instead of replication—and negligible waste product concentrations, viz. under ideal initial conditions, the growth order of the vast majority of macromolecular replicators remains parabolic." (Strazewski, P. (2019). The beginning of systems chemistry. Life, 9(1), 11.).

There are three growth orders in rate kinetics/population dynamics: hyperbolic ("accelerated"), exponential ("forceless" or "simple"), and parabolic ("inhibited"); where respectively, each generation produces more, the same, or less 'descendants' per 'parent' than the previous one. (Strazewski, P. (2019). The beginning of systems chemistry. Life, 9(1), 11.).

(Modified from Figure 5, Strazewski, P. (2019). The beginning of systems chemistry. Life, 9(1), 11.)