it has been estimated that the probability of a new relevant functional protein fold emerging through mutating the DNA strand is approximately 1 in 10e77, which is:
1 in 100,000,000,000,000,000,000,000,000,000,000,000,000......000,000,000,000,000,000,000,000,000,000,000,000,000 "the estimated prevalence of plausible hydropathic patterns (for any fold) and of relevant folds for particular functions, this implies the overall prevalence of sequences performing a specific function by any domain-sized fold may be as low as 1 in 10e77, adding to the body of evidence that functional folds require highly extraordinary sequences." (
pubmed.ncbi.nlm.nih.gov/1532…)
With this data we can estimate exactly how long it would take for mutations to be able to create a new functioning portion on a protein. In order to make this estimation, we will take into consideration all the bacteria on the planet, and the average mutation rate to determine how many total bacterial mutations occur per year. Also note, "e" simply means exponent. So 5e30 means 5,000,000...(with 30 total 0's) :
total number of bacteria on earth: 5e30
mutation rate per generation: .003
generation span: 12 hrs on average
First we have to determine how many mutations happen per bacterial line in a year. There are 8760 hrs in 1 year. Therefore 8760 hrs in a year divided by the 12 hrs in a bacterial generation = 730 mutations per year per bacterial generational line. To determine the total number of mutations of all the bacteria on earth per year we simply multiply the number of bacteria by the number of mutations per bacterial line per year: 5e30 x 730 =3.65e33
Given that the odds of a beneficial mutation to an enzyme fold are approximately 1 in 1e77, This global mutation rate is clearly not enough to satisfy even one successful enzyme fold change even over trillions upon trillions of year The reason an enzyme fold is so difficult to mutate is because it requires a long sequence of specific DNA changes that must be able to create an electrochemical function capable of performing a specific task. This is the operable part of proteins and enzymes that allow them to do anything at all, so it is absolutely necessary to know how something like this could emerge by simple genetic mutations. And the probabilities are unimaginably low.
Now going back to the 3.65e33 mutations per year for all bacterial life on the planet. If the odds are 1e77, then that means it would take 2.7e43 years just to make ONE successful mutation to an enzyme fold. That means it would take: 27,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years ...to make one functional change to an enzyme fold through mutations to the genetic code.
Given that the known universe is theorized to have existed for only around 14,000,000,000 years, we see how insufficient this amount of time is to create proteins through mutating genomes. Keep in mind that ATP synthase for example has multiple enzyme folds throughout, and that the electron transport chain itself has a multitude of proteins. All of which need to be in place and function properly for metabolism to be possible! So we are quite clearly seeing that even in the billions of years that have been ascribed to our universe, that would be vastly insufficient for allowing this probability to hit even once.