Haijun Wen

It is widely suspected that a small percentage of males have exceptional reproductive output (ERO) but progeny numbers of males are rarely measurable, even in humans. If we define the variance ratio of reproductive-output in males and females as α′ = VM/VF, the ERO hypothesis would predict α′ ≫ 1. Since autosomal, X, and, Y chromosomes are found in males 1/2, 1/3, and 100% of the time, their DNA diversities can inform about α′. For example, autosomal and Y-linked diversities are governed, respectively, by (VM + VF)/2 and VM. When comparing the chromosomal diversities, α′ appears to be near 20 for chimpanzees and orangutans, and 1–10 for gorillas. The exception is bonobos with α′ < 1. In humans, extensive genomic data are coupled to a theory, developed herein, that can filter out selection influences on Y-linked diversities. Hence, the estimation of α′ is rigorous, yielding values near or above 20, depending on the population. When α′ > 10, the presence of ERO males is very likely. These analyses can be applied more generally to species with XY sex determination.

It is widely suspected that a small percentage of males have exceptional reproductive output (ERO) but progeny numbers of males are rarely measurable, even in humans. If we define the variance ratio of reproductive-output in males and females as α’ = V _M / V _F , the ERO hypothesis would predict α’ >>1. Since autosomal, X, and Y chromosomes are found in males 1/2, 1/3, and 100% of the time, their DNA diversities can inform about α’ . For example, autosomal and Y-linked diversities are governed, respectively, by ( V _M + V _F )/2 and V _M . When comparing the chromosomal diversities, α’ appears to be near 20 for chimpanzees and orangutans, and 1-10 for gorillas. The exception is bonobos with α’ < 1. In humans, the extensive genomic data are coupled to a theory, developed herein, that can filter out selection influences on Y-linked diversities. Hence, the estimation of α’ is rigorous, yielding values near or above 20, depending on the population. When α’ >10, the presence of ERO males is very likely. These analyses can be applied more generally to species with XY sex determination.

Multi-copy gene systems that evolve within, as well as between, individuals are common. They include viruses, mitochondrial DNAs, multi-gene families etc. The paradox is that neutral evolution in two stages should be far slower than single-copy systems but the opposite is often true, thus leading to the suggestion of natural selection. We now apply the new Generalized Haldane (GH) model to quantify genetic drift in the mammalian ribosomal RNA genes (or rDNAs). On average, rDNAs have C ∼ 150 - 300 copies. A neutral mutation in rDNA should take 4NC* generations to become fixed (N, the population size; C*, the effective copy number). While C > C* >> 1 is expected, the observed fixation time in mouse and human is < 4N, hence the paradox of C*< 1. Genetic drift thus appears as much as 100 times stronger for rRNA genes as for single-copy genes. The large increases in genetic drift are driven by a host of molecular mechanisms such as gene conversion and unequal crossover. Although each mechanism of drift has been extremely difficult to quantify, the GH model permits the estimation of their total effects on genetic drift. In conclusion, the GH model can be generally applicable to multi-copy gene systems without being burdened by tracking the diverse molecular mechanisms individually.

Population genetic models, such as the Wright-Fisher (WF) model, track relative gene frequencies. The absolute gene copy number, or population size (N), is supplied externally for tracking genetic drift. JBS Haldane (1927) proposed an alternative model based on the branching process, whereby each gene copy is transmitted to K descendants with the mean and variance of E(K) and V(K). In this model, E(K) governs N, while V(K)/N governs genetic drift. Nevertheless, as the branching process allows N to drift unboundedly, a Generalized Haldane (GH) model that regulates N more tightly is proposed. The GH model can account for several paradoxes of molecular evolution. Notably, genetic drift may often become stronger as N becomes larger in the ecological setting, thus contradicting the general view. In particular, a very small population growing exponentially experiences little drift. Interestingly, when the population grows and N oscillates near the carrying capacity, the paradoxical trend is also observed in both field works and laboratory experiments. This paradox whereby population size in genetics (Ne) and ecology (N) could be negatively correlated is resolved by the GH model. Additional paradoxes include ii) The two sexes experiencing drift differently; iii) Genetic drift of advantageous mutations being independent of N; iv) Multi-copy gene systems (viruses, mitochondria, etc.) having no definable Ne (for effective N). In brief, the GH model defines genetic drift simply as V(K), or V(K)/N averaged over the population. It represents an attempt at integrating genetical and ecological analyses into one framework.

Tumorigenesis, like most complex genetic traits, is driven by the joint actions of many mutations. At the nucleotide level, such mutations are cancer-driving nucleotides (CDNs). The full sets of CDNs are necessary, and perhaps even sufficient, for the understanding and treatment of each cancer patient. Currently, only a small fraction of CDNs is known as most mutations accrued in tumors are not drivers. We now develop the theory of CDNs on the basis that cancer evolution is massively repeated in millions of individuals. Hence, any advantageous mutation should recur frequently and, conversely, any mutation that does not is either a passenger or deleterious mutation. In the TCGA cancer database (sample size n=300–1000), point mutations may recur in i out of n patients. This study explores a wide range of mutation characteristics to determine the limit of recurrences (i^*) driven solely by neutral evolution. Since no neutral mutation can reach i^*=3, all mutations recurring at i≥3 are CDNs. The theory shows the feasibility of identifying almost all CDNs if n increases to 100,000 for each cancer type. At present, only <10% of CDNs have been identified. When the full sets of CDNs are identified, the evolutionary mechanism of tumorigenesis in each case can be known and, importantly, gene targeted therapy will be far more effective in treatment and robust against drug resistance.

A central goal of cancer genomics is to identify, in each patient, all the cancer-driving mutations. Among them, point mutations are referred to as cancer-driving nucleotides (CDNs), which recur in cancers. The companion study shows that the probability of i recurrent hits in n patients would decrease exponentially with i; hence, any mutation with i ≥ 3 hits in The Cancer Genome Atlas (TCGA) database is a high-probability CDN. This study characterizes the 50–150 CDNs identifiable for each cancer type of TCGA (while anticipating 10 times more undiscovered ones) as follows: (i) CDNs tend to code for amino acids of divergent chemical properties. (ii) At the genic level, far more CDNs (more than fivefold) fall on noncanonical than canonical cancer-driving genes (CDGs). Most undiscovered CDNs are expected to be on unknown CDGs. (iii) CDNs tend to be more widely shared among cancer types than canonical CDGs, mainly because of the higher resolution at the nucleotide than the whole-gene level. (iv) Most important, among the 50–100 coding region mutations carried by a cancer patient, 5–8 CDNs are expected but only 0–2 CDNs have been identified at present. This low level of identification has hampered functional test and gene-targeted therapy. We show that, by expanding the sample size to 10⁵, most CDNs can be identified. Full CDN identification will then facilitate the design of patient-specific targeting against multiple CDN-harboring genes.

Tumorigenesis, like most complex genetic traits, is driven by the joint actions of many mutations. At the nucleotide level, such mutations are Cancer Driving Nucleotides (CDNs). The full sets of CDNs are necessary, and perhaps even sufficient, for the understanding and treatment of each cancer patient. Currently, only a small fraction of CDNs is known as most mutations accrued in tumors are not drivers. We now develop the theory of CDNs on the basis that cancer evolution is massively repeated in millions of individuals. Hence, any advantageous mutation should recur frequently and, conversely, any mutation that does not is either a passenger or deleterious mutation. In the TCGA cancer database (sample size n = 300 - 1000), point mutations may recur in i out of n patients. This study explores a wide range of mutation characteristics to determine the limit of recurrences (i*) driven solely by neutral evolution. Since no neutral mutation can reach i* = 3, all mutations recurring at i ≥ 3 are CDNs. The theory shows the feasibility of identifying almost all CDNs if n increases to 100,000 for each cancer type. At present, only < 10% of CDNs have been identified. When the full sets of CDNs are identified, the evolutionary mechanism of tumorigenesis in each case can be known and, importantly, gene targeted therapy will be far more effective in treatment and robust against drug resistance.

A central goal of cancer genomics is to identify, in each patient, all the cancer driving mutations. Among them, point mutations are referred to as Cancer Driving Nucleotides (CDNs), which recur in cancers. The companion study shows that the probability of i recurrent hits in n patients would decrease exponentially with i; hence, any mutation with i ≥ 3 hits in the TCGA database is a high-probability CDN. This study characterizes the 50∼150 CDNs identifiable for each cancer type of TCGA (while anticipating 10 times more undiscovered ones) as follows: i) CDNs tend to code for amino acids of divergent chemical properties. ii) At the genic level, far more CDNs (>5-fold) fall on non-canonical than canonical cancer driving genes (CDGs). Most undiscovered CDNs are expected to be on unknown CDGs. iii) CDNs tend to be more widely shared among cancer types than canonical CDGs, mainly because of the higher resolution at the nucleotide than the whole-gene level. iv) Most important, among the 50∼100 coding region mutations carried by a cancer patient, 5∼8 CDNs are expected but only 0∼2 CDNs have been identified at present. This low level of identification has hampered functional test and gene targeted therapy. We show that, by expanding the sample size to 105, most CDNs can be identified. Full CDN identification will then facilitate the design of patient-specific targeting against multiple CDN-harboring genes.

Multi-copy gene systems that evolve within, as well as between, individuals are common. They include viruses, mitochondrial DNAs, multi-gene families etc. The paradox is that neutral evolution in two stages should be slower than single-copy systems but the opposite is often true. We now apply the Haldane model, recently generalized as the GH model (1), to quantify genetic drift in mammalian ribosomal RNA genes (rDNAs). On average, the copy number ( C ) is 150 - 300 per haploid. A neutral mutation in rDNA should take 4 NC ^* generations to become fixed ( N , the population size; C ^* , the effective copy number within individuals). While C > C ^* >> 1 is expected, the observed fixation time in mouse is < 4 N , leading to the paradox of C ^* < 1. Genetic drift of rRNA genes thus appears 10-100 times stronger than in single-copy genes. The large increases are driven by a host of molecular mechanisms such as gene conversion and unequal crossover. Although each mechanism of drift is very difficult to quantify, the GH model permits the estimation of their total effects that constitute the aggregate “evolutionary noises”. In humans, the fixation rate of rRNA genes is higher than the theoretical maximum of drift, hence, justifying the inference of adaptive evolution. In conclusion, the stochastic evolution in multi-copy gene systems, including viruses and others, can be effectively tracked by GH model.

Recent studies have increasingly pointed to microRNAs (miRNAs) as the agent of GRN (gene regulatory network) stabilization as well as developmental canalization against constant but small environmental perturbations. To analyze mild perturbations, we construct a Dicer-1 knockdown line (dcr-1 KD) in Drosophila that modestly reduces all miRNAs by, on average, ∼ 20%. The defining characteristic of stabilizers is that, when their capacity is compromised, GRNs do not change their short-term behaviors. Indeed, even with such broad reductions across all miRNAs, the changes in the transcriptome are very modest during development in stable environment. By comparison, broad knock-downs of other regulatory genes (esp. transcription factors) by the same method should lead to drastic changes in the GRNs. The consequence of de-stabilization may thus be in long-term development as postulated by the theory of canalization. Flies with modest miRNA reductions may gradually deviate from the developmental norm, resulting in late-stage failures such as shortened longevity. In the optimal culture condition, the survival to adulthood is indeed normal in the dcr-1 KD line but, importantly, adult longevity is reduced by ∼ 90%. When flies are stressed by high temperature, dcr-1 KD induces lethality earlier in late pupation and, as the perturbations are shifted earlier, the affected stages are shifted correspondingly. Hence, in late stages of development with deviations piling up, GRN would be increasingly in need of stabilization. In conclusion, miRNAs appear to be a solution to weak but constant environmental perturbations.