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Error thresholds and stationary mutant distributions in multi-locus diploid genetics models
- Paul G. Higgs
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- Journal:
- Genetical Research / Volume 63 / Issue 1 / February 1994
- Published online by Cambridge University Press:
- 14 April 2009, pp. 63-78
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We study multi-locus models for the accumulation of disadvantagenous mutant alleles in diploid populations. The theory used is closely related to the quasi-species theory of molecular evolution. The stationary mutant distribution may either be localized close to a peak in the fitness landscape or delocalized throughout sequence space. In some cases there is a sharp transition between these two cases known as an error threshold. We study a multiplicative fitness landscape where the fitness of an individual with j homozygous mutant loci and k heterozygous loci is wjk = (1 − s)j (1 − hs)k. For a sexual population in this landscape there are two types of solution separated by an error threshold. For a parthenogenetic population there may be three types of solution and two error thresholds for some values of h. For a population reproducing by selfing the solution is independent of h, since the frequency of heterozygous individuals is negligible. The mean fitnesses of the populations depend on the reproductive method even for the multiplicative landscape. The sexual may have a higher or lower fitness than the parthenogen, depending on the values of h and u/s. Selfing leads to a higher mean fitness than either sexual reproduction or parthenogenesis. We also study a fitness landscape with epistatic interactions with wjk = exp(− s(2j + k)α). The sexual population has a higher fitness than the parthenogen when α > 1. This confirms previous theories that sexual reproduction is advantageous in cases of synergistic epistasis. The mean fitness of a selfing population was found to be higher than both the sexual and the parthenogen over the range of parameter values studied. We discuss these results in relation to the theory of the evolution of sex. The fitness of the stationary distribution in cases where unfavourable mutations accumulation is one factor which could explain the observed prevalence of sexual reproduction in natural populations, although other factors may be more important in many cases.
4 - From protoplanetary disks to prebiotic amino acids and the origin of the genetic code
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- By Paul G. Higgs, McMaster University, Ralph E. Pudritz, McMaster University
- Edited by Ralph Pudritz, McMaster University, Ontario, Paul Higgs, McMaster University, Ontario, Jonathon Stone, McMaster University, Ontario
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- Book:
- Planetary Systems and the Origins of Life
- Published online:
- 13 August 2009
- Print publication:
- 06 December 2007, pp 62-88
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Summary
Introduction
The robust formation of planets as well as abundant sources of water and organic molecules are likely to be important prerequisites for the wide-spread appearance of life in the cosmos. The nebular hypothesis of Kant and Laplace was the first to propose that the formation of planets occurs in gaseous disks around stars. The construction of new infrared and submillimetre observatories over the last decade and a half has resulted in the discovery of protoplanetary discs around most, if not all, forming stars regardless of their mass (e.g., reviews by Meyer et al. (2006), Dutrey et al. (2006)). The recent discoveries of extrasolar planets in over a hundred planetary systems provides good evidence that Jovian planets, at least, may be relatively abundant around solar-like stars (see Chapter 1). These results beg the question of whether protoplanetary disks are also natural settings for the manufacture of the molecular prerequisites for life. Life requires water and organic molecules such as amino acids, sugars, nucleobases, and lipids as building blocks out of which biological macromolecules and cellular structures are made, and many of these can be manufactured in protoplanetary disks.
In the first part of this chapter we review the properties of protoplanetary disks and how planets are believed to form within them. We then consider the evidence that these disks may be a major source of the water and biomolecules available for the earliest life, as on the Earth.
RNA secondary structure: physical and computational aspects
- Paul G. Higgs
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- Journal:
- Quarterly Reviews of Biophysics / Volume 33 / Issue 3 / August 2000
- Published online by Cambridge University Press:
- 12 January 2001, pp. 199-253
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1. Background to RNA structure 200
1.1 Types of RNA 200
1.1.1 Transfer RNA (tRNA) 200
1.1.2 Messenger RNA (mRNA) 201
1.1.3 Ribosomal RNA (rRNA) 201
1.1.4 Other ribonucleoprotein particles 202
1.1.5 Viruses and viroids 202
1.1.6 Ribozymes 202
1.2 Elements of RNA secondary structure 203
1.3 Secondary structure versus tertiary structure 205
2. Theoretical and computational methods for RNA secondary structure determination 208
2.1 Dynamic programming algorithms 208
2.2 Kinetic folding algorithms 210
2.3 Genetic algorithms 212
2.4 Comparative methods 213
3. RNA thermodynamics and folding mechanisms 216
3.1 The reliability of minimum free energy structure prediction 216
3.2 The relevance of RNA folding kinetics 218
3.3 Examples of RNA folding kinetics simulations 221
3.4 RNA as a disordered system 227
4. Aspects of RNA evolution 233
4.1 The relevance of RNA for studies of molecular evolution 233
4.1.1 Molecular phylogenetics 234
4.1.2 tRNAs and the genetic code 234
4.1.3 Viruses and quasispecies 235
4.1.4 Fitness landscapes 235
4.2 The interaction between thermodynamics and sequence evolution 236
4.3 Theory of compensatory substitutions in RNA helices 238
4.4 Rates of compensatory substitutions obtained from sequence analysis 240
5. Conclusions 246
6. Acknowledgements 246
7. References 246
This article takes an inter-disciplinary approach to the study of RNA secondary structure, linking together aspects of structural biology, thermodynamics and statistical physics, bioinformatics, and molecular evolution. Since the intended audience for this review is diverse, this section gives a brief elementary level discussion of the chemistry and structure of RNA, and a rapid overview of the many types of RNA molecule known. It is intended primarily for those not already familiar with molecular biology and biochemistry.
Ribonucleic acid consists of a linear polymer with a backbone of ribose sugar rings linked by phosphate groups. Each sugar has one of the four ‘bases’ adenine, cytosine, guanine and uracil (A, C, G, and U) linked to it as a side group. The structure and function of an RNA molecule is specific to the sequence of bases. The phosphate groups link the 5′ carbon of one ribose to the 3′ carbon of the next. This imposes a directionality on the backbone. The two ends are referred to as 5′ and 3′ ends, since one end has an unlinked 5′ carbon and one has an unlinked 3′ carbon. The chemical differences between RNA and DNA (deoxyribonucleic acid) are fairly small: one of the OH groups in ribose is replaced by an H in deoxyribose, and DNA contains thymine (T) bases instead of U. However, RNA structure is very different from DNA structure. In the familiar double helical structure of DNA the two strands are perfectly complementary in sequence. RNA usually occurs as single strands, and base pairs are formed intra-molecularly, leading to a complex arrangement of short helices which is the basis of the secondary structure. Some RNA molecules have well-defined tertiary structures. In this sense, RNA structures are more akin to globular protein structures than to DNA.
The role of proteins as biochemical catalysts and the role of DNA in storage of genetic information have long been recognised. RNA has sometimes been considered as merely an intermediary between DNA and proteins. However, an increasing number of functions of RNA are now becoming apparent, and RNA is coming to be seen as an important and versatile molecule in its own right.