Endosymbiosis before eukaryotes: mitochondrial establishment in protoeukaryotes

Endosymbiosis and organellogenesis are virtually unknown among prokaryotes. The single presumed example is the endosymbiogenetic origin of mitochondria, which is hidden behind the event horizon of the last eukaryotic common ancestor. While eukaryotes are monophyletic, it is unlikely that during billions of years, there were no other prokaryote–prokaryote endosymbioses as symbiosis is extremely common among prokaryotes, e.g., in biofilms. Therefore, it is even more precarious to draw conclusions about potentially existing (or once existing) prokaryotic endosymbioses based on a single example. It is yet unknown if the bacterial endosymbiont was captured by a prokaryote or by a (proto-)eukaryote, and if the process of internalization was parasitic infection, slow engulfment, or phagocytosis. In this review, we accordingly explore multiple mechanisms and processes that could drive the evolution of unicellular microbial symbioses with a special attention to prokaryote–prokaryote interactions and to the mitochondrion, possibly the single prokaryotic endosymbiosis that turned out to be a major evolutionary transition. We investigate the ecology and evolutionary stability of inter-species microbial interactions based on dependence, physical proximity, cost–benefit budget, and the types of benefits, investments, and controls. We identify challenges that had to be conquered for the mitochondrial host to establish a stable eukaryotic lineage. Any assumption about the initial interaction of the mitochondrial ancestor and its contemporary host based solely on their modern relationship is rather perilous. As a result, we warn against assuming an initial mutually beneficial interaction based on modern mitochondria–host cooperation. This assumption is twice fallacious: (i) endosymbioses are known to evolve from exploitative interactions and (ii) cooperativity does not necessarily lead to stable mutualism. We point out that the lack of evidence so far on the evolution of endosymbiosis from mutual syntrophy supports the idea that mitochondria emerged from an exploitative (parasitic or phagotrophic) interaction rather than from syntrophy

The Evolution of Microbial Facilitation: Sociogenesis, Symbiogenesis, and Transition in Individuality

Metabolic cooperation is widespread, and it seems to be a ubiquitous and easily evolvable interaction in the microbial domain. Mutual metabolic cooperation, like syntrophy, is thought to have a crucial role in stabilizing interactions and communities, for example biofilms. Furthermore, cooperation is expected to feed back positively to the community under higher-level selection. In certain cases, cooperation can lead to a transition in individuality, when freely reproducing, unrelated entities (genes, microbes, etc.) irreversibly integrate to form a new evolutionary unit. The textbook example is endosymbiosis, prevalent among eukaryotes but virtually lacking among prokaryotes. Concerning the ubiquity of syntrophic microbial communities, it is intriguing why evolution has not lead to more transitions in individuality in the microbial domain. We set out to distinguish syntrophy-specific aspects of major transitions, to investigate why a transition in individuality within a syntrophic pair or community is so rare. We review the field of metabolic communities to identify potential evolutionary trajectories that may lead to a transition. Community properties, like joint metabolic capacity, functional profile, guild composition, assembly and interaction patterns are important concepts that may not only persist stably but according to thought-provoking theories, may provide the heritable information at a higher level of selection. We explore these ideas, relating to concepts of multilevel selection and of informational replication, to assess their relevance in the debate whether microbial communities may inherit community-level information or not

Topological Excitations of One-Dimensional Correlated Electron Systems

Properties of low-energy excitations in one-dimensional superconductors and density-wave systems are examined by the bosonization technique. In addition to the usual spin and charge quantum numbers, a new, independently measurable attribute is introduced to describe elementary, low-energy excitations. It can be defined as a number w which determines, in multiple of $\pi$, how many times the phase of the order parameter winds as an excitation is transposed from far left to far right. The winding number is zero for electrons and holes with conventional quantum numbers, but it acquires a nontrivial value w=1 for neutral spin-1/2 excitations and for spinless excitations with a unit electron charge. It may even be irrational, if the charge is irrational. Thus, these excitations are topological, and they can be viewed as composite particles made of spin or charge degrees of freedom and dressed by kinks in the order parameter.Comment: 5 pages. And we are not only splitting point

Transitions from small to large Fermi momenta in a one-dimensional Kondo lattice model

We study a one-dimensional system that consists of an electron gas coupled to a spin-1/2 chain by Kondo interaction away from half-filling. We show that zero-temperature transitions between phases with "small" and "large" Fermi momenta can be continuous. Such a continuous but Fermi-momentum-changing transition arises in the presence of spin anisotropy, from a Luttinger liquid with a small Fermi momentum to a Kondo-dimer phase with a large Fermi momentum. We have also added a frustrating next-nearest-neighbor interaction in the spin chain to show the possibility of a similar Fermi-momentum-changing transition, between the Kondo phase and a spin-Peierls phase, in the spin isotropic case. This transition, however, appears to involve a region in which the two phases coexist.Comment: The updated version clarifies the definitions of small and large Fermi momenta, the role of anisotropy, and how Kondo interaction affects Luttinger liquid phase. 12 pages, 5 figure

Non-perturbative approach to Luttinger's theorem in one dimension

The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins in one-dimensional lattice. The existence of a low-energy state is generally proved except for special commensurate fillings where a gap may occur. Moreover, the crystal momentum of the constructed low-energy state is $2k_F$, where $k_F$ is the Fermi momentum of the non-interacting model, corresponding to Luttinger's theorem. For the Kondo lattice model, our result implies that $k_F$ must be calculated by regarding the localized spins as additional electrons.Comment: Note added on the rigorous proof given by H. Tasaki; also added some references; 5 pages, REVTEX (no figure

Localized charged states and phase separation near second order phase transition

Localized charged states and phase segregation are described in the framework of the phenomenological Ginzburg-Landau theory of phase transitions. The Coulomb interactions determines the charge distribution and the characteristic length of the phase separated states. The phase separation with charge segregation becomes possible because of the large dielectric constant and the small density of extra charge in the range of charge localization. The phase diagram is calculated and the energy gain of the phase separated state is estimated. The role of the Coulomb interaction is elucidated

Relationship between incommensurability and superconductivity in Peierls distorted charge-density-wave systems

We study the pairing potential induced by fluctuations around a charge-density wave (CDW) with scattering vector Q by means of the Froehlich transformation. For general commensurability M, defined as |k+M*Q>=|k>, we find that the intraband pair scattering within the M subbands scales with M whereas the interband pair scattering becomes suppressed with increasing CDW order parameter. As a consequence superconductivity is suppressed when the Fermi energy is located between the subbands as it is usually the case for nesting induced CDW's, but due to the vertex renormalization it can be substantially enhanced when the chemical potential is shifted sufficiently inside one of the subbands. The model can help to understand the experimentally observed dependence of the superconducting transition temperature from the stripe phase incommensurability in the lanthanum cuprates.Comment: 6 pages, 3 figure

Ordering of localized moments in Kondo lattice models

We describe the transition from a ferromagnetic phase, to a disordered para- magnetic phase, which occurs in one-dimensional Kondo lattice models with partial conduction band filling. The transition is the quantum order-disorder transition of the transverse-field Ising chain, and reflects double-exchange ordered regions of localized spins being gradually destroyed as the coupling to the conduction electrons is reduced. For incommensurate conduction band filling, the low-energy properties of the localized spins near the transition are dominated by anomalous ordered (disordered) regions of localized spins which survive into the paramagnetic (ferromagnetic) phase. Many interesting properties follow, including a diverging susceptibility for a finite range of couplings into the paramagnetic phase. Our critical line equation, together with numerically determined transition points, are used to determine the range of the double-exchange interaction. Models we consider are the spin 1/2 Kondo lattices with antiferromagnetic (Kondo) coupling, with ferromagnetic (Hund's rule) coupling, and the Kondo lattice with repulsive interactions between the conduction electrons.Comment: 18 pages, 6 embedded eps figures. To appear in Phys Rev

Impurity correlations in dilute Kondo alloys

The single impurity Kondo model is often used to describe metals with dilute concentrations (n_i) of magnetic impurities. Here we examine how dilute the impurities must be for this to be valid by developing a virial expansion in impurity density. The O(n_i^2) term is determined from results on the 2-impurity Kondo problem by averaging over the RKKY coupling. The non-trivial fixed point of the 2-impurity problem could produce novel singularities in the heat capacity of dilute alloys at O(n_i^2).Comment: 6 pages, no figure