Allometric scaling and metabolic ecology of microorganisms and major evolutionary transitions

My dissertation centers around investigating big-picture questions related to understanding the consequences of metabolism and energetics on the evolution, ecology, and physiology of life. The evolutionary transitions from prokaryotes to unicellular eukaryotes to multicellular organisms were accompanied by major innovations in metabolic design. In my first chapter, I show that the scaling of metabolic rate, population growth rate, and production efficiency with body size have changed across these transitions. Metabolic rate scales with body mass superlinearly in prokaryotes, linearly in protists, and sublinearly in metazoans, so Kleibers 3/4 power scaling law does not apply universally across organisms. This means that major changes in metabolic processes during the early evolution of life overcame existing physical constraints, exploited new opportunities, and imposed new constraints on organism physiology. Surface areas of physiological structures of organisms impose fundamental constraints on metabolic rate. In my second chapter, I demonstrate that organisms have a variety of options for increasing the scaling of the area of their metabolic surfaces with body sizes. I develop models and examples illustrating the role of cell membrane elaborations, mitochondria, vacuoles, vesicles, inclusions, and shape-shifting in the architectural design, evolution, and ecology of unicellular microbes. I demonstrate how these surface-area scaling adaptations have played important roles in the evolution of major biological designs of cells and the physiological ecology of organisms. In my third and final chapter, I integrate and synthesize findings from the previous two chapters with important developments in geochemistry, microbiology, and astrobiology in order to identify the fundamental physical and biological dimensions that characterize a metabolic theory of ecology of microorganisms. These dimensions are thermodynamics, chemical kinetics, physiological harshness, cell size, and levels of biological organization. I show how addressing these dimensions can inform understanding of the physical and biological factors governing the metabolic rate, growth rate, and geographic distribution of cells. I propose a unifying theory to understand how the major ecological and evolutionary transitions that led to increases in levels of organization of life, such as endosymbiosis, multicellularity, eusociality, and multi-domain complexes, influences the metabolism and growth and the metabolic scaling of these complexes

Evaluating space measures in P systems

P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented

Giant adsorption of microswimmers: duality of shape asymmetry and wall curvature

The effect of shape asymmetry of microswimmers on their adsorption capacity at confining channel walls is studied by a simple dumbbell model. For a shape polarity of a forward-swimming cone, like the stroke-averaged shape of a sperm, extremely long wall retention times are found, caused by a non-vanishing component of the propulsion force pointing steadily into the wall, which grows exponentially with the self-propulsion velocity and the shape asymmetry. A direct duality relation between shape asymmetry and wall curvature is proposed and verified. Our results are relevant for the design microswimmer with controlled wall-adhesion properties. In addition, we confirm that pressure in active systems is strongly sensitive to the details of the particle-wall interactions.Comment: 6 pages, 7 figure

A sublinear Sudoku solution in cP Systems and its formal verification

Sudoku is known as a NP-complete combinatorial number-placement puzzle. In this study, we propose the first cP system solution to generalised Sudoku puzzles with m×m cells grouped in m blocks. By using a fixed constant number of rules, our cP system can solve all Sudoku puzzles in sublinear steps. We evaluate the cP system and discuss its formal verification

Logarithmic SAT Solution with Membrane Computing

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., which solves SAT in square-root-sublinear time, this paper proposes an orders-of-magnitude-faster solution, running in logarithmic time, and using a small fixed-sized alphabet and ruleset (25 rules). To the best of our knowledge, this is the fastest deterministic solution across all extant P system variants. Like all other cP solutions, it is a complete solution that is not a member of a uniform family (and thus does not require any preprocessing). Consequently, according to another reduction result by Henderson et al., cP systems can also solve k-colouring and several other NP-complete problems in logarithmic time

On a Model for Phase Separation on Biological Membranes and its Relation to the Ohta-Kawasaki Equation

We provide a detailed mathematical analysis of a model for phase separation on biological membranes which was recently proposed by Garcke, R\"atz, R\"oger and the second author. The model is an extended Cahn-Hilliard equation which contains additional terms to account for the active transport processes. We prove results on the existence and regularity of solutions, their long-time behaviour, and on the existence of stationary solutions. Moreover, we investigate two different asymptotic regimes. We study the case of large cytosolic diffusion and investigate the effect of an infinitely large affinity between membrane components. The first case leads to the reduction of coupled bulk-surface equations in the model to a system of surface equations with non-local contributions. Subsequently, we recover a variant of the well-known Ohta-Kawasaki equation as the limit for infinitely large affinity between membrane components.Comment: 41 page

Space complexity equivalence of P systems with active membranes and Turing machines

We prove that arbitrary single-tape Turing machines can be simulated by uniform families of P systems with active membranes with a cubic slowdown and quadratic space overhead. This result is the culmination of a series of previous partial results, finally establishing the equivalence (up to a polynomial) of many space complexity classes defined in terms of P systems and Turing machines. The equivalence we obtained also allows a number of classic computational complexity theorems, such as Savitch's theorem and the space hierarchy theorem, to be directly translated into statements about membrane systems

Tracer diffusion inside fibrinogen layers

We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen molecules are significantly anisotropic and therefore they can form structures where orientational ordering, similar to the one observed in nematic liquid crystals, appears. The work focuses on the dependence between level of the orientational order (degree of environmental crowding) of fibrinogen molecules inside a layer and non-Fickian character of the diffusion process of spherical tracer particles moving within the domain. It is shown that in general particles motion is subdiffusive and strongly anisotropic, and its characteristic features significantly change with the orientational order parameter, concentration of fibrinogens and radius of a diffusing probe.Comment: 8 pages, 12 figure