Book•
Random walks in biology
01 Jan 1983-
TL;DR: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know.
Abstract: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.
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TL;DR: A conceptual framework depicting the interplay among four basic mechanistic components of organismal movement is introduced, providing a basis for hypothesis generation and a vehicle facilitating the understanding of the causes, mechanisms, and spatiotemporal patterns of movement and their role in various ecological and evolutionary processes.
Abstract: Movement of individual organisms is fundamental to life, quilting our planet in a rich tapestry of phenomena with diverse implications for ecosystems and humans. Movement research is both plentiful and insightful, and recent methodological advances facilitate obtaining a detailed view of individual movement. Yet, we lack a general unifying paradigm, derived from first principles, which can place movement studies within a common context and advance the development of a mature scientific discipline. This introductory article to the Movement Ecology Special Feature proposes a paradigm that integrates conceptual, theoretical, methodological, and empirical frameworks for studying movement of all organisms, from microbes to trees to elephants. We introduce a conceptual framework depicting the interplay among four basic mechanistic components of organismal movement: the internal state (why move?), motion (how to move?), and navigation (when and where to move?) capacities of the individual and the external factors affecting movement. We demonstrate how the proposed framework aids the study of various taxa and movement types; promotes the formulation of hypotheses about movement; and complements existing biomechanical, cognitive, random, and optimality paradigms of movement. The proposed framework integrates eclectic research on movement into a structured paradigm and aims at providing a basis for hypothesis generation and a vehicle facilitating the understanding of the causes, mechanisms, and spatiotemporal patterns of movement and their role in various ecological and evolutionary processes. "Now we must consider in general the common reason for moving with any movement whatever." (Aristotle, De Motu Animalium, 4th century B.C.).
2,133 citations
TL;DR: An approach to fabricate solid capsules with precise control of size, permeability, mechanical strength, and compatibility is presented, which are hollow, elastic shells whose permeability and elasticity can be precisely controlled.
Abstract: We present an approach to fabricate solid capsules with precise control of size, permeability, mechanical strength, and compatibility. The capsules are fabricated by the self-assembly of colloidal particles onto the interface of emulsion droplets. After the particles are locked together to form elastic shells, the emulsion droplets are transferred to a fresh continuous-phase fluid that is the same as that inside the droplets. The resultant structures, which we call "colloidosomes," are hollow, elastic shells whose permeability and elasticity can be precisely controlled. The generality and robustness of these structures and their potential for cellular immunoisolation are demonstrated by the use of a variety of solvents, particles, and contents.
1,976 citations
Cites background from "Random walks in biology"
...04) and s are the area fraction and radius of holes, which we approximate as circles (33)....
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TL;DR: The motion of an artificial microscale swimmer that uses a chemical reaction catalyzed on its own surface to achieve autonomous propulsion is fully characterized experimentally and suggests strategies for designing artificial chemotactic systems.
Abstract: The motion of an artificial microscale swimmer that uses a chemical reaction catalyzed on its own surface to achieve autonomous propulsion is fully characterized experimentally. It is shown that at short times it has a substantial component of directed motion, with a velocity that depends on the concentration of fuel molecules. At longer times, the motion reverts to a random walk with a substantially enhanced diffusion coefficient. Our results suggest strategies for designing artificial chemotactic systems.
1,828 citations
TL;DR: It is shown that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Lévy flight motion, is an optimal strategy.
Abstract: We address the general question of what is the best statistical strategy to adapt in order to search efficiently for randomly located objects ('target sites'). It is often assumed in foraging theory that the flight lengths of a forager have a characteristic scale: from this assumption gaussian, Rayleigh and other classical distributions with well-defined variances have arisen. However, such theories cannot explain the long-tailed power-law distributions of flight lengths or flight times that are observed experimentally. Here we study how the search efficiency depends on the probability distribution of flight lengths taken by a forager that can detect target sites only in its limited vicinity. We show that, when the target sites are sparse and can be visited any number of times, an inverse square power-law distribution of flight lengths, corresponding to Levy flight motion, is an optimal strategy. We test the theory by analysing experimental foraging data on selected insect, mammal and bird species, and find that they are consistent with the predicted inverse square power-law distributions.
1,416 citations
TL;DR: The mathematical theory behind the simple random walk is introduced and how this relates to Brownian motion and diffusive processes in general and a reinforced random walk can be used to model movement where the individual changes its environment.
Abstract: Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.
1,313 citations
Cites background from "Random walks in biology"
...Indeed the so-called chemotaxis of bacteria (Alt 1980; Berg 1983) is mainly a DK-kinesis where...
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...Indeed the so-called chemotaxis of bacteria (Alt 1980; Berg 1983) is mainly a DK-kinesis where the sinuosity is modulated through step length rather than turning angle variance (called a run-and-tumble mechanism)....
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...For example, the classical run-and-tumble behaviour observed in chemotactic bacteria is usually modelled through a low rate of turning when moving in the preferred direction (runs) and a high rate of turning (tumbles) otherwise (Berg 1983)....
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