No abstract

We present a quantitative continuum theory of "flocking": the collective coherent motion of large numbers of self-propelled organisms. In agreement with everyday experience, our model predicts the existence of an "ordered phase" of flocks, in which all members of even an arbitrarily large flock move together with the same mean velocity v = 0. This coherent motion of the flock is an example of spontaneously broken symmetry: no preferred direction for the motion is picked out a priori in the model; rather, each flock is allowed to, and does, spontaneously pick out some completely arbitrary direction to move in. By analyzing our model we can make detailed, quantitative predictions for the long-distance, long-time behavior of this "broken symmetry state". The "Goldstone modes" associated with this "spontaneously broken rotational symmetry" are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a 1 whole. These "Goldstone modes" mix with modes associated with conservation of bird number to produce propagating sound modes. These sound modes lead to enormous fluctuations of the density of the flock, far larger, at long wavelengths, than those in, e. g., an equilibrium gas. Our model is similar in many ways to the Navier-Stokes equations for a simple compressible fluid; in other ways, it resembles a relaxational time dependent GinsburgLandau theory for an n = d component isotropic ferromagnet. In spatial dimensions d > 4, the long distance behavior is correctly described by a linearized theory, and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems. For d < 4, non-linear fluctuation effects radically alter the long distance behavior, making it different from that of any known equilibrium model. In particular, we find that in d = 2, where we can calculate the scaling exponents exactly, flocks exhibit a true, longrange ordered, spontaneously broken symmetry state, in contrast to equilibrium systems, which cannot spontaneously break a continuous symmetry in d = 2 (the "Mermin-Wagner" theorem). We make detailed predictions for various correlation functions that could be measured either in simulations, or by quantitative imaging of real flocks. We also consider an anisotropic model, in which the birds move preferentially in an "easy" (e. g., horizontal) plane, and make analogous, but quantitatively different, predictions for that model as well. For this anisotropic model, we obtain exact scaling exponents for all spatial dimensions, including the physically relevant case d = 3.

We review the past decadeÕs theoretical and experimental studies of flocking: the collective,

B cell–derived chronic lymphocytic leukemia (B-CLL) represents a common malignancy whose cell derivation and pathogenesis are unknown. Recent studies have shown that >50% of CLLs display hypermutated immunoglobulin variable region (IgV) sequences and a more favorable prognosis, suggesting that they may represent a distinct subset of CLLs which have transited through germinal centers (GCs), the physiologic site of IgV hypermutation. To further investigate the phenotype of CLLs, their cellular derivation and their relationship to normal B cells, we have analyzed their gene expression profiles using oligonucleotide-based DNA chip microarrays representative of ∼12,000 genes. The results show that CLLs display a common and characteristic gene expression profile that is largely independent of their IgV genotype. Nevertheless, a restricted number of genes (<30) have been identified whose differential expression can distinguish IgV mutated versus unmutated cases and identify them in independent panels of cases. Comparison of CLL profiles with those of purified normal B cell subpopulations indicates that the common CLL profile is more related to memory B cells than to those derived from naive B cells, CD5+ B cells, and GC centroblasts and centrocytes. Finally, this analysis has identified a subset of genes specifically expressed by CLL cells of potential pathogenetic and clinical relevance.

Adaptation is the essential process by which an organism becomes better suited to its environment. The benefits of adaptation are well documented, but the cost it incurs remains poorly understood. Here, by analysing a stochastic model of a minimum feedback network underlying many sensory adaptation systems, we show that adaptive processes are necessarily dissipative, and continuous energy consumption is required to stabilize the adapted state. Our study reveals a general relation among energy dissipation rate, adaptation speed and the maximum adaptation accuracy. This energy-speed-accuracy relation is tested in the Escherichia coli chemosensory system, which exhibits near-perfect chemoreceptor adaptation. We identify key requirements for the underlying biochemical network to achieve accurate adaptation with a given energy budget. Moreover, direct measurements confirm the prediction that adaptation slows down as cells gradually de-energize in a nutrient-poor medium without compromising adaptation accuracy. Our work provides a general framework to study cost-performance tradeoffs for cellular regulatory functions and information processing.