Many single-molecule experiments aim to characterize biomolecular processes in terms of kinetic models that specify the rates of transition between conformational states of the biomolecule. Estimation of these rates often requires analysis of a population of molecules, in which the conformational trajectory of each molecule is represented by a noisy, time-dependent signal trajectory. Although hidden Markov models (HMMs) may be used to infer the conformational trajectories of individual molecules, estimating a consensus kinetic model from the population of inferred conformational trajectories remains a statistically difficult task, as inferred parameters vary widely within a population. Here, we demonstrate how a recently developed empirical Bayesian method for HMMs can be extended to enable a more automated and statistically principled approach to two widely occurring tasks in the analysis of single-molecule fluorescence resonance energy transfer (smFRET) experiments: 1), the characterization of changes in rates across a series of experiments performed under variable conditions; and 2), the detection of degenerate states that exhibit the same FRET efficiency but differ in their rates of transition. We apply this newly developed methodology to two studies of the bacterial ribosome, each exemplary of one of these two analysis tasks. We conclude with a discussion of model-selection techniques for determination of the appropriate number of conformational states. The code used to perform this analysis and a basic graphical user interface front end are available as open source software.

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed 100 µm. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant Chara, whose cells can exceed 10 cm in length and 1 mm in diameter. Two spiralling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to 100 µm s−1, motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as ‘cytoplasmic streaming’, found in a wide range of eukaryotic organisms—algae, plants, amoebae, nematodes and flies—often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

We report a novel transition to core precession for granular flows in a split-bottomed shear cell. This transition is related to a qualitative change in the 3D flow structure: For shallow layers of granular material, the shear zones emanating from the split reach the free surface, while for deep layers the shear zones meet below the surface, causing precession. The surface velocities reflect this transition by a change of symmetry. As a function of layer depth, we find that three qualitatively different smooth and robust granular flows can be created in this simple shearing geometry.

Found in many large eukaryotic cells, particularly in plants, cytoplasmic streaming is the circulation of their contents driven by fluid entrainment from particles carried by molecular motors at the cell periphery. In the more than two centuries since its discovery, streaming has frequently been conjectured to aid in transport and mixing of molecular species in the cytoplasm and, by implication, in cellular homeostasis, yet no theoretical analysis has been presented to quantify these processes. We show by a solution to the coupled dynamics of fluid flow and diffusion appropriate to the archetypal ''rotational streaming'' of algal species such as Chara and Nitella that internal mixing and the transient dynamical response to changing external conditions can indeed be enhanced by streaming, but to an extent that depends strongly on the pitch of the helical flow. The possibility that this may have a developmental consequence is illustrated by the coincidence of the exponential growth phase of Nitella and the point of maximum enhancement of those processes. Since Bonaventura Corti's discovery (1) in 1774 of the persistent circulation of the cytoplasm of plant cells, the phenomenon now known as cytoplasmic streaming or cyclosis has been conjectured to play an important role in metabolism (2). It occurs in organisms as diverse as amoebae (3), algae and terrestrial plants (4,5), and fungi (6). In plants (4, 5, 7) it is driven by multitudes of the motor protein myosin moving along bundled actin at the boundary of the cytoplasm, carrying microscopic particles or organelles (8, 9), and entraining fluid. The motion of protoplasmic granules entrained in the flow includes unidirectional streaming, ''fountain streaming'' (in which the motion near the central axis of the cell is opposite to that near the periphery), and spiral ''rotational streaming.'' Plant myosins can move at tens of micrometers per second (10-13), considerably faster than most animal myosins (although some can reach Ϸ30 m/s), and the speed U of cyclosis can reach Ϸ100 m/s in cells whose radius R can reach 0.5 mm. These speeds greatly outpace diffusion, as measured by the Péclet number Pe ϭ UR/D, where D is a molecular diffusion constant. For the smallest molecules, with D ϳ 10 Ϫ5 cm 2 /s, we see that Pe ϳ 50, and it can easily reach 500-1,000 for larger proteins. The fact that transport by fluid motion becomes necessary to outrun the slow pace of diffusion in larger organisms, as emphasized in the celebrated essay by Haldane on size in biology (14), has been a theme in discussions of cytoplasmic streaming for many years. Yet, there has been little theoretical work and fewer experiments that have quantified the full implications of cytoplasmic streaming for transport and mixing. Only recently has it been recognized (2, 15) that the large Péclet numbers found in vivo could enhance metabolite exchange with organelles such as chloroplasts. Still, a range of basic questions has remained unanswered (16): What is the role of cytoplasmic streaming in homeostasis? Ho...

Anglican is a probabilistic programming system designed to interoperate with Clojure and other JVM languages. We introduce the programming language Anglican, outline our design choices, and discuss in depth the implementation of the Anglican language and runtime, including macrobased compilation, extended CPS-based evaluation model, and functional representations for probabilistic paradigms, such as a distribution, a random process, and an inference algorithm.We show that a probabilistic functional language can be implemented efficiently and integrated tightly with a conventional functional language with only moderate computational overhead. We also demonstrate how advanced probabilistic modeling concepts are mapped naturally to the functional foundation.

Cytoplasmic streaming circulates the contents of large eukaryotic cells, often with complex flow geometries. A largely unanswered question is the significance of these flows for molecular transport and mixing. Motivated by "rotational streaming" in Characean algae, we solve the advection-diffusion dynamics of flow in a cylinder with bidirectional helical forcing at the wall. A circulatory flow transverse to the cylinder's long axis, akin to Dean vortices at finite Reynolds numbers, arises from the chiral geometry. Strongly enhanced lateral transport and longitudinal homogenization occur if the transverse Péclet number is sufficiently large, with scaling laws arising from boundary layers.

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In aquatic plants such as the Characean algae, the force generation that drives cyclosis is localized within the cytoplasm, yet produces fluid flows throughout the vacuole. For this to occur the tonoplast must transmit hydrodynamic shear efficiently. Here, using magnetic resonance velocimetry, we present the first whole-cell measurements of the cross-sectional longitudinal velocity field in Chara corallina and show that it is in quantitative agreement with a recent theoretical analysis of rotational cytoplasmic streaming driven by bidirectional helical forcing in the cytoplasm, with direct shear transmission by the tonoplast.