Oxidative stress and mitochondrial dynamics malfunction are linked in Pelizaeus‐Merzbacher disease

Pelizaeus‐Merzbacher disease (PMD) is a fatal hypomyelinating disorder characterized by early impairment of motor development, nystagmus, choreoathetotic movements, ataxia and progressive spasticity. PMD is caused by variations in the proteolipid protein gene PLP1, which encodes the two major myelin proteins of the central nervous system, PLP and its spliced isoform DM20, in oligodendrocytes. Large duplications including the entire PLP1 gene are the most frequent causative mutation leading to the classical form of PMD. The Plp1 overexpressing mouse model (PLP‐tg^66/66) develops a phenotype very similar to human PMD, with early and severe motor dysfunction and a dramatic decrease in lifespan. The sequence of cellular events that cause neurodegeneration and ultimately death is poorly understood. In this work, we analyzed patient‐derived fibroblasts and spinal cords of the PLP‐tg^66/66 mouse model, and identified redox imbalance, with altered antioxidant defense and oxidative damage to several enzymes involved in ATP production, such as glycolytic enzymes, creatine kinase and mitochondrial proteins from the Krebs cycle and oxidative phosphorylation. We also evidenced malfunction of the mitochondria compartment with increased ROS production and depolarization in PMD patient''s fibroblasts, which was prevented by the antioxidant N‐acetyl‐cysteine. Finally, we uncovered an impairment of mitochondrial dynamics in patient''s fibroblasts which may help explain the ultrastructural abnormalities of mitochondria morphology detected in spinal cords from PLP‐tg^66/66 mice. Altogether, these results underscore the link between redox and metabolic homeostasis in myelin diseases, provide insight into the pathophysiology of PMD, and may bear implications for tailored pharmacological intervention.     

INAUGURAL ARTICLE by a Recently Elected Academy Member:Helicity and singular structures in fluid dynamics

Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described.This inaugural article, although long delayed, is now fortuitously quite timely for various reasons. First, helicity in fluid dynamics is a measure of the knottedness and/or linkage of the vortex lines of a flow (1), invariant under ideal-fluid Euler evolution. Knotted vortices were first conceived by Lord Kelvin (then Sir William Thomson) in 1868 (2), but have only recently been unambiguously observed: a vortex in the form of a trefoil knot has been generated in a remarkable experiment by Kleckner and Irvine (3) by means of an ingenious technique that can in principle be adapted to generate vortices of arbitrarily linked or knotted form. The possible existence of knotted vortices is therefore no longer a matter of mere speculation!Second, helicity has long been known to be of crucial importance in turbulent dynamo theory—the theory of the spontaneous growth of a magnetic field in a conducting fluid in turbulent motion. The associated chirality of the flow is responsible for the α-effect (4), which is a crucial ingredient of the dynamo process in stars and planets. The von Karman sodium (VKS) experiment (5) developed in France over the last decade has at last provided convincing evidence for a turbulent dynamo mechanism that undoubtedly involves this α-effect in conjunction with differential rotation and strong diffusive processes.Third, the process of magnetic relaxation of a knotted magnetic flux tube in a perfectly conducting fluid under the topological constraint of invariant helicity leads in a natural physical way to the concept of the energy spectrum of knots and links (6). The minimum energy configurations obtained by this procedure are, with certain qualifications, essentially the same as the ideal or tight knot configurations introduced by Katritch et al. (7) which minimize the length-to-diameter ratio of knotted tubes. Tight knots have found wide application in polymer physics and molecular biology, as discussed in recent workshops of the Isaac Newton Institute for Mathematical Sciences (8, 9), and huge progress has been made in determining all tight configurations for links and knots up to 9 and 10 crossings, respectively (10). In particle physics, a striking correlation has been noted between the knot/link energies and the mass/energies of glueballs in the quark–gluon plasma (11); the subject has perhaps come full circle since the time of Kelvin!The time is therefore ripe to review some of the salient features of these and related phenomena in which helicity plays a central role, and I take this welcome opportunity to do so. I include also, at the suggestion of a referee of this article, a section on certain structures that can arise in flows that are dominated by viscosity, and that nevertheless exhibit structures of nontrivial topology.     

Acoustic excitations and elastic heterogeneities in disordered solids

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nanoscale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly affect the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphization transition, we investigate the relationship between sound waves and elastic heterogeneities in a unified framework by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound wave features and the extent of the heterogeneous mechanical response at the nanoscale.In crystals, molecules thermally oscillate around the periodic lattice sites and vibrational excitations are well understood in terms of quantized plane waves, the phonons (1). The vibrational density of states (vDOS) in the low-frequency regime is well described by the Debye model, where the vibrational modes are the acoustic phonons. In contrast, disordered solids, including structural glasses and disordered crystals, exhibit specific vibrational properties compared with the corresponding pure crystalline phases. It is not possible here to give a fair review of the extensive theoretical and experimental work generated by these issues; we therefore mention below a few facts that we consider the most relevant in the present context. The origin of the vDOS modes in excess over the Debye prediction around ω ∼1 THz, the so-called Boson peak (BP), is still debated (see, among many others, refs. 2 and 3). At the BP frequency, Ω^BP, localized modes have also been observed (4). Acoustic plane waves, which are exact normal modes in crystals, can still propagate in disordered solids. Indeed, at low frequencies, Ω, and long wavelengths, Λ, acoustic sound waves do not interact with disorder and can propagate conforming to the expected macroscopic limit. However, as Ω is increased beyond the Ioffe–Regel (IR) limit, Ω^IR, acoustic excitations interact with the disorder and are significantly scattered (5–7). Interestingly, this strong scattering regime occurs around the BP position, Ω^IR ∼ Ω^BP (8, 9). The exact origin of this phenomenon and its connection to the BP remain elusive.A possible rationalization of the above issues is based on the existence of elastic heterogeneities (10), which can originate from structural disorder, as in structural glasses (2), or disordered interparticle potentials, even in lattice structures such as disordered colloidal crystals (11). In the heterogeneous-elasticity theory of refs. 7 and 12 this amounts to consider spatial statistical fluctuations of the shear modulus. Within the framework of jamming approaches and using effective medium theories, elastic heterogeneities are related to the proximity of local elastic instabilities (13). Recent simulation work (14–16) has clearly demonstrated their existence in disordered solids. This is at variance with the case of simple crystals, which are characterized by a fully affine response and homogeneous moduli distributions (17). More specifically, in the large length scale limit, macroscopic moduli are observed. In contrast, as the length scale is reduced, moduli heterogeneities are detected, at a typical length scale ξ ≃ 10−15σ (15), where σ is the typical atomic diameter. Breakdown of both continuum mechanics (18) and Debye approximation (5, 6) has been demonstrated at the same mesoscopic length-scale ξ, where they are still valid for crystals. Remarkably, the wave frequency corresponding to the wavelength Λ ∼ ξ is very close to Ω^IR ∼ Ω^BP (19). Altogether these results indicate that a close connection must exist between elastic heterogeneities and acoustic excitations. In this paper we precisely address this point.In ref. 20 we considered a numerical model featuring an amorphization transition (21). We showed how to systematically deform the local moduli distributions, evaluated by coarse-graining the system in small domains of linear length scale w. We characterized the degree of elastic heterogeneity in terms of SD of those distributions and studied the effect on normal modes (eigenvalues of the Hessian matrix) and thermal conductivity. Building on that work, we are now in the position to investigate the relation between elastic heterogeneities and acoustic excitations, unifying in a single framework ordered and disordered solid states and considering quantities directly probed by experiments. By interpolating in a controlled way from perfect crystals, through increasingly defective phases, to fully developed amorphous structures, we (i) calculate the dynamical structure factors, extracting the relevant spectroscopic parameters; (ii) characterize the wave vector dependence of sound velocity and broadening of the acoustic excitations and clarify their nature in terms of the IR limit; and (iii) provide, for the first time to our knowledge, direct evidence of the correlation of the excitations lifetimes and Ω^IR with the magnitude of the elastic heterogeneities.     

Hybrid-fuel bacterial flagellar motors in Escherichia coli

The bacterial flagellar motor rotates driven by an electrochemical ion gradient across the cytoplasmic membrane, either H⁺ or Na⁺ ions. The motor consists of a rotor ∼50 nm in diameter surrounded by multiple torque-generating ion-conducting stator units. Stator units exchange spontaneously between the motor and a pool in the cytoplasmic membrane on a timescale of minutes, and their stability in the motor is dependent upon the ion gradient. We report a genetically engineered hybrid-fuel flagellar motor in Escherichia coli that contains both H⁺- and Na⁺-driven stator components and runs on both types of ion gradient. We controlled the number of each type of stator unit in the motor by protein expression levels and Na⁺ concentration ([Na⁺]), using speed changes of single motors driving 1-μm polystyrene beads to determine stator unit numbers. De-energized motors changed from locked to freely rotating on a timescale similar to that of spontaneous stator unit exchange. Hybrid motor speed is simply the sum of speeds attributable to individual stator units of each type. With Na⁺ and H⁺ stator components expressed at high and medium levels, respectively, Na⁺ stator units dominate at high [Na⁺] and are replaced by H⁺ units when Na⁺ is removed. Thus, competition between stator units for spaces in a motor and sensitivity of each type to its own ion gradient combine to allow hybrid motors to adapt to the prevailing ion gradient. We speculate that a similar process may occur in species that naturally express both H⁺ and Na⁺ stator components sharing a common rotor.Molecular motors are tiny machines that perform a wide range of functions in living cells. Typically each motor generates mechanical work using a specific chemical or electrochemical energy source. Linear motors such as kinesin on microtubules or myosin on actin filaments and rotary motors such as F₁-ATPase, the soluble part of ATP-synthase, run on ATP, whereas the rotary bacterial flagellar motor embedded in the bacterial cell envelope is driven by the flux of ions across the cytoplasmic membrane (1–4). Coupling ions are known to be either protons (H⁺) or sodium ions (Na⁺) (5, 6).The bacterial flagellar motor consists of a rotor ∼50 nm in diameter surrounded by multiple stator units (7–10). Each unit contains two types of membrane proteins forming ion channels: MotA and MotB in H⁺ motors in neutrophiles (e.g., Escherichia coli and Salmonella) and PomA and PomB in Na⁺ motors in alkalophiles and Vibrio species (e.g., Vibrio alginolyticus) (1, 11). Multiple units interact with the rotor to generate torque independently in a working motor (9, 10, 12, 13). The structure and function of H⁺ and Na⁺ motors are very similar, to the extent that several functional chimeric motors have been made containing different mixtures of H⁺- and Na⁺-motor components (11). One such motor that runs on Na⁺ in E. coli combines the rotor of the H⁺-driven E. coli motor with the chimeric stator unit PomA/PotB, containing PomA from V. alginolyticus and a fusion protein between MotB from E. coli and PomB from V. alginolyticus (14).In most flagellated bacteria, motors are driven by ion-specific rotor–stator combinations. However, some species (e.g., Bacillus subtilis and Shewanella oneidensis) combine a single set of rotor genes with multiple sets of stator genes encoding both H⁺ and Na⁺ stator proteins, and it has been speculated that these stator components may interact with the rotor simultaneously, allowing a single motor to use both H⁺ and Na⁺. An appealing hypothesis that the mixture of stator components is controlled dynamically depending on the environment has arisen from the observation that the localization of both stator components depends upon Na⁺ (15). However, despite some experimental effort there is as yet no direct evidence of both H⁺ and Na⁺ stator units interacting with the same rotor (16).The rotation of single flagellar motors can be monitored in real time by light microscopy of polystyrene beads (diameter ∼1 μm) attached to truncated flagellar filaments (17). Under these conditions, the E. coli motor torque and speed are proportional to the number of stator units in both H⁺-driven MotA/MotB and Na⁺-driven PomA/PotB (17–19) motors. The maximum number of units that can work simultaneously in a single motor has been shown to be at least 11 by “resurrection” experiments, in which newly produced functional units lead to restoration of motor rotation in discrete speed increments in an E. coli strain lacking functional stator proteins (19). Stator units are not fixed permanently in a motor: Each dissociates from the motor with a typical rate of ∼2 min⁻¹, exchanging between the motor and a pool of diffusing units in the cytoplasmic membrane (20). Removal of the relevant ion gradient inactivates both H⁺ and Na⁺ stator units, most likely leading to dissociation from the motor into the membrane pool (2, 21, 22).Here we demonstrate a hybrid-fuel motor containing both H⁺-driven MotA/MotB and Na⁺-driven PomA/PotB stator components, sharing a common rotor in E. coli. We control the expression level of each stator type by induced expression from plasmids, and the affinity of Na⁺-driven stator units for the motor by external [Na⁺]. Units of each type compete for spaces around the rotor, and the motor torque is simply the sum of the independent contributions, with no evidence of direct interaction between units. Thus, we demonstrate the possibility of modularity in the E. coli flagellar motor, with ion selectivity determined by the choice of stator modules interacting with a common rotor. Our artificial hybrid motor demonstrates that species with multiple types of stator gene and a single set of rotor genes could contain natural hybrid motors that work on a similar principle (15, 16, 23).     

Taxodione and arenarone inhibit farnesyl diphosphate synthase by binding to the isopentenyl diphosphate site

We used in silico methods to screen a library of 1,013 compounds for possible binding to the allosteric site in farnesyl diphosphate synthase (FPPS). Two of the 50 predicted hits had activity against either human FPPS (HsFPPS) or Trypanosoma brucei FPPS (TbFPPS), the most active being the quinone methide celastrol (IC₅₀ versus TbFPPS ∼20 µM). Two rounds of similarity searching and activity testing then resulted in three leads that were active against HsFPPS with IC₅₀ values in the range of ∼1–3 µM (as compared with ∼0.5 µM for the bisphosphonate inhibitor, zoledronate). The three leads were the quinone methides taxodone and taxodione and the quinone arenarone, compounds with known antibacterial and/or antitumor activity. We then obtained X-ray crystal structures of HsFPPS with taxodione+zoledronate, arenarone+zoledronate, and taxodione alone. In the zoledronate-containing structures, taxodione and arenarone bound solely to the homoallylic (isopentenyl diphosphate, IPP) site, not to the allosteric site, whereas zoledronate bound via Mg²⁺ to the same site as seen in other bisphosphonate-containing structures. In the taxodione-alone structure, one taxodione bound to the same site as seen in the taxodione+zoledronate structure, but the second located to a more surface-exposed site. In differential scanning calorimetry experiments, taxodione and arenarone broadened the native-to-unfolded thermal transition (T_m), quite different to the large increases in ΔT_m seen with biphosphonate inhibitors. The results identify new classes of FPPS inhibitors, diterpenoids and sesquiterpenoids, that bind to the IPP site and may be of interest as anticancer and antiinfective drug leads.Farnesyl diphosphate synthase (FPPS) catalyzes the condensation of isopentenyl diphosphate (IPP; compound 1 in Fig. 1) with dimethylallyl diphosphate (DMAPP; compound 2 in Fig. 1) to form the C₁₀ isoprenoid geranyl diphosphate (GPP; compound 3 in Fig. 1), which then condenses with a second IPP to form the C₁₅ isoprenoid, farnesyl diphosphate (FPP; compound 4 in Fig. 1). FPP then is used in a wide range of reactions including the formation of geranylgeranyl diphosphate (GGPP) (1), squalene (involved in cholesterol and ergosterol biosynthesis), dehydrosqualene (used in formation of the Staphylococcus aureus virulence factor staphyloxanthin) (2), undecaprenyl diphosphate (used in bacterial cell wall biosynthesis), and quinone and in heme a/o biosynthesis. FPP and GGPP also are used in protein (e.g., Ras, Rho, Rac) prenylation, and FPPS is an important target for the bisphosphonate class of drugs (used to treat bone resorption diseases) such as zoledronate (compound 5 in Fig. 1) (3). Bisphosphonates targeting FPPS have activity as antiparasitics (4), act as immunomodulators (activating γδ T cells containing the Vγ2Vδ2 T-cell receptor) (5), and switch macrophages from an M2 (tumor-promoting) to an M1 (tumor-killing) phenotype (6). They also kill tumor cells (7) and inhibit angiogenesis (8). However, the bisphosphonates in clinical use (zoledronate, alendronate, risedronate, ibandronate, etidronate, and clodronate) are very hydrophilic and bind avidly to bone mineral (9). Therefore, there is interest in developing less hydrophilic species (10) that might have better activity against tumors in soft tissues and better antibacterial (11) and antiparasitic activity.Open in a separate windowFig. 1.Chemical structures of FPPS substrates, products, and inhibitors.The structure of FPPS (from chickens) was first reported by Tarshis et al. (12) and revealed a highly α-helical fold. The structures of bacterial and Homo sapiens FPPS (HsFPPS) are very similar; HsFPPS structure (13, 14) is shown in Fig. 2A. There are two substrate-binding sites, called here “S1” and “S2.” S1 is the allylic (DMAPP, GPP) binding site to which bisphosphonates such as zoledronate bind via a [Mg²⁺]₃ cluster (15) (Fig. 2B). S2 is the homoallylic site to which IPP binds, Fig. 2B. Recently, Jahnke et al. (10) and Salcius et al. (16) discovered a third ligand-binding site called the “allosteric site” (hereafter the “A site”). A representative zoledronate+A-site inhibitor structure [Protein Data Bank (PDB) ID code 3N46] (Nov_980; compound 6 in Fig. 1) showing zoledronate in S1 and Nov_980 (compound 6) in the A site is shown in a stereo close-up view in Fig. 2B, superimposed on a zoledronate+IPP structure (PDB ID code 2F8Z) in S2. Whether the allosteric site serves a biological function (e.g., in feedback regulation) has not been reported. Nevertheless, highly potent inhibitors (IC₅₀ ∼80 nM) have been developed (10), and the best of these newly developed inhibitors are far more hydrophobic than are typical bisphosphonates (∼2.4–3.3 for cLogP vs. ∼−3.3 for zoledronate) and are expected to have better direct antitumor effects in soft tissues (10).Open in a separate windowFig. 2.Structures of human FPPS. (A) Structure of HsFPPS showing zoledronate (compound 5) and IPP (compound 1) bound to the S1 (allylic) and S2 (homoallylic) ligand-binding sites (PDB ID code 2F8Z). (B) Superposition of the IPP-zoledronate structure (PDB ID code 2F8Z) on the zoledronate-Nov_980 A-site inhibitor structure (PDB ID code 3N46). Zoledronate binds to the allylic site S1, IPP binds to the homoallylic site S2, and the allosteric site inhibitor binds to the A site. Active-site “DDXXD” residues are indicated, as are Mg²⁺ molecules (green and yellow spheres, respectively). The views are in stereo.In our group we also have developed more lipophilic compounds (e.g., compound 7 in Fig. 1) (17, 18) as antiparasitic (19) and anticancer drug leads (18) and, using computational methods, have discovered other novel nonbisphosphonate FPPS inhibitors (e.g., compound 8 in Fig. 1) that have micromolar activity against FPPS (20). In this study, we extended our computational work and tried to discover other FPPS inhibitors that target the A site. Such compounds would be of interest because they might potentiate the effects of zoledronate and other bisphosphonates, as reported for other FPPS inhibitors (21), and have better tissue distribution properties in general.     

Small-scale universality in fluid turbulence

Turbulent flows in nature and technology possess a range of scales. The largest scales carry the memory of the physical system in which a flow is embedded. One challenge is to unravel the universal statistical properties that all turbulent flows share despite their different large-scale driving mechanisms or their particular flow geometries. In the present work, we study three turbulent flows of systematically increasing complexity. These are homogeneous and isotropic turbulence in a periodic box, turbulent shear flow between two parallel walls, and thermal convection in a closed cylindrical container. They are computed by highly resolved direct numerical simulations of the governing dynamical equations. We use these simulation data to establish two fundamental results: (i) at Reynolds numbers Re ∼ 10² the fluctuations of the velocity derivatives pass through a transition from nearly Gaussian (or slightly sub-Gaussian) to intermittent behavior that is characteristic of fully developed high Reynolds number turbulence, and (ii) beyond the transition point, the statistics of the rate of energy dissipation in all three flows obey the same Reynolds number power laws derived for homogeneous turbulence. These results allow us to claim universality of small scales even at low Reynolds numbers. Our results shed new light on the notion of when the turbulence is fully developed at the small scales without relying on the existence of an extended inertial range.An enduring notion in the phenomenology of turbulence is the universality of small scales. It has been taken for granted in theoretical approaches (e.g., refs. 1–8) and analyzed in numerical simulations (9–11) as well as various laboratory experiments (e.g., refs. 5 and 12). The standard paradigm is that whereas the large scales are nonuniversal, reflecting the circumstances of their generation, an increasingly weaker degree of nonuniversality is imparted to small scales with increasing separation between the large and small scales. This scale separation is thought to increase with the flow Reynolds number, so a proper test of universality has been thought to require very high Reynolds numbers. Consequently, many substantial efforts have been made to produce such high-Reynolds-number flows (e.g., ref. 12).Here, we show evidence for an alternative point of view: If one resolves small scales accurately, one observes, even at low Reynolds numbers, universal scaling of velocity gradients that manifest primarily at small scales. We stress that small-scale dynamics are strongly nonlinear even in low-Reynolds-number flows driven by large-scale forcing. There is thus considerable merit in measuring or simulating low-Reynolds-number flows much more accurately than has been the practice and exploring the evidence for universality (or lack thereof), instead of advancing as inevitable the notion that useful lessons about universality are possible only at very high Reynolds numbers. Indeed, another result of this paper is that there exists a threshold Reynolds number above which Gaussian-like fluctuations tend to assume intermittent characteristics of fully developed flows and that these features can be extracted by accessing increasingly smaller scales even if the Reynolds numbers are quite moderate. The latter result is especially important for purposes of identifying a fixed point in certain renormalization group expansion procedures (8).     

Flow disturbances generated by feeding and swimming zooplankton

Interactions between planktonic organisms, such as detection of prey, predators, and mates, are often mediated by fluid signals. Consequently, many plankton predators perceive their prey from the fluid disturbances that it generates when it feeds and swims. Zooplankton should therefore seek to minimize the fluid disturbance that they produce. By means of particle image velocimetry, we describe the fluid disturbances produced by feeding and swimming in zooplankton with diverse propulsion mechanisms and ranging from 10-µm flagellates to greater than millimeter-sized copepods. We show that zooplankton, in which feeding and swimming are separate processes, produce flow disturbances during swimming with a much faster spatial attenuation (velocity u varies with distance r as u ∝ r⁻³ to r⁻⁴) than that produced by zooplankton for which feeding and propulsion are the same process (u ∝ r⁻¹ to r⁻²). As a result, the spatial extension of the fluid disturbance produced by swimmers is an order of magnitude smaller than that produced by feeders at similar Reynolds numbers. The “quiet” propulsion of swimmers is achieved either through swimming erratically by short-lasting power strokes, generating viscous vortex rings, or by “breast-stroke swimming.” Both produce rapidly attenuating flows. The more “noisy” swimming of those that are constrained by a need to simultaneously feed is due to constantly beating flagella or appendages that are positioned either anteriorly or posteriorly on the (cell) body. These patterns transcend differences in size and taxonomy and have thus evolved multiple times, suggesting a strong selective pressure to minimize predation risk.Zooplankters move to feed, find food, and find mates, so moving is critical to the efficient execution of essential functions. However, moving comes at a predation risk: Swimming increases the predator encounter velocity (encounter rate increases with prey velocity to a power ≤1), and feeding and swimming generate fluid disturbances that may be perceived by rheotactic predators, thus increasing the predator’s detection distance (encounter rate increases with detection distance squared) (1–5). So, the advantages of moving and feeding must be traded off against the associated risks, and organisms should aim at moving and foraging in ways that reduce the predation risk and optimize the trade-off (6, 7). They may do so by moving in patterns that minimize encounter rates (8) and/or they may feed and propel themselves in ways that generate only small fluid disturbances (9). For example, theoretical models suggest that zooplankton that swim by a sequence of jumps may create a smaller fluid disturbance than similar-sized ones that swim smoothly (9), that a hovering zooplankter generates a larger fluid signal than one that cruises through the water (10, 11), and that a zooplankter moving at low Reynolds numbers will generate a relatively larger fluid signal than one moving at higher Reynolds numbers (11). Thus, motility patterns and propulsion modes may strongly influence predation risk and must be subject to strong selection pressure during evolution.Zooplankton span a huge taxonomic diversity and a large size range (from microns to centimeters) and their propulsion mechanisms vary substantially (12). Unicellular plankton may use one or more flagella or cilia, and the flagella may be smooth or plumose, which has implications for whether the cell is pulled or pushed by the beating flagellum (13). Ciliates may have the cilia rather evenly distributed on the cell surface or concentrated on certain parts of the cell, typically either anteriorly or as an equatorial band. Small animals may have an anterior “corona” of cilia (e.g., rotifers and many pelagic invertebrate larvae) to generate feeding currents and propulsion, or they may have beating or vibrating appendages that can be positioned anteriorly, ventrally, or laterally. The implications and potential adaptive value of this diversity of propulsion modes for feeding and survival are largely unexplored.Various idealized models, simplifying the swimming organisms to combinations of point forces acting on the water, have been used to describe the fluid disturbance generated by moving and feeding plankton. A self-propelled plankton is often described by a so-called stresslet (two oppositely directed point forces of equal magnitude), a hovering one by a stokeslet (a stationary point force), and a jumping animal by an impulsive stresslet (a stresslet working impulsively) (9, 11, 12). These highly idealized models yield very different predictions of the spatial attenuation of the fluid disturbance and, thus, of how far away the feeding and swimming animal can be detected. A few studies have compared observed flow patterns with those predicted from these simple models and in some cases found fair comparisons (4, 14–17). However, numerical simulations as well as observations of self-propelled microplankton have demonstrated that the distribution of propulsion forces, i.e., the position of flagella, cilia, or appendages on the (cell) body, may have a profound effect on the imposed fluid flow (18, 19). Also, most of the idealized models ignore the fact that swimming in most cases is unsteady, which leads to fluctuating flows at scales smaller than the Stokes length scale (ν/ω, where ν is the kinematic viscosity and ω is the beat frequency) (e.g., ref. 19). The simple, idealized models hitherto applied may be insufficient to represent the diverse propulsion modes observed in real organisms and to understand the associated trade-offs.Feeding and swimming are often part of the same process in zooplankton. Many zooplankton generate a feeding current that at the same time propels the animal through the water. In others, feeding and swimming are separate processes. For example, ambush feeding “sit-and-wait” zooplankters do not move as part of feeding but may swim to undertake vertical migration or to search for mates or patches of elevated food availability. Also, many of the plankton that generate a feeding current by vibrating appendages may in addition swim by using the same appendages in a different way (e.g., the nauplius larvae of most crustaceans) or by using other swimming appendages dedicated to propel themselves (most pelagic copepods and cladocerans).Whereas feeding and swimming may both compromise the survival of the organism, the trade-offs may be different. To get sufficient food, zooplankters need to daily clear a volume of water for prey that corresponds to about 10⁶ times their own body volume (20, 21) and hence, implicit in the feeding process is the need to examine or process large volumes of water. In contrast, dedicated swimming should translate the organism through the water as quietly as possible. Thus, we hypothesize that in microplankton, dedicated swimming produces flow fields that attenuate more readily and/or have a smaller spatial extension than the cases in which feeding and propulsion are intimately related.In this study we use particle image velocimetry (PIV) to describe the flow fields generated by micron- to millimeter-sized feeding and swimming zooplankton that use a variety of propulsion modes. We show that—across taxa and sizes—dedicated swimming produces flow fields with a much smaller spatial extension and a faster spatial attenuation than those produced by the plankton for which feeding and swimming are integrated, and we characterize the propulsion modes that minimize susceptibility to rheotactic predators.     

Interactions between chromosomal and nonchromosomal elements reveal missing heritability

The measurement of any nonchromosomal genetic contribution to the heritability of a trait is often confounded by the inability to control both the chromosomal and nonchromosomal information in a population. We have designed a unique system in yeast where we can control both sources of information so that the phenotype of a single chromosomal polymorphism can be measured in the presence of different cytoplasmic elements. With this system, we have shown that both the source of the mitochondrial genome and the presence or absence of a dsRNA virus influence the phenotype of chromosomal variants that affect the growth of yeast. Moreover, by considering this nonchromosomal information that is passed from parent to offspring and by allowing chromosomal and nonchromosomal information to exhibit nonadditive interactions, we are able to account for much of the heritability of growth traits. Taken together, our results highlight the importance of including all sources of heritable information in genetic studies and suggest a possible avenue of attack for finding additional missing heritability.A fundamental problem in genetics is unraveling the link between genotype and phenotype. Ascertaining the heritability of a trait is a key step toward harnessing the predictive capacity of genetic information for human disease risk assessment and therapy (1). Knowledge of all of the elements contributing to heritability would facilitate the establishment of a causal relationship between the information that is passed down from generation to generation and the resulting phenotype. Genome-wide association studies (GWASs) have successfully identified many human polymorphisms that are associated with traits such as height, eye color, or susceptibility to common diseases, but these variants typically explain only a small proportion of the observed heritability of a trait (2, 3).A number of explanations for missing heritability have been suggested (2), including the existence of many weak variants with effects too small to achieve statistical significance (4), interactions between variants that cannot be identified with current studies (5), rare variants that were not identified by GWAS, and epigenetic effects (6–8). The contribution of nonchromosomal information to the missing heritability is rarely considered, despite the fact that there is a long history documenting the effect in many organisms of diverse cytoplasmic elements on phenotype. Recent work on a mouse model of Crohn disease supports a combinatorial model of complex disease traits in which the pathology requires the interaction between a specific mutation in the mouse and a specific strain of virus (9). Another recent study showed strong effects on the plant metabolome stemming from variation in mitochondrial and chloroplast genomes (10). In humans, the importance of nonchromosomal information has been supported by targeted analyses, but these studies have not analyzed its impact on heritability in a well-controlled context (11–13). Such nonchromosomal interactions might help explain why shared mutations in humans do not always produce the same phenotype, thus reducing the apparent heritability of a trait (14, 15).We sought to characterize explicitly how nonchromosomal modifiers collectively influence the heritability of a trait, colony size, in a system unique to yeast where we use a defined chromosomal genotype and vary the cytoplasmic genetic information. Yeast has at least four well-studied sources of inherited, nonchromosomal information: mitochondrial DNA, an endogenous dsRNA virus (16, 17), prions (18, 19), and a 2µ plasmid (20, 21).Our results show that the nonchromosomal contribution to heritability can be large, adding another dimension to the estimation of heritability in wild populations. Nonchromosomal information is not under the usual constraints of the nuclear genome. These nonchromosomal elements are extremely unstable: they mutate at higher frequencies than the DNA of the chromosomal genome, may be lost at high frequencies without loss of viability, and can vary in copy number from cell to cell. Thus, careful controls and measurements are necessary to characterize the effects of nonchromosomal modifiers.