Second-Chance Signal Transduction Explains Cooperative Flagellar Switching

<div><p>The reversal of flagellar motion (switching) results from the interaction between a switch complex of the flagellar rotor and a torque-generating stationary unit, or stator (motor unit). To explain the steeply cooperative ligand-induced switching, present models propose allosteric interactions between subunits of the rotor, but do not address the possibility of a reaction that stimulates a bidirectional motor unit to reverse direction of torque. During flagellar motion, the binding of a ligand-bound switch complex at the dwell site could excite a motor unit. The probability that another switch complex of the rotor, moving according to steady-state rotation, will reach the same dwell site before that motor unit returns to ground state will be determined by the independent decay rate of the excited-state motor unit. Here, we derive an analytical expression for the energy coupling between a switch complex and a motor unit of the stator complex of a flagellum, and demonstrate that this model accounts for the cooperative switching response without the need for allosteric interactions. The analytical result can be reproduced by simulation when (1) the motion of the rotor delivers a subsequent ligand-bound switch to the excited motor unit, thereby providing the excited motor unit with a second chance to remain excited, and (2) the outputs from multiple independent motor units are constrained to a single all-or-none event. In this proposed model, a motor unit and switch complex represent the components of a mathematically defined signal transduction mechanism in which energy coupling is driven by steady-state and is regulated by stochastic ligand binding. Mathematical derivation of the model shows the analytical function to be a general form of the Hill equation (Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40: iv–vii).</p> </div

Summary of Dependent and Independent Variables.

<p>Summary of Dependent and Independent Variables.</p

Second-chance scenario for a bacterial flagellar motor unit.

<p>The diagram shows the pathways by which traveling switch components of the rotor (circles) stimulate a motor unit (square sides). At time zero, the motor in the ground state (C) has the null probability of being excited (blue). Formation of a collision complex (C_j*; j = 1,2) stimulates a motor unit to an excited state (M) with probability (P_M) of unity (red). While P_M decays (color key in inset), the rotor traveling at a constant rate, <i>k</i>_r, breaks contact with one switch complex (U₁) at rate <i>k</i>_r− = <i>k</i>_r and delivers another switch complex (U_i, i>1) to the motor unit at rate <i>k</i>_r+ = <i>k</i>_r. The ligand concentration, [L], determines whether a switch can form a collision complex (filled circle; U) or not (open circle; u). If by chance, θ = <i>K</i>_L[L]/(1+<i>K</i>_L[L]), the switch complex at the dwell site is occupied by ligand, and the formation of C_j* restores P_M to unity. An equilibrium pathway is required to initiate motor unit excitation (Eq. 1, 2, and 4; <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#pone-0041098-g001" target="_blank">Fig. 1</a>). The second-chance pathway (Eq. 1, 3, and 4; <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#pone-0041098-g001" target="_blank">Fig. 1</a>) can sustain the excited state. To emphasize the pathway-dependent free energy of the collision complex, the subscripts in C₁* and C₂* are included in the symbols for intermediate products of the equilibrium and second-chance pathways (Reactions 2 and 3), respectively. It should be noted that C₁*, C₂*, and C_j* represent the same change in physical structure of the motor unit as is represented by the transition between diamonds and squares in the schematic. To recapitulate, temporal changes in P_M may be traced for the scenario shown (inset). Decay of the excited state is by single exponential (inset). In a different scenario, had the motor unit returned to the ground state before being stimulated again, the equilibrium pathway would have been required to initiate a new excited state.</p

Relationship of IANBD fluorescence data and total myosin binding.

<p>All data are replotted from Trybus and Taylor <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone.0008052-Trybus1" target="_blank">[16]</a>. Fluorescence data (circles) are fit by eye with Eq. 24, given and ; the curve through the data is generated by Eq. 23 using . Total myosin binding data (squares) are fit with a curve representing the sum of coupled and free myosin binding using Eq. 25. As inputs to Eq. 25, coupled myosin binding is given by the change in fluorescence generated by Eq. 23 () and the free myosin binding is generated by simple mass action (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone.0008052-McKillop1" target="_blank">[4]</a>; Eq. 26). <u>Inset.</u> Simulated calcium binding to Tn is non-cooperative. The sum of B₂, B₃, T₂, and T₃ (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone-0008052-t001" target="_blank">Table 1</a>), which represents the total calcium bound to Tn, is plotted on the Y-axis. Values for these dependent variables were determined by solving Eqs. 9, 18, 21, 22 for arbitrary calcium. Total calcium binding with zero myosin (−M) and saturating myosin (+M) was simulated using <i>K</i>₀ = 0 and , respectively. Fixed inset parameters: , , , , .</p

Summary of Parameters.

<p>Summary of Parameters.</p

Factors that determine cooperative activation by calcium.

<p>Activation is calculated as the sum of the dependent variables C and M (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone-0008052-t001" target="_blank">Table 1</a>) by solving Eqs. 9, 18, 21, and 22 given arbitrary calcium. <u>Inset.</u> Non-cooperative fractional activation in the absence of myosin. Myosin is excluded by setting the parameter <i>K</i>₀ (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone-0008052-t002" target="_blank">Table 2</a>) to zero. Fractional Activation is the dependent variable C (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0008052#pone-0008052-t001" target="_blank">Table 1</a>) as a function of calcium. <u>Inset adjustable parameters: </u> (Curve A); (Curve B); (Curve C); (Curve D); (Curve E). <u>Outset.</u> Myosin induces cooperative fractional activation. All curves except Curve 1 include myosin contribution by setting the parameter, <i>K</i>₀, to one; for visual comparison to a non-cooperative activation, Curve 1 is reproduced (Curve E; inset). Curves 2, 3, 5, 7, and 8 illustrate the effects of parameters that control cooperativity: Curves 2 and 3 compare the effects of varying <i>α</i> and <i>n</i> given fixed and Curves 5, 7, and 8 compare the effects of varying <i>n</i> given fixed <i>α</i> and . For constant <i>n</i> and <i>α</i> (Curves 4–6), increasing shifts the curves toward greater calcium sensitivity while the steepness remains nearly the same. Curve 0 shows the mole fraction of Tm in Position C as a function of calcium. <u>Outset adjustable parameters: </u>, (Curve 1); , , , (Curve 2); , , , (Curve 3); , , , (Curve 4); , , , (Curve 5); , , , (Curve 6); , , , (Curve 7); , , , (Curve 8). <u>Outset constants: </u>, .</p

Annotated equilibrium model.

<p>B₁, B₂, B₃, C, and M represent mole fractions of binding states coupled to the positions of Tm denoted by the letters (blocking, central, and myosin dependent, respectively). B₁, B₂, and B₃ are represented by Tm (open rectangle) held in a blocking position on actin by interactions between actin and Tn in each of three possible calcium bound states, namely, zero sites filled (open circle), one site filled (one dot), and two sites filled (two dots). Tn held by Tm in Positions C and M is uncoupled. T₁, T₂, and T₃, represent the mole fractions of uncoupled Tn with zero, one, and two calcium bound respectively (single symbol with open circle, one dot, and two dots). T₁, T₂, and T₃ must be carried by thermal motions of Tm to the vicinity of actin binding sites in Position B for coupling to occur. The mole fraction of Tm in Position B, {C/<i>K</i>_B} (brackets denote non-equilibrium state), determines the mole fraction of actin binding sites available for interaction with T₁, T₂, and T₃ (circle, one dot, and two dots dissociated from actin in Position B). The segment conformation of Tm (filled rectangle) requires the formation of a coupled myosin state (closed myosin head). The coupled myosin state is stabilized by the mole fraction of free myosin present in segments (open myosin head attached to actin) and the mole fraction of C transiently present in Position M (given by {C/<i>K</i>_A}). Each segment is composed of a variable number of Tm subunits (1+αP_M; P_M is the probability of the M state) and a super segment is composed of <i>n</i> segments. The mole fractions of segments (S) and super segments (S_s) each equal M. Tm in Positions C and M supports cycling myosin intermediates (pair of myosin heads) for sliding filaments and isometric tension respectively. Omitted from the diagram for clarity are the redundant reactions for calcium binding to Tn in Positions C and M and the explicit reaction with actin that forms free myosin.</p

Model prediction compared with published and simulated data.

<p><b>A and B.</b> Panels show the relationships of published data <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#pone.0041098-Cluzel1" target="_blank">[20]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#pone.0041098-Sourjik1" target="_blank">[21]</a> and representative plots using the analytical expression (Eq. 2.14) for arbitrary [CheYP] and <i>K</i>_L = 3.7 µM <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#pone.0041098-Sourjik1" target="_blank">[21]</a>. The parameters <i>α</i>, <i>K</i>₀, and <i>n</i> of the analytical expression were adjusted to attain plots that were fit by appearance to the data. <b>Panel A.</b> We maintained constant <i>n</i> (<i>n</i> = 5) and varied <i>α</i> and <i>K</i>₀. Shown are the fits for <i>α</i> and <i>K</i>₀ given by 1 and 2 (purple), 1.5 and 0.7 (blue), and 2 and 0.3 (rose), respectively. <b>Panel B.</b> We maintained constant <i>α</i> and <i>K</i>₀ (2 and 0.45, respectively) and varied <i>n</i>. Shown are the fits given <i>n</i> = 3 (purple), <i>n</i> = 4 (blue), and <i>n</i> = 5 (rose). <b>C and D.</b> Panels show relationships between plots of the M function (lines) and the results of simulation (symbols). Plots are generated as with Eq. 2.14 using <i>K</i>₀ = 1, <i>K</i>_L = 1, and either <i>α</i> = 0 (green), <i>α</i> = 1 (rose), or <i>α</i> = 2 (blue). <b>Panel C.. </b><i>n</i> = 1. <b>Panel D.. </b><i>n</i> = 5. For the simulations, the rate of sample times and θ are as described in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041098#s2" target="_blank"><i>Methods</i></a> and the decay rates of the excited state (<i>k</i>₋₂) are 0.8 (squares) or 10 (circles), which were determined in preliminary measurements (details in Methods S1).</p

Genkwalathins A and B, new lathyrane-type diterpenes from <i>Daphne genkwa</i>

<p>Screening for new natural anti-neuroinflammatory compounds was performed with the traditional folk medicine Genkwa Flos, which potently inhibited nitric oxide (NO) production by LPS-activated microglial BV-2 cells. Two new lathyrane-type diterpenes, genkwalathins A (<b>1</b>) and B (<b>2</b>), and 14 known daphnane-type diterpenes (<b>3</b>–<b>16</b>) were isolated. The lathyrane-type diterpenes were isolated for the first time from the Thymelaeaceae family in this study. Compounds <b>1</b> and <b>2</b> moderately inhibited LPS-induced NO production in BV-2 cells without affecting cell viability, while six daphnane-type diterpenes (<b>3</b>, <b>4</b>, <b>6</b>, <b>7</b>, <b>9</b> and <b>10</b>) potently reduced NO production with IC₅₀ values less than 1 μM, although they did display weak cytotoxicity. A structure–activity relationship study on the daphnane-type diterpenes indicated that the stereochemistry at C-19, the benzoate group at C-20, and the epoxide moiety could be important for their anti-neuroinflammatory effects.</p