doi:10.1016/j.biosystems.2006.08.012
Copyright © 2006 Elsevier Ireland Ltd All rights reserved.
Brownian motion, fluctuation and life
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Toshio Yanagidaa, b,
,
,
, Masahiro Uedaa,
, Tsutomu Muratac,
, Seiji Esakia,
and Yoshiharu Ishiib, 
aGraduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
bFormation of Soft Nano-machines, CREST, 1-3 Yamadaoka, Suita, Osaka 565-0871, Japan
cKobe Advanced ICT Research Center, Brain Information Project, Iwaoka, Nishi-ku, Kobe, Hyogo 651-2492, Japan
Received 26 June 2006;
accepted 25 August 2006.
Available online 9 November 2006.
Abstract
The measurements of dynamic behaviors of biomolecules in relation to their functions have been allowed using single molecule measurements. Thermal Brownian motion causes random step motion of motor proteins and structural fluctuation of protein molecules between multiple states. In hierarchic structure of life, the fluctuation is modulated. Random fluctuation is biased to directional motion and reactions as a result of interaction of proteins. The fluctuation of kinetic state of signaling proteins results in polarization and localization of cells. A recognition process in brain is also explained by the equation analogous to biochemical reaction at the molecular level. Thus dynamic processes originated from thermal motion may play an important role in activation processes in life.
Keywords: Fluctuation, Brownian motion, Single molecule measurement, Molecular motor, Cell signaling process, Dynamic structure of protein, Recognition in brain
Fig. 1. Hierarchic structure of biological structures. Thermal motion in different stages of hierarchic structures of biological systems.
Fig. 2. Manipulation of molecular motors and force measurements. (A) Manipulation of a single myosin molecule with a microneedle. A myosin molecule captured at a tip of the microneedle is allowed to interact with an actin filament placed on a glass surface. (B) Manipulation of an actin filament by a laser trap. Two beads attached at both ends of an actin filament are trapped by laser. The actin filament is manipulated to interact with myosin molecules on the filament placed on a glass surface. In both cases, the movement takes place against the bending and trapping force. The relative movement between actin and myosin is measured by displacement of the microneedle or beads trapped by laser. The microneedle or beads undergoes thermal motion and the strong interaction between myosin and actin reduces the thermal motion.
Fig. 3. Photon-counting and fluorescence measurements. (A) Mechanism for fluorescence emission. Photons are emitted after series of photochemical reactions of electronic states of fluorescent molecules in the timescale of nanoseconds. (B) Photon emission from a single fluorescent molecule occurs randomly. (C) Fluorescence measurements are performed by counting the number of photon emitted from a single molecule detected in a period of time (ms–s). Reflecting the stochastic nature of the photon detection, the fluorescence intensity fluctuates.
Fig. 4. Energy landscape for dynamics of biomolecules. Energy landscape is described as free energy of biomolecules as a function of their coordinates such as positions and structural parameters. At local minima, biomolecules are stable and fluctuate around the minima. When biomolecules change from one local minimum to the other through an activation energy barrier, the rate, k± for forward and backward steps, is represented by the ratio of the activation energy ΔU± to thermal energy kBT in Arrhenius equilibrium k±
exp[−(ΔU±/kBT)]. The free energy of the molecules fluctuates and they undertake a transition when the energy value is greater than the activation energy.
 |
Fig. 5. Forward and backward step movement of kinesin. (A) A single kinesin molecule moving on microtubules. A kinesin molecule is attached to a bead trapped by a focused laser as a cargo for measurements. (B) Time trajectory of displacement and force of kinesin. In the laser trap measurement, when kinesin moves the trapping force or external load increases indicted. (C) Energy landscape for the forward and backward step of kinesin. The thermodynamic parameters obtained for the forward and backward step movement of kinesin are included in the figure. The rates for the forward and backward steps, k±, are related to the activation energy U± and external load F, k± = constant exp[−(U± + Fd±)/kBT] where d± is a characteristic distance and ± denotes forward and backward steps. U± was break down to enthalpic contribution H± and entropic contribution S±, U± = H± − TS±. The difference in the activation energy is mainly explained by the difference in entropy. (D) A model for preferential binding of kinesin to one direction based on the experimental results summarized in (C).
Fig. 6. Diffusion-anchored processive movement of single-headed myosin VI. (A) Non-processive motion of single-headed myosin VI without any cargo. The motion was visualized using green fluorescence protein (GFP) attached. (B) Processive movement of myosin VI with a bead attached as a cargo. (C) Model for diffusion-anchored processive movement of myosin VI.
Fig. 7. Biased Brownian movement of myosin II. (A) Non-processive movement of myosin II. (Top) The displacement of the microneedle attached to single myosin II head (S1) was measured as a function of time and the binding of myosin to actin was measured by stiffness calculated from the displacement record (bottom). (B) Expansion of the rising phase of the displacement record above.
 |
Fig. 8. Spontaneous conformational transition of actin and activation of myosin motility through actin conformational changes. (A) An actin molecule (colored blue) is labeled specifically with donor (green) and acceptor (red) and polymerized with large excess of unlabeled actin (colored grey). (B) Structural dynamics of actin was measured using fluorescence resonance energy transfer (FRET). The time trajectories of the donor (green) and acceptor (red) fluorescence changed due to the changes in FRET; that is, the donor fluorescence increased when the acceptor fluorescence decreased and vice versa. (C) Distribution of the FRET efficiency (IA/(ID + IA) when ID and IA are donor and acceptor fluorescence intensity, respectively) from actin. The distribution was fit to two Gaussian distributions corresponding to the high FRET efficiency state or active state in which actin activates the motility of myosin and the low FRET efficiency state or inactive state in which actin inhibits the motility of myosin. (D) Energy landscape of actin. The energy landscape of actin shows two minima corresponding to the active state and inactive state. The energy landscape for actin in the presence of myosin is similar to the active state and that for the cross-linked actin in which myosin motility is inhibited is similar to the inactive state.
 |
Fig. 9. Multiple conformational and kinetic states of Ras in vitro and in vivo. (A) Conformational dynamics of Ras in vitro. The FRET efficiency changes with time among several FRET efficiency values. Right is the replot of the FRET efficiency in a histogram. (B) Energy landscape model for Ras based on the single molecule measurements of conformational dynamics. Top: Refractory state is distinguished from other multiple active states. Middle: Among the active states, there are transitions with timescale of
30 ms. Bottom: One of the states is selected upon the binding to effectors. (C) Imaging of the binding of Raf to Ras after stimulation with EGF in living cell cells. Accumulation of fluorescence or GFP labeled Raf was observed (right). After photo bleaching, fluorescence spots (arrows) were observed (right). The binding duration of Raf onto the plasma membrane was measured at accumulation areas (left) and bulk membrane (right). The distribution of the duration time was fit to one or two exponential curves and the decay times determined are indicated.
Fig. 10. Heterogeneity of kinetic state in chemotaxis of dictyostelium cells. (A) Image of the binding of fluorescent analogue of cAMP to moving dictyostelium amoeba. (B) The histogram of the duration time of the cAMP binding at the pseudopod and tail halves of the moving cell.
Fig. 11. Figures that can be interpreted in two ways. Necker cube (NC), vase and face (RU) and young and old woman (BO) are depicted.

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