A consequence of mechanosensitivity: non-linear stiffness of myosin

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Partial activation of muscles

Muscle fibres need to be activated by calcium to induce contraction and force generation. By using an intermediate calcium concentration (pCa~5.5 – 6.5) lying between the concentration at a relaxed state and concentration at complete activation, it is possible to activate the muscle partially. Partial activation means that the tension developed by the fibre is a fraction of the maximum tension one can obtain during total activation.

Mechano-electrical transduction in the inner ear of vertebrates

Hair cells are located in the inner ear of vertebrates. They are responsible for the transduction of mechanical stimuli into nervous impulses in the hearing process. The most striking organelle of those cells is the hair bundle that extends from the apical surface of each hair cell. The hair bundle acts as a mechano-receptive antenna. A hair bundle is made up of stereocilia, which are rigid cylindrical processes containing bundled parallel actin filaments. The stereocilia are arranged by increasing height similar to the pipes of a church organ (Figure. 0.1.33). They are connected to each other by lateral links, including diagonal tip links going from the top of one stereocilium to the flank of the nearest taller neighbour.

Myosin 1c as an adaptation motor

Like all sensory systems, the hair cells are endowed with an adaptation mechanism that allows them to remain sensitive to small transient stimuli in presence of persistent and constant  saturating stimuli. The adaptation mechanism can be studied by imposing steps to the hair bundles and observing the transduction current.
In response to positive deflections, the absolute value of the current increases meaning that the channels open. The current then gradually decreases to its initial value, indicating that the channels are reclosing (Figure. 0.1.34(a)). The role of adaptation is to return the open probability of the channels to its resting value in order to restore sensitivity of the hair bundles to transient stimuli. The kinetics of the adaptation processed can be described by two time constants. The fast time constant varies from tens of microseconds in the rat to a few milliseconds in the frog. The slow timescale of adaptation varies between 10 to 100 ms. For weak displacements, the rapid phase is largely responsible for adaptation. Conversely, it does not intervene for large displacements ( Figure. 0.1.34(c)).
According to the gating-spring model of mechanoelectrical transduction, the channels open in response to a positive stimulus due to an increase in the tension in the elastic element coupled to the channel. Adaptation can be explained by a mechanism which releases the tension in the gating spring during a static positive stimulus, leading to reclosure of the channels. In the case of a negative stimulus, such a mechanism would be required to increase tip-link tension and must thus be active. Myosin 1c is a strong candidate for the role of adaptation motor in the inner ear (Gillespie & Cyr, 2004). This motor is indeed necessary for adaptation to take place (Stauffer et al., 2005). However, it remains uncertain that myosin motors are fast enough to mediate adaptation in the submillisecond timescale. For fast adaptation, electromechanical feedback of the Ca2+ component of the transduction channel on the state of the transduction channels appear to be necessary (Wu, Ricci & Fettiplace, 1999)

Force-Displacement relation of a hair bundle

The mechanical properties of the hair-cell bundle can be studied by measuring its forcedisplacement relation. This is done by imposing displacement steps to the bundle and measuring the force necessary to maintain this displacement (P Martin & Hudspeth, 2001). The measurements are performed over short timescales (~3ms after application of the first step) in order to avoid the influence of adaptation as much as possible. For large displacements both positive and negative, the force-displacement curve is linear showing behaviour analogous to a simple Hookean spring. However, near the resting position of the hair cell bundle, the relation is no longer linear and a zone of negative stiffness can be observed.

Spontaneous oscillations of acto-myosin systems

We have described the general architecture of muscles and hair-cell bundles, as well as their mechanical properties. Both biological systems are organized myosin-based systems and both show interesting properties thanks to the action of the actomyosin system. Those two systems are also known to oscillate spontaneously under certain conditions and there is strong evidence that myosins have an active role in these oscillatory properties.

Spontaneous oscillations in muscle fibres

In some insects, the flight muscles display oscillations that are asynchronous to the activating nervous impulses they receive (Pringle, 1978). Similar spontaneous oscillations are present in cardiac muscles (Fabiato & Fabiato, 1978; Fukuda, Fujita, Fujita, & Ishiwata, 1996) and more surprisingly in skeletal muscles (Okamura & Ishiwata, 1988). In the latter, the oscillations do not occur in physiological conditions In in-vitro experiments, the oscillatory behaviour of muscle fibres can be observed by spontaneous tension oscillations in isometric conditions (Figure. 0.1.36(a)) or by monitoring spontaneous oscillations in the length of sarcomeres (Figure. 0.1.36(b)). These oscillations have a characteristic triangular shape, with a slow phase in the direction of the natural mechanical motor activity and a rapid phase in the opposite direction. For the spontaneous oscillations to appear in skeletal and cardiac muscle fibres, a number of conditions must be met:
· The fibre must be partially activated either by calcium (Fabiato & Fabiato, 1978) or ADP (Okamura & Ishiwata, 1988). The need for activation implies that myosin is involved in the oscillation process.
· The average length of the sarcomeres must be lower than 3μm.
· A load must be applied to the fibre. Oscillations are never observed in-vitro on freefloating muscle fibres.
It is interesting to note that the conditions necessary for oscillations to occur are identical to those in which the relation between tension and sarcomere length is non-monotonous (See Section 1.4 and Figure. 0.1.31). Moreover, the range of sarcomere lengths over which oscillations appear coincides with the range of sarcomere lengths in which the isometric tension in a partially activated muscle fibre increases, strongly suggesting a link between the two phenomena.

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Table of contents :

A/. Introduction to molecular motors
1) Actin
1.1 Biochemical Properties of Actin
1.2 Mechanical properties of actin filaments
2) Myosin
2.1 Myosin II
2.2 Myosin 1
B/. Mechanical properties of molecular motors
1) Experiments on single molecules
1.1 The Three-Bead Geometry
1.2 Two-step force generation by myosins
1.3 Effects of an external load on myosin activity
1.4 Calcium regulation of myosin 1 activity
1.5 Non-productive attachments
2) In-vitro Motility Assay
2.1 General Principle
2.2 Processivity
C/. Working model for myosin
1) The power stroke model
2) A consequence of mechanosensitivity: non-linear stiffness of myosin
D/. Myosin in biological systems
1) Myosin II in muscles
1.1 Muscle contractions
1.2 Mechanical properties of muscle fibres : Force-Velocity relation
1.3 Transient response of a muscle fibre to sudden changes in length
1.4 Partial activation of muscles
1.5 Stretch activation of muscles
2) Myosin 1c and the mechanosensitivity of hair cells in the inner ear
2.1 Mechano-electrical transduction in the inner ear of vertebrates
2.2 Myosin 1c as an adaptation motor
2.3 Force-Displacement relation of a hair bundle
3) Spontaneous oscillations of acto-myosin systems
3.1 Spontaneous oscillations in muscle fibres
3.2 Spontaneous oscillations of hair cell bundles
3.3 Summary
E/. An intermediate scale
1) Evidence for collective motor effects
2) Theoretical descriptions of collective motor effects and oscillations
3) Spontaneous motor oscillations in a minimal actomyosin system
Part I Chapter I
A/. Instrumentation
1) The Optical Tweezers
1.1 Principle of the Optical Tweezers
1.2 Characteristics of our Optical Tweezers
2) Acousto-Optic Deflectors
2.1 Principle of Acousto-Optic Deflectors
2.2 Characteristics of our AODs
3) The Detection Method
3.1 Photodiodes
3.2 Calibration
4) Controlling the set-up
4.1 Moving the laser
4.2 Moving the stage
B/. Biochemical Tools
1) Myosins
1.1 Myosin II
1.2 Myosin 1b
2) Actin
2.1 Polymerisation
2.2 Actin bundles
3) Functionalization of the beads
4) Protein Attachment
4.1 Nitrocellulose Surfaces
4.2 Antibody-treated Surfaces
4.3 Silanized Surfaces
5) Additional molecular cocktails.
5.1 Anti-Bleaching Mixture
5.2 ATP regeneration
6) Experimental Procedure
6.1 Flow Cell Preparation
6.2 Molecular Motor Attachment
6.3 Incubation of actin and functionalized beads
6.4 Injection of the experimental solution and starting the experiment
6.5 Recording the collective effects of the motors
Part I Chapter II
A/. Characterization of the molecular motors
1) In-vitro motility assay
1.1 Nitrocellulose surfaces
1.2 Silane surfaces
2) Force generation
B/. Spontaneous oscillations under elastic loading
1) With single actin filaments
2) With polarized actin bundles
C/. Mechanical stimulus : Alternating steps
Part I Chapter III
A/. Motility Assay
B/. Force exerted by the motors
C/. Spontaneous oscillations and stimulation
Part II Introduction
A/. The Need for a New Molecular Force Sensor
B/. Auto-Assembled Magnetic Columns
C/. Magnetic columns as force sensors
Part II Chapter I
A/. Making the magnetic bead pattern
1) PDMS substrate fabrication
1.1 – Making the moulds
1.2 – PDMS casting
2) Depositing nucleator beads by capillary assembly
B/. Formation of the columns
1) The Magnetic Beads
2) The Electromagnet
2.1 Making the Electromagnet
2.2 Calibration of the Electromagnet
2.3 – Limits of the Electromagnet
C/. Characterization of the properties of the columns
1) The Experimental Set-Up
1.1 – The custom stage.
1.2 – The Cooling System
1.3 – The detection system
2) Observation of the columns from the side
3) Experimental Procedure
3.1 Procedure with the electromagnet
3.2 – Procedure with the permanent magnet
3.3 – Viewing the profile of the columns
Part II Chapter II
A/. Mechanical properties of magnetic columns
1) Stiffness
1.1 Variation of stiffness along the length of a column
1.2 Viewing the deformation profile of the columns:
2) Stiffness as a function of column length
3) Responsiveness and drag coefficients of the columns.
4) Influence of the external magnetic field on stiffness
B/. Theoretical behaviour of a magnetic column: interactions between magnetic dipoles .
1) Formation of the columns
2) Rotation of the beads in the magnetic field
3) Orientation of the individual dipoles in a deflected column
4) Stiffness of a column
5) Linearity of the force-displacement relation
6) Friction on a pivoting column
C/. Towards biological applications
Part II Chapter III
A/. Viability of the magnetic bead columns as force sensors
B/. A magnetic column as a biomimetic stereocilium
C/. Control of the height of the columns
D/. Future developments
Conclusion
A/. Part I: Molecular motor oscillations under elastic loading
B/. Part II: Auto-assembled magnetic bead columns as force sensors

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