Isolated cardiac myocyte in culture undergoing periodic contractions Courtesy of Jan Lammerding Used with permissi Structure of dle mage removed due to copyright considerations
undergoing periodic contractions Structure of muscle Courtesy of Jan Lammerding. Used with permission. Isolated cardiac myocyte in culture 1� Image removed due to copyright considerations
Skeletal (striated)and smooth muscle O (b)Smooth muscle Temporal patterns of muscle contraction Single twitch Periodic sequence of excitations Fused tetanus(Fmav) 日 Unfused Time(sec)
Skeletal (striated) and smooth muscle� Temporal patterns of muscle contraction • • • max) l (a) Skeletal muscle (b) Smooth muscle Single twitch Periodic sequence of excitations Fused tetanus (F 2
Tension-length curves for a muscle fiber (relaxed and maximally stimulated) =(0+阝) Passive Length l∥ Hills equation Empirically determined force-velocity relationship obtained from macroscopic measurements vF/Fv v/vmax 1-(F/F F1-(F/F) C(F/Fma) Fmax(Fmas/F)+C
Tension-length curves for a muscle fiber (relaxed and maximally stimulated) l Empirically determined force-velocity relationship obtained Hill’s equation from macroscopic measurements v vmax = 1- (F Fmax) 1+ ( max) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 v/vmax F/Fmax or P/Pmax vF vmaxFmax = 1- ( CFF (Fmax F) +C F/Fmax vF/Fmaxvmax F Fmax) 3�
ource of ener rgy for muscle口 Hydrolysis of adenosine triphosphate(ATP) creating adenosine diphosphate(ADP) ATP →ADP+P ATPase △G=AGn-67l ATP ADPIIP or approximately -25 kT(displacement -5 nm) Power/weight same as an automobile engine
Source of energy for muscle� Hydrolysis of adenosine triphosphate (ATP) creating adenosine diphosphate (ADP): ATP æ Æ actomy æææsin ADP + Pi ATPase Ê [ATP] ˆ DG = DG0 - kT lnÁ ˜ Ë [ADP][ ] Pi ¯ or approximately -25 kT (displacement ~ 5 nm) Power/weight ~ same as an automobile engine 4
A rise in cytosolic Ca2+ triggers muscle contraction(part D) Sarcomere Myofibrils Sarcoplasmic reticulum Transverse tubule Plasma membrane Terminal cisterna of SR A rise in cytosolic Ca2+ triggers muscle contraction(part Il Step 1: An excitation signal travels along the efferent nervous pathways towards the muscle Qee Step 2: The excitation signal de-polarizes the cell membrane Step 3: The potential triggers the release of calcium into the sarcoplasmic matrix surrounding the filaments of the motor Step 4: This removes the hindrance( tropomyosin)for interactions between actin and myosin filaments through chemical. mechanical and electrostatic actions. Step 5: The stepping action of myosin along the adjacent actin filament causes the two to slide relative to each other reducing the length of the sarcomere, producing contraction. Step 6: Sequestration of calcium ions in the sarcoplasmic reticulum(ATP-dependent) switches the contraction activity
A rise in cytosolic Ca2+ triggers muscle contraction (part I) 2+ Step 1: An excitation signal travels along the efferent nervous pathways towards the muscle. Step 2: The excitation signal de-polarizes the cell membrane. This allows spread of the action potential along the Step 3: The potential triggers the release of calcium into the unit. Step 4: chemical, mechanical, and electrostatic actions. Step 5: The stepping action of myosin along the adjacent Step 6: reticulum (ATP-dependent) switches the contraction activity off. A rise in cytosolic Ca triggers muscle contraction (part II) sarcoplasmic reticulum. sarcoplasmic matrix surrounding the filaments of the motor This removes the hindrance (tropomyosin) for interactions between actin and myosin filaments through actin filament causes the two to slide relative to each other, reducing the length of the sarcomere, producing contraction. Sequestration of calcium ions in the sarcoplasmic 5�
Skeletal muscle contains a regular array of actin and myosin Actin thin filament Myosin thick filament 000000 9o0000000 e-band A-band 4-band- Sarcomere
array of actin and myosin Skeletal muscle contains a regular 6�
http://www.scripps.edu/milligan/research/movies/myosin_text.html Conformational changes in the myosin head couple atP hydrolysis to movement 1 Nucleoid binding binds fo a Divots ADP release
http://www.scripps.edu/milligan/research/movies/myosin_text.html couple ATP hydrolysis to movement Conformational changes in the myosin head 8�
MyosiN compl AcaiN Helix sopo)yos http://www.sci.sdsu.edu/movies/actin_myosin.html mage removed due to copyright considerations Rhodamine phalloidin labeled actin moves on a myosin coated cover slip(black) observed with epifluorescence microscopy. This motility assay uses the antibody D. A. Winkelmann, L. Bourdieu, A OtL, F. Kinose, A. Libchaber: "Flexibility of Myosin Attachment to Surfaces Influences F-Actin Motion"Biophys J. 68, 199 244-2453
http://www.sci.sdsu.edu/movies/actin_myosin.html Image removed due to copyright considerations. Rhodamine phalloidin labeled actin moves on a myosin coated cover slip (black) observed with epifluorescence microscopy. This motility assay uses the antibody capture technique. D. A. Winkelmann, L. Bourdieu, A. Ott, F. Kinose, A. Libchaber: "Flexibility of Myosin Attachment to Surfaces Influences F-Actin Motion" Biophys J. 68, 1995, 2444-2453. 9
The sliding filament model A. Huxley Niedergerke, H. Huxley Hanson a quantitative model A Huxley 1957 See also textbooks by t. McMahon or J. Howard While in the bound state, the myosin head behaves as though loaded by linear springs with spring constant, K, and that it passes through the necessary biochemical processes including binding of ATP, Only the case of constant(time-invariant) relative sliding The muscle is assumed to be maximally activated throughout. Attachment and detachment is assumed to obey simple kinetics Effects of other elastic components in the muscle are ignored Myosin filament Myosin head Actin binding site Actin filament As the actin filament filament. the myosin head can bind to When it does, the springs are either stretched or at the bindi 10
The sliding filament model A. Huxley & Niedergerke, H. Huxley & Hanson, Nature, 1954 A quantitative model A. Huxley 1957 See also textbooks by T. McMahon or J. Howard While in the bound state, the myosin head behaves as though loaded by linear springs with spring constant, k, and that it passes through the necessary biochemical processes including binding of ATP, ATP hydrolysis, and release of ADP. Only the case of constant (time-invariant) relative sliding velocity and force generation is considered. The muscle is assumed to be maximally activated throughout. Attachment and detachment is assumed to obey simple kinetics. Effects of other elastic components in the muscle are ignored. Myosin head Myosin filament Actin binding site Actin filament x� As the actin filament moves past the (fixed) myosin filament, the k myosin head can bind to + it at the red triangle. When it does, the springs k- are either stretched or compressed and a force kx acts at the binding x site. 10
Equations governing the probability D n(x, t)that a cross-bridge is attached dn(x, t) dn(x, t) an(x, t) -m(x1)k(x)-n(x1)k( dt At steady state In= n(x) d I-n(x)k(x)-n(x)k_( k. =attachment rate k= probability of attachment The sliding filament model In this region the actin binding site is approaching the free myosin head, unoccupied. D Since both k+ and k are zero, no binding occurs D h-x≤x<h:口 region where the binding rate constant is large, described by the equation: D k
Equations governing the probability� n(x,t) that a cross-bridge is attached� dn(x,t) ∂n(x,t) ∂n(x,t) = - v = [1- n(x,t)]k+ (x)- n(x,t)k (x) - dt ∂t ∂x Formation of new Detachment of existing bonds bonds At steady state [n = n(x)] dn(x) -v = [1- n(x)]k+ (x)- n(x)k (x) - k dx + k+ = attachment rate; k- = k-� detachment rate; n =� probability of attachment� x h The sliding filament model x > h:� In this region the actin binding site is approaching the free myosin head, unoccupied.� Since both k+ and k- are zero, no binding occurs:� n(x) = n(h) = 0 h-x0 < x <h:� If binding is to occur, it has to do so (according to this simple model) within this narrow� region where the binding rate constant is large, described by the equation:� -v dn = (1 - n)k 0� dx +� k+ k- Ê k 0 + x0 ˆ n(h - x0 ) =1 - expÁ �- ˜� Ë v ¯� x h 11
