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Mechanics of Vascular Smooth Muscle

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ABSTRACT

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress‐development, sustained stress‐maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip‐catch bond, and a regulated two‐step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress‐strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure‐function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM. © 2016 American Physiological Society. Compr Physiol 6:111‐168, 2016.

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Figure 1. Figure 1. Diagram of vascular smooth muscle (VSM, A) and cell structural hierarchy (B‐E). VSM structure includes cells that are embedded in and mechanically attached to ECM comprised largely of elastin and collagens (Coll) I and III (A). Several models of smooth muscle cell ultrastructure have been proposed (20,274); Small's model is shown in panels B and C. An extensive cytoskeleton interconnects a filamin‐actin‐desmin filament domain (FAD) with an actomyosin (AM) domain attached to dense bodies and dense plaques (B and C). The smooth muscle sarcomere structure remains to be fully elucidated and appears to be highly dynamic. However, a general view is that the thick filaments (M) are side polar (C and D) and the thin filaments (A) and FAD attach to dense bodies (B and C). Myosin is a heterohexamer comprised of two heavy chains and two pairs of light chains (E, only a single heavy chain and single pair of light chains is shown). The light meromyosin (LMM) tail region of individual myosin heavy chains associate with other myosin heavy chain tails to form thick filaments (D). The catalytic region of the myosin S1 head extends from the α‐helical S1 neck wrapped by one essential (ELC) and one regulatory light chain (RLC), which in turn extends from the myosin S2 region, to reach actin‐binding sites. Panels A‐D adapted from, respectively (419,426,105), and (529), with permission.
Figure 2. Figure 2. Smooth muscle cell and arterial structures. 3D fluorescence micrograph of antibody‐labeled artery cross‐section revealing the alternating pattern of, respectively, caveolae (C, green) and dense plaques (D, red) within a single VSM cell digitally isolated from other cells and the ECM. Each square = 1 μ2 (A). Transmission electron micrograph of a VSM cell from rabbit renal artery shown in cross‐section (B) revealing extensive thin filaments and alternating caveolae (C) and dense plaques (D). Note that microtubules (arrow) reside adjacent to caveolae and mitochondria, supporting the notion that these structures, acting as cargo for microtubule motor proteins, are adjusted in space and time. Thin filaments occupy much of the cytosol [for examples of electron micrographs of smooth muscle revealing the relative abundance of thick and thin filaments, see (20,93,201)]. Diagram of a model of dense bodies (dots) and actomyosin filaments (lines) in a single contracted and relaxed smooth muscle cell in cut‐away lateral and cross‐sectional views (C). Electron micrograph of a rabbit femoral artery cut transverse to the long axis of the arterial tube revealing outer adventitia (A), middle media (M), and inner intima (I) (D). Fluorescence micrograph revealing the long, fusiform shapes of isolated single VSM cells (E). A single relaxed (upper panel) and contracted (lower panel) VSM cell attached at one end to a micropipette (upper right) (F). Note dramatic degree of shortening and formation of blebs (B) upon shortening. Panel A adapted from (374). Panel C adapted from (80) with permission. Panels D‐F adapted, with permission, from, respectively (191,113), and (110).
Figure 3. Figure 3. The minimum solution pO2 required to support full isometric contraction of swine carotid media stimulated with epinephrine is dependent on arterial tissue thickness such that a bathing solution bubbled with room air would suffice for tissues ≤400 μ thick (A). Arteries can be classified, according to the strength of force maintenance (tonic phase) compared to that developed during the early phasic phase of contraction, into tonic (B) and phasic (C) arteries; FA = rabbit femoral artery, SA = rabbit saphenous artery (contractile stimulus: K+‐depolarization). Compared to elastic arteries (D: abdominal aorta, AA, and E: common iliac artery, CIA), muscular arteries (D: femoral artery, FA, and E: external iliac artery, EIA) express a higher VSM/ECM ratio and therefore produce significantly stronger contractions when normalized to tissue cross‐sectional area (F). Data adapted, with permission, for panel A from (332). Solid and dashed lines in panels B‐E are, respectively, average and SE values, n = 5‐7 rabbits. * = P < 0.05 compared to AA.
Figure 4. Figure 4. Analog elements used to form mechanical circuits include a spring (A) and dashpot (B) that are fixed at one end and attached to other elements at their free end (filled circle). (C) To measure force, these elements (ele) are attached to a force transducer (FT) of known very high stiffness (kFT).
Figure 5. Figure 5. Preconditioning (B, note decline in peak force from cycle 1 to 7 and from cycle 8 to 14) of a strip of naïve rabbit bladder incubated in a Ca2+‐free solution resulting from (A) 7 sequential 1 mm ramp load‐unload cycles at 1 mm/s (1, 2, … 7), followed immediately by 7 sequential 2 mm ramp load‐unload cycles at 1 mm/s (8, 9, … 14). In this context, a naïve tissue is one mounted on a myograph that has not yet been subjected to load‐unload cycling. Clockwise force versus length work loops of data shown in panels A and B reveal a high, linear stiffness during loading for the first cycle from 0 to 1 mm (C), and during the “new” strain region (from 1 to 2 mm) of the eigth cycle (D) only. All other cycles display nonlinear length‐force curves and much smaller work loop areas. The loading curve for the first mm of cycle 8 is superimposable on the loading curve of cycle 7. Cycles 6 (not shown) and 7, and cycles 13 (not shown) and 14 are identical. Adapted, with permission, from (445).
Figure 6. Figure 6. A stepper motor controlled to stretch and compress a spring (A‐F) can reveal the linear stress (σ) versus strain (ϵ) (G) and constant stress/strain quotient (H, stiffness E) characteristic of a linear spring. The free and fixed ends of the spring are represented by, respectively, r and q. The nonstretched resting position of r is j0. Spring compression involves moving r toward j‐1 and beyond, and spring tensioning involves moving r toward j+1 and beyond. A nonlinear spring (G, dash‐dotted curve) would result in a nonconstant E (H, dash‐dotted curve). Drawings of sheets of different widths w (I) and a rectangular block of thickness h (J) showing direction of applied displacement producing measured uniaxial force, f (I), which can be normalized to calculate tension, T (I), and stress, σ (J).
Figure 7. Figure 7. Rapidly activated swine carotid media displays a linear relationship between active stiffness (dσ/dl0) and stress (σ). Adapted from (423) with permission.
Figure 8. Figure 8. A stepper motor controlled to stretch a dashpot (A‐D) can reveal the linear relationship between stress (σ) and strain‐rate (ϵ·) and constant σ/ϵ· quotient (viscosity η) characteristic of a linear dashpot (F). Stepper motor ramp stretches (E) at two different rates (ϵ vs. time: lower curves, fast and slow strains from j to j+1) induce two different levels of stress (σ: upper square‐wave curves, fast and slow). Honey has a higher viscosity than H2O (F). Thus, a slow ramp stretch of a honey‐filled dashpot will induce a higher level of stress than the same slow ramp stretch of a H2O‐filled dashpot (E, honey; slow compared to H2O; slow).
Figure 9. Figure 9. Soft tissues display stress (σ)‐relaxation (B, σ‐relaxation of rabbit renal artery, RA) over time when subjected to an imposed rapid stretch to a new tissue length [A; length (l), stretch‐ratio (λ), or strain (ϵ)‐step)] and held there for some time (l, λ, or ϵ‐clamp). Simulations of the stress responses (D, F) to a strain‐step/strain‐clamp protocol (C, E) for a spring of stiffness E = 3 (C, D) and dashpot of viscosity η = 3 (E, F). As dt approaches zero in the strain‐step rate, stress will increase toward ∞ (F).
Figure 10. Figure 10. Simulations of the stress (σ) responses (B, E, H) to a sinusoidal strain (ϵ)‐oscillation protocol (A, D, G) for a spring of stiffness E = 3 (A‐C), dashpot of viscosity η = 3 (D‐F) and 2 element Maxwell Model (G‐I). The stress‐strain (σ‐ϵ) relationships for a spring and dashpot reveal, respectively, no time dependency (C) and time dependency (F and I). The time dependency of the dashpot is revealed by a lag in the imposed length change compared to the stress response, and damping of the maximum stress value. In a Maxwell Model, the spring (s) element requires some strain to develop stress, so the dashpot (d) element dampens the stress response to the strain (i) proportionally to the spring compliance (see Fig. 11). How far the dashpot plunger is from its new equilibrium position determines stress‐strain work loop area and position on the y‐axis; the position was further from the new equilibrium during the first than the second loading. l = length, f = force.
Figure 11. Figure 11. Simulations of the stress (σ) responses (B, C, E, and F) to sinusoidal strain (ϵ)‐oscillation (A) and strain‐step/strain‐clamp (D) protocols for a two‐element Maxwell Model with spring (s) stiffness E = 3 and dashpot (d) viscosity η = 10‐fold that of Figure 10. 1, 2, … 7 identify load‐unload cycles 1, 2, … 7. In panels D‐F, segment 1 to 2 refers to the instantaneous strain‐step, and segments 2 to 3 refer to the strain‐clamp period lasting 45 s. See text for details.
Figure 12. Figure 12. Sequential loading‐unloading curves of dog femoral artery rings reveal clockwise force (F)‐length (L) loops and strain softening (force achieved during the tenth loop is less than that achieved during the first loop). Adapted, with permission, from (389).
Figure 13. Figure 13. Sequential stretch strain (ϵ)‐step/strain‐clamps applied to a viscoelastic soft tissue over time (a temporal staircase‐strain protocol) produces an instantaneous stress (σ) response due to the strain‐step and an equilibrium stress response at the end of stress‐relaxation (A, plot over time; B, stress‐strain plot). For each strain‐step, the elastic stress equals the equilibrium stress, and the viscous stress equals the difference between instantaneous and equilibrium stresses (B, C). Elastic and viscous stress‐strain plots for vena cava (VC), abdominal aorta (Ab Ao), and carotid artery (CA) reveal considerable differences for different vascular tree segments (D). Panels A‐C adapted from (406) and panel D adapted from (420), with permission.
Figure 14. Figure 14. The final viscoelastic stress‐strain (σ‐ϵ) cycle (8) from the simulation shown in Figure 11c oscillates around zero stress and is linear (A), unlike that of a swine carotid artery (B). Nonlinearity can be incorporated into a Maxwell Model stress‐strain relationship (C; for this simulation, constants for spring stress, σs, were a = 0.3, b = 0.3, and c = −0.5), but the function chosen should have some mechanistic basis. Panel B adapted, with permission, from (408).
Figure 15. Figure 15. Preconditioned soft tissues such as arteries display a passive stiffness‐stress (dσdλσ) relationship that can be modeled as a 1 (or 2) component curve consisting and a linear portion fitting the equation, dσdλ=ασ+αβ (plus a nonlinear portion at very low stress values), where σ = stress, λ = stretch ratio, and α and β are constants (459). Extrapolation of the linear portion provides a stiffness value at zero stress, E0, the product of α and β, that can be used to characterize different tissues. Compared to muscular arteries and heart (B) that display low E0 values, those for elastic arteries (A, dog aortic arch) are relatively high (356,459). The slope of the linear portion, α, is the deviation from constant stiffness. Panels A and B adapted from, respectively, (459) and (356), with permission.
Figure 16. Figure 16. Simulations of the stress (σ) response (B and C) to a sinusoidal strain (ϵ)‐oscillation protocol (A) for a two‐element Voigt Model and stress response (E and F) to a strain‐step/strain‐clamp followed by a quick‐release, small strain‐step protocol (D) for a three‐element Generalized Maxwell Model. A simulation that includes only the springs of a generalized Maxwell model is also shown (F, dash‐dotted line). See text for details.
Figure 17. Figure 17. A quick‐release small strain (ϵ)‐step protocol performed on passive (unstimulated) swine carotid artery reveals weak force redevelopment (A), adapted from (199), with permission. A three‐element generalized Voigt Model (B) and two depictions of a multielement Hill Model (C). Simulations of the stress (σ) response (E and F) to a strain (ϵ)‐step/strain‐clamp followed by a quick‐release small strain‐step protocol (D) for a three‐element Generalized Voigt Model. See text for details.
Figure 18. Figure 18. A generalized model of multiple stress‐strain (σ‐ϵ) behaviors for various types of materials (A). Examples of stress‐strain curves for elastic fibers, elastin, and resilin (B), viscoelastic biomaterials such as skeletal muscle treated to remove thin filaments and retain titin (C) and keratin fibers (D), and viscoelastic‐plastic materials such as Hagfish thread (E). The pressure‐volume (P‐Vol) relationship for femoral artery (F) reveals apparent viscoelastic‐plastic behavior. See text for details. Panels B, D, and E adapted from (315), panel C adapted from (165), and panel F adapted from (39), with permission.
Figure 19. Figure 19. A steady‐state model of the actomyosin cross‐bridge cycle showing four myosin (M) states (A) that include actin (A) plus myosin (M; 1), actin (A) + phosphorylated M (Mp; 2), a phosphorylated cross‐bridge species (AMp; 3) and a dephosphorylated cross‐bridge species, the latchbridge (AM; 4); k values represent rate constants. Rabbit femoral artery activated at time zero with a maximum KCl stimulus produces a counterclockwise [Ca2+]i‐force response revealing two phases, a rapid (∼15 s) phasic phase in which [Ca2+]i increases to its maximum level and force develops to ∼70% maximum, and a tonic phase in which force slowly (from ∼15 s to 3 min) increases further to the maximum level while [Ca2+]i declines to its steady‐state supra‐basal level (B). A comparison of the rabbit slow, tonic femoral artery (FA) and fast, phasic saphenous artery (SA) reveal that during the fast phasic phase, force (C), [Ca2+]i (D, Pk) and myosin phosphorylation (MLC‐p, E, second data point at ∼40% MLC‐p) responses are identical. With time, however, force (C) and MLC‐p (E) dissociate whereas the [Ca2+]i response does not (D, 5 and 10 min). * indicates significant difference (P < 0.05). Panel B adapted from (378) and panels C‐E adapted from (191), with permission.
Figure 20. Figure 20. Hai‐Murphy four‐state kinetic latchbridge model (L) simulation (dashed lines), a four‐state no latchbridge model (NL) simulation [dashed dotted lines (E‐H)] and empirical data (solid lines and symbols) for femoral artery (FA) and saphenous artery (SA). The simulated L model employs a very slow k7 = 0.005 compared to k4 = 0.05, whereas the NL model simulation excludes a latchbridge by assigning k7 = k4 = 0.05. The L model fits the data for the slow, tonic femoral artery (A, B, D), and the NL model fits the falling tonic phase contraction and falling intracellular free Ca2+ concentration and myosin phosphorylation (E, F, H) characteristic of the fast, phasic saphenous artery, suggesting that fast arteries lack latchbridges. Adapted, with permission, from (191).
Figure 21. Figure 21. Isolated whole rabbit femoral (A) and saphenous (B) arteries were pressurized (P) to 60 mmHg, contracted with a maximum [KCl] and allowed to constrict isobarically to measure the degree of reduction in artery lumen diameter at steady state. After recording steady‐state constriction, the arteries were fully relaxed (dilated), pressurized to the next pressure level, activated with KCl and constriction was measured at that pressure (isobaric constriction). This procedure was continued until full steady‐state pressure‐diameter curves were produced for activated femoral (A, open circles) and saphenous (B, open squares) arteries. Diameter data were normalized afterward to maximally constricted (zero) and dilated (one) values. After generation of these active pressure‐diameter curves, fully relaxed arteries were depressurizing to 60 mmHg, activated with KCl to produce full isobaric constriction at 60 mmHg (vertical down arrow), and subjected to a pressure ramp from 60 to 120 mmHg (A, femoral artery, solid circles and arrow) and 60 to 140 mmHg (B, saphenous artery, solid squares and arrow). The activated femoral artery, fully constricted at 60 mmHg, remained nearly fully constricted when subjected to the ramp pressure increase (A, solid circles). By contrast, the activated saphenous artery, also fully constricted at 60 mmHg, dilated along the isobaric constriction curve when pressurized (B, solid squares). Thus, shortened VSM of femoral artery can resist lengthening when subjected to pressures much higher than the muscle can shorten against, suggesting that latchbridges endow slow arteries with dilatation‐resistance (C). See text for additional details. Adapted, with permission, from (60).
Figure 22. Figure 22. Active stress (σ)‐strain (ϵ) (tension‐length, force‐length) curves (A‐F) and “passive” stress‐strain curves for skeletal muscle (E) and artery (F). Bottle brush cartoon illustrates the concept that the degree of overlap (solid bars) of actin (bottle wall) with myosin cross‐bridges (bristles) determines the strength of active stress on the descending limb (d.l.) of the active stress‐strain curve (A). Additional complexity is required to explain the shape of the ascending limb (a.l.). Examples of active stress‐strain curves for striated muscle sarcomere (B), carotid media (C), and small mesenteric artery displaying an initial active stress‐strain curve (D, day 0) and one produced after the tissue had been incubated in culture medium at 0.4‐fold lref for 16 h with the contractile agent endothelin (D, day 1). Also shown is the total stress‐strain curve for small mesenteric artery, which is the sum of the “passive” and active curves (F). See text for details. Panels B, C, D, and E adapted from, respectively (370,522,474) and (527), with permission. Panel F adapted, with permission, from (535).
Figure 23. Figure 23. A schematic illustrating a Maxwell Model (representing muscle) attached to a generalized apparatus designed to measure and control the degree of force and length over time (A) to assess the stress (σ)‐strain (ϵ) relationship of the series elastic component (SEC, B) and the hyperbolic relationship between force, f, or stress, σ, and velocity (v, C‐E). Asymptotes for the force‐velocity Hill equation (vertical and horizontal dashed lines) are not on the force‐velocity curve, and protocols designed to lengthen contracted muscle reveals that muscle can resist lengthening at much greater force levels than the muscle can develop isometrically (thick, curved dashed line, D). Peak power (force‐velocity product) occurs at ∼1/3 the maximum shortening velocity at zero load (V0). Assembly of additional actomyosin cross‐bridges during smooth muscle contraction may explain changes in the force‐velocity relationship known to occur over the course of a contraction (E, see text for details). wt = weight. Panels D and E adapted from, respectively (309) and (129), with permission.
Figure 24. Figure 24. Isotonic quick‐release (A‐C) and slack test (D‐F) protocols for measurement of force‐velocity and series elastic component stress‐strain curves (see text for details). In striated muscle, maximum shortening velocity (V0) is independent of muscle (sarcomere) length except at very short and long lengths (G). In smooth muscle, V0 is dependent on the level of myosin phosphorylation (MLC‐p) and not active stress (σ, H). Panels A‐F adapted from (253), with permission. Panel G adapted from (114), with permission. Panel H adapted from (375), with permission.
Figure 25. Figure 25. The mechanical contributions of the extracellular matrix components elastin and collagen can be revealed by selective digestion (A; l0 = initial unstretched muscle length). One recent model [B; nitroprusside‐relaxed artery at rest versus decellularized artery (minus VSM)] of the mechanical relationship between the three major components of an artery, VSM (diamond), elastin and collagen (labels as in panel C), derived from decellularization experiments, envisions that “passive” VSM generates considerable tone, causing compression (C) of elastin and collagen in‐parallel with VSM, and tension (T) of elastin and collagen in‐series with VSM. The “minus VSM” artery elongated by ∼12% to 20% of the nitroprusside‐relaxed (“rest”) artery. A hook‐on model used to explain the J‐shaped passive length‐tension relationship of arteries envisions longer collagen fibers in‐parallel becoming engaged at longer strain values (c.i.‐c.iv.). An alternate model envisions different in‐series collagen groups becoming stiff at different strain values (c.v.). Panels A and B adapted from, respectively (391) and (396), with permission. Panel C adapted from (491), with permission.
Figure 26. Figure 26. Arterial stiffness (estimated here as the pressure/diameter tangent at a particular diameter) is highly dependent on the level of VSM activation (A). A working model of acute adaptive plasticity of smooth muscle stress (σ)‐strain (ϵ) relationships (B) for actively contracted muscle (σa), and unstimulated muscle that includes an adjustable preload component (σap) and a purely passive component (σp). The length at which contraction is maximum (lref) and the degree of adjustable preload stress at any given strain is dependent on strain history and activation history. The degree of shift is likely greater for smooth muscle tissues that display wider physiological working length ranges (see text for details). An example of acute changes in active and passive stress values in rabbit renal artery that are dependent on activation history and strain history (C). After identification of an initial lref value by a standard stress‐strain protocol, the artery ring was released to 0.5‐fold lref and contracted twice for ∼3 min each with a maximum stimulus (black bars) and relaxed fully (“a” and “b” in c.ii.). A stretch strain‐step/strain‐clamp back to 1‐fold lref (“1a” in c.i.) produced an immediate large stiffness response reflected by the peak stress followed by considerable stress‐relaxation. After a quick release to 0.9‐fold, then 0.5‐fold lref (respectively, “1b” and “1c” in c.i.) and no contraction at 0.5‐fold lref, a subsequent stretch strain‐step/strain‐clamp (“2a” in c.i.) produced a much weaker peak stress response (0.4 × 105 N/m2) and a subsequent quick release to 0.9‐fold lref (“2b” in c.i.) produced a much weaker steady‐state adjustable preload stress (0.05 × 105 N/m2) compared to that produced by the prior release (“1b”, 0.07 × 105 N/m2). Two additional contraction‐relaxation cycles at 0.5‐fold lref (“c” and “d” in c.ii.) caused a 150% increase in the peak stress upon the subsequent third stretch strain‐step/strain‐clamp (“3a” in c.i.) compared to the second stretch (“2a” in c.i.). A subsequent release to 0.9‐fold lref (“3b” in c.i.) revealed that adjustable preload stress was also increased (by 60% to 0.08 × 105 N/m2) because of contractions “c” and “d”. Lastly, contractions at 0.5‐fold lref improved 33% over the course of four stimulations “a”‐”d”). Panel A adapted from (336), with permission, and panel B adapted from (21), with permission.


Figure 1. Diagram of vascular smooth muscle (VSM, A) and cell structural hierarchy (B‐E). VSM structure includes cells that are embedded in and mechanically attached to ECM comprised largely of elastin and collagens (Coll) I and III (A). Several models of smooth muscle cell ultrastructure have been proposed (20,274); Small's model is shown in panels B and C. An extensive cytoskeleton interconnects a filamin‐actin‐desmin filament domain (FAD) with an actomyosin (AM) domain attached to dense bodies and dense plaques (B and C). The smooth muscle sarcomere structure remains to be fully elucidated and appears to be highly dynamic. However, a general view is that the thick filaments (M) are side polar (C and D) and the thin filaments (A) and FAD attach to dense bodies (B and C). Myosin is a heterohexamer comprised of two heavy chains and two pairs of light chains (E, only a single heavy chain and single pair of light chains is shown). The light meromyosin (LMM) tail region of individual myosin heavy chains associate with other myosin heavy chain tails to form thick filaments (D). The catalytic region of the myosin S1 head extends from the α‐helical S1 neck wrapped by one essential (ELC) and one regulatory light chain (RLC), which in turn extends from the myosin S2 region, to reach actin‐binding sites. Panels A‐D adapted from, respectively (419,426,105), and (529), with permission.


Figure 2. Smooth muscle cell and arterial structures. 3D fluorescence micrograph of antibody‐labeled artery cross‐section revealing the alternating pattern of, respectively, caveolae (C, green) and dense plaques (D, red) within a single VSM cell digitally isolated from other cells and the ECM. Each square = 1 μ2 (A). Transmission electron micrograph of a VSM cell from rabbit renal artery shown in cross‐section (B) revealing extensive thin filaments and alternating caveolae (C) and dense plaques (D). Note that microtubules (arrow) reside adjacent to caveolae and mitochondria, supporting the notion that these structures, acting as cargo for microtubule motor proteins, are adjusted in space and time. Thin filaments occupy much of the cytosol [for examples of electron micrographs of smooth muscle revealing the relative abundance of thick and thin filaments, see (20,93,201)]. Diagram of a model of dense bodies (dots) and actomyosin filaments (lines) in a single contracted and relaxed smooth muscle cell in cut‐away lateral and cross‐sectional views (C). Electron micrograph of a rabbit femoral artery cut transverse to the long axis of the arterial tube revealing outer adventitia (A), middle media (M), and inner intima (I) (D). Fluorescence micrograph revealing the long, fusiform shapes of isolated single VSM cells (E). A single relaxed (upper panel) and contracted (lower panel) VSM cell attached at one end to a micropipette (upper right) (F). Note dramatic degree of shortening and formation of blebs (B) upon shortening. Panel A adapted from (374). Panel C adapted from (80) with permission. Panels D‐F adapted, with permission, from, respectively (191,113), and (110).


Figure 3. The minimum solution pO2 required to support full isometric contraction of swine carotid media stimulated with epinephrine is dependent on arterial tissue thickness such that a bathing solution bubbled with room air would suffice for tissues ≤400 μ thick (A). Arteries can be classified, according to the strength of force maintenance (tonic phase) compared to that developed during the early phasic phase of contraction, into tonic (B) and phasic (C) arteries; FA = rabbit femoral artery, SA = rabbit saphenous artery (contractile stimulus: K+‐depolarization). Compared to elastic arteries (D: abdominal aorta, AA, and E: common iliac artery, CIA), muscular arteries (D: femoral artery, FA, and E: external iliac artery, EIA) express a higher VSM/ECM ratio and therefore produce significantly stronger contractions when normalized to tissue cross‐sectional area (F). Data adapted, with permission, for panel A from (332). Solid and dashed lines in panels B‐E are, respectively, average and SE values, n = 5‐7 rabbits. * = P < 0.05 compared to AA.


Figure 4. Analog elements used to form mechanical circuits include a spring (A) and dashpot (B) that are fixed at one end and attached to other elements at their free end (filled circle). (C) To measure force, these elements (ele) are attached to a force transducer (FT) of known very high stiffness (kFT).


Figure 5. Preconditioning (B, note decline in peak force from cycle 1 to 7 and from cycle 8 to 14) of a strip of naïve rabbit bladder incubated in a Ca2+‐free solution resulting from (A) 7 sequential 1 mm ramp load‐unload cycles at 1 mm/s (1, 2, … 7), followed immediately by 7 sequential 2 mm ramp load‐unload cycles at 1 mm/s (8, 9, … 14). In this context, a naïve tissue is one mounted on a myograph that has not yet been subjected to load‐unload cycling. Clockwise force versus length work loops of data shown in panels A and B reveal a high, linear stiffness during loading for the first cycle from 0 to 1 mm (C), and during the “new” strain region (from 1 to 2 mm) of the eigth cycle (D) only. All other cycles display nonlinear length‐force curves and much smaller work loop areas. The loading curve for the first mm of cycle 8 is superimposable on the loading curve of cycle 7. Cycles 6 (not shown) and 7, and cycles 13 (not shown) and 14 are identical. Adapted, with permission, from (445).


Figure 6. A stepper motor controlled to stretch and compress a spring (A‐F) can reveal the linear stress (σ) versus strain (ϵ) (G) and constant stress/strain quotient (H, stiffness E) characteristic of a linear spring. The free and fixed ends of the spring are represented by, respectively, r and q. The nonstretched resting position of r is j0. Spring compression involves moving r toward j‐1 and beyond, and spring tensioning involves moving r toward j+1 and beyond. A nonlinear spring (G, dash‐dotted curve) would result in a nonconstant E (H, dash‐dotted curve). Drawings of sheets of different widths w (I) and a rectangular block of thickness h (J) showing direction of applied displacement producing measured uniaxial force, f (I), which can be normalized to calculate tension, T (I), and stress, σ (J).


Figure 7. Rapidly activated swine carotid media displays a linear relationship between active stiffness (dσ/dl0) and stress (σ). Adapted from (423) with permission.


Figure 8. A stepper motor controlled to stretch a dashpot (A‐D) can reveal the linear relationship between stress (σ) and strain‐rate (ϵ·) and constant σ/ϵ· quotient (viscosity η) characteristic of a linear dashpot (F). Stepper motor ramp stretches (E) at two different rates (ϵ vs. time: lower curves, fast and slow strains from j to j+1) induce two different levels of stress (σ: upper square‐wave curves, fast and slow). Honey has a higher viscosity than H2O (F). Thus, a slow ramp stretch of a honey‐filled dashpot will induce a higher level of stress than the same slow ramp stretch of a H2O‐filled dashpot (E, honey; slow compared to H2O; slow).


Figure 9. Soft tissues display stress (σ)‐relaxation (B, σ‐relaxation of rabbit renal artery, RA) over time when subjected to an imposed rapid stretch to a new tissue length [A; length (l), stretch‐ratio (λ), or strain (ϵ)‐step)] and held there for some time (l, λ, or ϵ‐clamp). Simulations of the stress responses (D, F) to a strain‐step/strain‐clamp protocol (C, E) for a spring of stiffness E = 3 (C, D) and dashpot of viscosity η = 3 (E, F). As dt approaches zero in the strain‐step rate, stress will increase toward ∞ (F).


Figure 10. Simulations of the stress (σ) responses (B, E, H) to a sinusoidal strain (ϵ)‐oscillation protocol (A, D, G) for a spring of stiffness E = 3 (A‐C), dashpot of viscosity η = 3 (D‐F) and 2 element Maxwell Model (G‐I). The stress‐strain (σ‐ϵ) relationships for a spring and dashpot reveal, respectively, no time dependency (C) and time dependency (F and I). The time dependency of the dashpot is revealed by a lag in the imposed length change compared to the stress response, and damping of the maximum stress value. In a Maxwell Model, the spring (s) element requires some strain to develop stress, so the dashpot (d) element dampens the stress response to the strain (i) proportionally to the spring compliance (see Fig. 11). How far the dashpot plunger is from its new equilibrium position determines stress‐strain work loop area and position on the y‐axis; the position was further from the new equilibrium during the first than the second loading. l = length, f = force.


Figure 11. Simulations of the stress (σ) responses (B, C, E, and F) to sinusoidal strain (ϵ)‐oscillation (A) and strain‐step/strain‐clamp (D) protocols for a two‐element Maxwell Model with spring (s) stiffness E = 3 and dashpot (d) viscosity η = 10‐fold that of Figure 10. 1, 2, … 7 identify load‐unload cycles 1, 2, … 7. In panels D‐F, segment 1 to 2 refers to the instantaneous strain‐step, and segments 2 to 3 refer to the strain‐clamp period lasting 45 s. See text for details.


Figure 12. Sequential loading‐unloading curves of dog femoral artery rings reveal clockwise force (F)‐length (L) loops and strain softening (force achieved during the tenth loop is less than that achieved during the first loop). Adapted, with permission, from (389).


Figure 13. Sequential stretch strain (ϵ)‐step/strain‐clamps applied to a viscoelastic soft tissue over time (a temporal staircase‐strain protocol) produces an instantaneous stress (σ) response due to the strain‐step and an equilibrium stress response at the end of stress‐relaxation (A, plot over time; B, stress‐strain plot). For each strain‐step, the elastic stress equals the equilibrium stress, and the viscous stress equals the difference between instantaneous and equilibrium stresses (B, C). Elastic and viscous stress‐strain plots for vena cava (VC), abdominal aorta (Ab Ao), and carotid artery (CA) reveal considerable differences for different vascular tree segments (D). Panels A‐C adapted from (406) and panel D adapted from (420), with permission.


Figure 14. The final viscoelastic stress‐strain (σ‐ϵ) cycle (8) from the simulation shown in Figure 11c oscillates around zero stress and is linear (A), unlike that of a swine carotid artery (B). Nonlinearity can be incorporated into a Maxwell Model stress‐strain relationship (C; for this simulation, constants for spring stress, σs, were a = 0.3, b = 0.3, and c = −0.5), but the function chosen should have some mechanistic basis. Panel B adapted, with permission, from (408).


Figure 15. Preconditioned soft tissues such as arteries display a passive stiffness‐stress (dσdλσ) relationship that can be modeled as a 1 (or 2) component curve consisting and a linear portion fitting the equation, dσdλ=ασ+αβ (plus a nonlinear portion at very low stress values), where σ = stress, λ = stretch ratio, and α and β are constants (459). Extrapolation of the linear portion provides a stiffness value at zero stress, E0, the product of α and β, that can be used to characterize different tissues. Compared to muscular arteries and heart (B) that display low E0 values, those for elastic arteries (A, dog aortic arch) are relatively high (356,459). The slope of the linear portion, α, is the deviation from constant stiffness. Panels A and B adapted from, respectively, (459) and (356), with permission.


Figure 16. Simulations of the stress (σ) response (B and C) to a sinusoidal strain (ϵ)‐oscillation protocol (A) for a two‐element Voigt Model and stress response (E and F) to a strain‐step/strain‐clamp followed by a quick‐release, small strain‐step protocol (D) for a three‐element Generalized Maxwell Model. A simulation that includes only the springs of a generalized Maxwell model is also shown (F, dash‐dotted line). See text for details.


Figure 17. A quick‐release small strain (ϵ)‐step protocol performed on passive (unstimulated) swine carotid artery reveals weak force redevelopment (A), adapted from (199), with permission. A three‐element generalized Voigt Model (B) and two depictions of a multielement Hill Model (C). Simulations of the stress (σ) response (E and F) to a strain (ϵ)‐step/strain‐clamp followed by a quick‐release small strain‐step protocol (D) for a three‐element Generalized Voigt Model. See text for details.


Figure 18. A generalized model of multiple stress‐strain (σ‐ϵ) behaviors for various types of materials (A). Examples of stress‐strain curves for elastic fibers, elastin, and resilin (B), viscoelastic biomaterials such as skeletal muscle treated to remove thin filaments and retain titin (C) and keratin fibers (D), and viscoelastic‐plastic materials such as Hagfish thread (E). The pressure‐volume (P‐Vol) relationship for femoral artery (F) reveals apparent viscoelastic‐plastic behavior. See text for details. Panels B, D, and E adapted from (315), panel C adapted from (165), and panel F adapted from (39), with permission.


Figure 19. A steady‐state model of the actomyosin cross‐bridge cycle showing four myosin (M) states (A) that include actin (A) plus myosin (M; 1), actin (A) + phosphorylated M (Mp; 2), a phosphorylated cross‐bridge species (AMp; 3) and a dephosphorylated cross‐bridge species, the latchbridge (AM; 4); k values represent rate constants. Rabbit femoral artery activated at time zero with a maximum KCl stimulus produces a counterclockwise [Ca2+]i‐force response revealing two phases, a rapid (∼15 s) phasic phase in which [Ca2+]i increases to its maximum level and force develops to ∼70% maximum, and a tonic phase in which force slowly (from ∼15 s to 3 min) increases further to the maximum level while [Ca2+]i declines to its steady‐state supra‐basal level (B). A comparison of the rabbit slow, tonic femoral artery (FA) and fast, phasic saphenous artery (SA) reveal that during the fast phasic phase, force (C), [Ca2+]i (D, Pk) and myosin phosphorylation (MLC‐p, E, second data point at ∼40% MLC‐p) responses are identical. With time, however, force (C) and MLC‐p (E) dissociate whereas the [Ca2+]i response does not (D, 5 and 10 min). * indicates significant difference (P < 0.05). Panel B adapted from (378) and panels C‐E adapted from (191), with permission.


Figure 20. Hai‐Murphy four‐state kinetic latchbridge model (L) simulation (dashed lines), a four‐state no latchbridge model (NL) simulation [dashed dotted lines (E‐H)] and empirical data (solid lines and symbols) for femoral artery (FA) and saphenous artery (SA). The simulated L model employs a very slow k7 = 0.005 compared to k4 = 0.05, whereas the NL model simulation excludes a latchbridge by assigning k7 = k4 = 0.05. The L model fits the data for the slow, tonic femoral artery (A, B, D), and the NL model fits the falling tonic phase contraction and falling intracellular free Ca2+ concentration and myosin phosphorylation (E, F, H) characteristic of the fast, phasic saphenous artery, suggesting that fast arteries lack latchbridges. Adapted, with permission, from (191).


Figure 21. Isolated whole rabbit femoral (A) and saphenous (B) arteries were pressurized (P) to 60 mmHg, contracted with a maximum [KCl] and allowed to constrict isobarically to measure the degree of reduction in artery lumen diameter at steady state. After recording steady‐state constriction, the arteries were fully relaxed (dilated), pressurized to the next pressure level, activated with KCl and constriction was measured at that pressure (isobaric constriction). This procedure was continued until full steady‐state pressure‐diameter curves were produced for activated femoral (A, open circles) and saphenous (B, open squares) arteries. Diameter data were normalized afterward to maximally constricted (zero) and dilated (one) values. After generation of these active pressure‐diameter curves, fully relaxed arteries were depressurizing to 60 mmHg, activated with KCl to produce full isobaric constriction at 60 mmHg (vertical down arrow), and subjected to a pressure ramp from 60 to 120 mmHg (A, femoral artery, solid circles and arrow) and 60 to 140 mmHg (B, saphenous artery, solid squares and arrow). The activated femoral artery, fully constricted at 60 mmHg, remained nearly fully constricted when subjected to the ramp pressure increase (A, solid circles). By contrast, the activated saphenous artery, also fully constricted at 60 mmHg, dilated along the isobaric constriction curve when pressurized (B, solid squares). Thus, shortened VSM of femoral artery can resist lengthening when subjected to pressures much higher than the muscle can shorten against, suggesting that latchbridges endow slow arteries with dilatation‐resistance (C). See text for additional details. Adapted, with permission, from (60).


Figure 22. Active stress (σ)‐strain (ϵ) (tension‐length, force‐length) curves (A‐F) and “passive” stress‐strain curves for skeletal muscle (E) and artery (F). Bottle brush cartoon illustrates the concept that the degree of overlap (solid bars) of actin (bottle wall) with myosin cross‐bridges (bristles) determines the strength of active stress on the descending limb (d.l.) of the active stress‐strain curve (A). Additional complexity is required to explain the shape of the ascending limb (a.l.). Examples of active stress‐strain curves for striated muscle sarcomere (B), carotid media (C), and small mesenteric artery displaying an initial active stress‐strain curve (D, day 0) and one produced after the tissue had been incubated in culture medium at 0.4‐fold lref for 16 h with the contractile agent endothelin (D, day 1). Also shown is the total stress‐strain curve for small mesenteric artery, which is the sum of the “passive” and active curves (F). See text for details. Panels B, C, D, and E adapted from, respectively (370,522,474) and (527), with permission. Panel F adapted, with permission, from (535).


Figure 23. A schematic illustrating a Maxwell Model (representing muscle) attached to a generalized apparatus designed to measure and control the degree of force and length over time (A) to assess the stress (σ)‐strain (ϵ) relationship of the series elastic component (SEC, B) and the hyperbolic relationship between force, f, or stress, σ, and velocity (v, C‐E). Asymptotes for the force‐velocity Hill equation (vertical and horizontal dashed lines) are not on the force‐velocity curve, and protocols designed to lengthen contracted muscle reveals that muscle can resist lengthening at much greater force levels than the muscle can develop isometrically (thick, curved dashed line, D). Peak power (force‐velocity product) occurs at ∼1/3 the maximum shortening velocity at zero load (V0). Assembly of additional actomyosin cross‐bridges during smooth muscle contraction may explain changes in the force‐velocity relationship known to occur over the course of a contraction (E, see text for details). wt = weight. Panels D and E adapted from, respectively (309) and (129), with permission.


Figure 24. Isotonic quick‐release (A‐C) and slack test (D‐F) protocols for measurement of force‐velocity and series elastic component stress‐strain curves (see text for details). In striated muscle, maximum shortening velocity (V0) is independent of muscle (sarcomere) length except at very short and long lengths (G). In smooth muscle, V0 is dependent on the level of myosin phosphorylation (MLC‐p) and not active stress (σ, H). Panels A‐F adapted from (253), with permission. Panel G adapted from (114), with permission. Panel H adapted from (375), with permission.


Figure 25. The mechanical contributions of the extracellular matrix components elastin and collagen can be revealed by selective digestion (A; l0 = initial unstretched muscle length). One recent model [B; nitroprusside‐relaxed artery at rest versus decellularized artery (minus VSM)] of the mechanical relationship between the three major components of an artery, VSM (diamond), elastin and collagen (labels as in panel C), derived from decellularization experiments, envisions that “passive” VSM generates considerable tone, causing compression (C) of elastin and collagen in‐parallel with VSM, and tension (T) of elastin and collagen in‐series with VSM. The “minus VSM” artery elongated by ∼12% to 20% of the nitroprusside‐relaxed (“rest”) artery. A hook‐on model used to explain the J‐shaped passive length‐tension relationship of arteries envisions longer collagen fibers in‐parallel becoming engaged at longer strain values (c.i.‐c.iv.). An alternate model envisions different in‐series collagen groups becoming stiff at different strain values (c.v.). Panels A and B adapted from, respectively (391) and (396), with permission. Panel C adapted from (491), with permission.


Figure 26. Arterial stiffness (estimated here as the pressure/diameter tangent at a particular diameter) is highly dependent on the level of VSM activation (A). A working model of acute adaptive plasticity of smooth muscle stress (σ)‐strain (ϵ) relationships (B) for actively contracted muscle (σa), and unstimulated muscle that includes an adjustable preload component (σap) and a purely passive component (σp). The length at which contraction is maximum (lref) and the degree of adjustable preload stress at any given strain is dependent on strain history and activation history. The degree of shift is likely greater for smooth muscle tissues that display wider physiological working length ranges (see text for details). An example of acute changes in active and passive stress values in rabbit renal artery that are dependent on activation history and strain history (C). After identification of an initial lref value by a standard stress‐strain protocol, the artery ring was released to 0.5‐fold lref and contracted twice for ∼3 min each with a maximum stimulus (black bars) and relaxed fully (“a” and “b” in c.ii.). A stretch strain‐step/strain‐clamp back to 1‐fold lref (“1a” in c.i.) produced an immediate large stiffness response reflected by the peak stress followed by considerable stress‐relaxation. After a quick release to 0.9‐fold, then 0.5‐fold lref (respectively, “1b” and “1c” in c.i.) and no contraction at 0.5‐fold lref, a subsequent stretch strain‐step/strain‐clamp (“2a” in c.i.) produced a much weaker peak stress response (0.4 × 105 N/m2) and a subsequent quick release to 0.9‐fold lref (“2b” in c.i.) produced a much weaker steady‐state adjustable preload stress (0.05 × 105 N/m2) compared to that produced by the prior release (“1b”, 0.07 × 105 N/m2). Two additional contraction‐relaxation cycles at 0.5‐fold lref (“c” and “d” in c.ii.) caused a 150% increase in the peak stress upon the subsequent third stretch strain‐step/strain‐clamp (“3a” in c.i.) compared to the second stretch (“2a” in c.i.). A subsequent release to 0.9‐fold lref (“3b” in c.i.) revealed that adjustable preload stress was also increased (by 60% to 0.08 × 105 N/m2) because of contractions “c” and “d”. Lastly, contractions at 0.5‐fold lref improved 33% over the course of four stimulations “a”‐”d”). Panel A adapted from (336), with permission, and panel B adapted from (21), with permission.
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Paul H. Ratz. Mechanics of Vascular Smooth Muscle. Compr Physiol 2015, 6: 111-168. doi: 10.1002/cphy.c140072