Pre-existing Tension Research Articles

The scale of two cities: the geographies of Paris and London in the 1720s

This essay considers an early eighteenth-century quarrel about the geographical dimensions of Paris and London. The dispute involved representatives of the Académie Royale des Sciences in Paris and the Royal Society in London. The three participants—Guillaume Delisle (1675–1726), Jean-Jacques Dortous de Mairan (1678–1771) and Peter Davall (?–1763)—were French, the first two resident in Paris, the third an exiled Huguenot based in London. From an initial, relatively trivial, confusion about trigonometrical calculations, this inconclusive debate ultimately embraced several wider questions about the nature of cities in classical antiquity and early eighteenth-century Europe, the changing meaning of urban life on the eve of the industrial age, the relationship between population size and urban space, and the relative economic, political and cultural vitality of Catholic absolutist France and Protestant Hanoverian England. Informed by rival claims promoted by Cartesians and Newtonians in London and Paris, the dispute also reflected a pre-existing tension within the Paris Academy about the remit of established and emerging scientific disciplines, specifically astronomy and geography. Subsequent cartographic representations of these two cities, including the Plan Turgot of Paris in the 1730s and the Rocque map of London in the 1740s, can be re-considered with reference to this now forgotten controversy.

Classifying the satellite plane membership of Centaurus A’s dwarf galaxies using orbital alignment constraints

ABSTRACT The flattened, possibly co-rotating plane of satellite galaxies around Centaurus A, if more than a fortuitous alignment, adds to the pre-existing tension between the well-studied Milky Way and M31 planes and the Lambda cold dark matter model of structure formation. It was recently reported that the Centaurus A satellite plane (CASP) may be rotationally supported, but a further understanding of the system’s kinematics is elusive in the absence of full 3D velocities. We constrain the transverse velocities of 27 satellites that would rotationally stabilize the Centaurus A plane, and classify the satellites by whether their possible orbits are consistent with the CASP. Five satellites are identified to be unlikely to participate in the plane, two of which are clearly non-members. Despite their previously reported line-of-sight velocity trend suggestive of a common co-rotating motion, 17 out of 22 potential CASP members are consistent with either orbital direction within both the full range of possible kinematics as well as when limiting orbits to those within the plane. On the other hand, disregarding the 5 off-plane satellites found to be inconsistent with CASP membership enhances the significance of the CASP’s line-of-sight velocity trend fivefold. Our results are robust with different mass estimates of the Centaurus A halo, and the adoption of either spherical or triaxial NFW potentials.

Omissions, Moral Luck, and Minding the (Epistemic) Gap

AbstractThis paper warns of two threats to moral responsibility that arise when accounting for omissions, given some plausible assumptions about how abilities are related to responsibility. The first problem threatens the legitimacy of our being responsible by expanding the preexisting tension that luck famously raises for moral responsibility. The second threat to moral responsibility challenges the legitimacy of our practices of holding responsible. Holding others responsible for their omissions requires us to bridge an epistemic gap that does not arise when holding others responsible for their actions—one that we might often fail to cross.

Importance of axial stretch on the determination of Young’s modulus of electrospun poly(ε-caprolactone) nanofibres by atomic force microscopy

With increasing interest in the use of polymeric nanofibres for biomedical applications such as composite materials and tissue scaffolding, accurate determination of their mechanical properties is essential. Fibre orientation and the stiffness of individual fibres determine the overall elastic modulus of nanofibrous materials. However, accurate measurements of the elastic properties of single fibres are challenging at the nanoscale, and distinguishing between results arising from competing models can be difficult. We report here on investigations of the Young’s modulus of single poly(ε-caprolactone) (PCL) electrospun nanofibres by measuring the deflection of fibres due to a loading force applied by an atomic force microscope (AFM). Although such testing is often performed with the tacit assumption that bending resistance alone is responsible for the fibre response, we found that consistent results could only be obtained if the overall fibre stretch is taken into account. The Young’s modulus we measured for electrospun PCL fibres with diameters ranging from 100 to 400 nm was 0.48 ± 0.03 GPa, which is similar to the modulus of bulk PCL, with no apparent dependence on diameter. Our findings highlight the importance of the assumptions used in the analysis of bending data, as discounting the effects of axial stretch and pre-existing tension typically lead to an overestimate of the Young’s modulus.

Investigation of Hydraulic Fracturing Behavior in Heterogeneous Laminated Rock Using a Micromechanics-Based Numerical Approach

Understanding hydraulic fracturing mechanisms in heterogeneous laminated rocks is important for designing and optimizing well production, as well as for predicting shale gas production. In this study, a micromechanics-based numerical approach was used to understand the physical processes and underlying mechanisms of fracking for different strata orientations, in-situ stresses, rock strengths, and injection parameters. The numerical experiments revealed a very strong influence of the pre-existing weakness planes on fracking. Geological models for rock without weakness planes and laminated rock behave very differently. Most simulated fractures in the rock without weakness planes were caused by tensile failure of the rock matrix. In an intact rock model, although a radial damage zone was generated around the injection hole, most of the small cracks were isolated, resulting in poor connectivity of the fracture network. For rock models with pre-existing weakness planes, tension and shear failure of these structural planes formed an oval-shaped network. The network was symmetrically developed around the injection well because the strength of the pre-existing weakness planes is generally lower than the rock matrix. The research shows that the angular relations between the orientation of the structural planes and the maximum horizontal stress, as well as the in-situ stress ratios, have significant effects on the morphology and extent of the networks. The strength of the pre-existing weakness planes, their spacing, and the injection rate can dramatically influence the effectiveness of hydraulic fracturing treatments.

P 168 Prevalence and characteristics of headache induced by inhalation or ingestion of a cold stimulus (HICS) in a group of adult subjects

Background Headache attributed to ingestion or inhalation of a cold stimulus (HICS) is a well-known phenomenon. Previously published data documented the prevalence in healthy subjects in childhood. Also an association between HICS and migraine is assumed. HICS is classified as a primary headache (IHS 4.5.2). Data on prevalence in adults does not exist as of now. Objectives To find out how frequently HICS occurs in healthy adults. Reevaluate the current IHS classification ( Classification Committee of the (IHS), 2013 ) regarding the reported symptoms. Reveal probable association with other types of primary headache. Methods Biographic data and HICS criteria of the IHS were collected by a structured interview via standardized questionnaire. Data evaluation was made by means of EvaSys and SPSS. The ethical committee of MLU Halle-Wittenberg gave their consent for executing this trail. Results Trail sample: Of 1213 distributed questionnaires, 618 (51%) were evaluated. Participants were women, n = 426 (68.9%) and men, n = 192 (31.3%). The mean age was 24 years (range: 17–63 years). Frequency: Prevalence of HICS n = 317, 51.3% (women n = 102, 67.8%; men n = 102, 32.2%). Pain intensity: In the case of no coincidental primary headache, the pain intensity averaged 4.58/10 (NRS-10). With preexisting tension type headache or migraine, the pain intensity averaged 6.54/10 (NRS-10). Localization: Most frequent localizations of HICS were frontal (73.6%) and temporal (72.5%). Pain quality: 52% of the participants experienced the pain quality of HICS as stabbing, more seldom as pulling (28%), dull/pressing (10%) and pulsating (4%). Attendant symptoms: The majority (46%) of the participants didn’t show any attendant symptoms, 32% described classical aura symptoms as flashes or speech disorders. Lacrimation (11%), rhinorrhea (6%), conjunctival injection (5%) were possible trigeminal autonomic symptoms, which were also found in association with HICS by Mages et al. (2016) . Conclusion HICS is a common phenomenon. Patients with coincidental primary headaches showed higher pain intensities in HICS. A part of the patients reported aura and trigeminal autonomic symptoms associated with HICS. The reported symptoms conform only partially to the criteria of the recent IHS classification (e.g. a stabbing pain character, frequently frontotemporal localized).

Cell Migration in Mechanically Resistive Environment

The mechanical environment of a cell influences its migration. It has been observed that certain cell types such as Dictyostelium and cancer cells tend to migrate by forming blebs rather than pseudopodia in mechanically resistive environment. However, very little is known about the mechanisms governing this transition between different modes of migration. In this work, we disentangle the contributions of two key mechanical factors that might trigger this switch, the environment's stiffness (the extent of local deformation of extra-cellular matrix) and its state of stress (amount of pre-existing tension or compression).A custom built device, “cell squasher”, is used to apply dynamically controlled and uniform force on cells chemotaxing under an agaorse layer. Our results show that switch to bleb mode of migration can be triggered by an increase in either the external load imposed by the device or gel stiffness. This transition is also associated with a decrease in cell speed. Increasing the load even further triggers the rounding up of the cells and dramatically slows down the retraction of blebs; migration ceased in most of the cases. These results show quantitatively that a lower threshold of load is required for switching as gel stiffness increases which implies a collaborative effect of both the physical parameters. Surprisingly, the cells also undergo a significant reduction in their volume within few minutes of the imposition of the load. We also show that cells become highly contractile under load and myosin recruitment to cortex takes place leading to some loss of polarity. The cells also migrate in less adhesive manner under load condition. The involvement of Pip3, Rac, Ras and SCAR signaling in protrusion switching is also seen. This work is of significant importance in quantitatively understanding the effect of physical changes in migration of cells.

Measurement of the elastic modulus of spider mite silk fibers using atomic force microscopy

Bio-nanomaterials are one of the fastest developing sectors of industry and technology. Spider silk, a highly attractive light-weight biomaterial, has high tensile strength and elasticity and is compatible with human tissues, allowing for many areas of application. In comparison to spider silk fibers with diameters of several micrometers, spider mite silk fibers have much smaller diameters of tens of nanometers, making conventional tensile testing methods impractical. To determine the mechanical properties of adult and larval Tetranychus urticae silk fibers, we have performed three-point bending tests with an atomic force microscope. We found that because of the small diameters of these fibers, axial tension—due to both the applied force and a pre-existing strain—has a significant effect on the fiber response, even in the small-deformation limit. As a result, the typical Euler-Bernoulli-Timoshenko theory cannot be applied. We therefore follow the approach of Heidelberg et al. to develop a mechanical model of the fiber response that accounts for bending, an initial tension in the fibers, and a tension due to elongation during testing. This model provides self-consistent results, allowing us to determine that adult and larval fibers have Young's moduli of 24±3 GPa and 15±3 GPa, respectively. Both adult and larval fibers have an estimated ultimate strength of 200–300 MPa and a toughness of order 9 MJ/m3. We note that with increasing interest in the mechanical properties of very high aspect ratio nanomaterials, the influence of pre-existing tension must be considered in any measurements involving a bending test.

Mass psychogenic illness and the social network: is it changing the pattern of outbreaks?

In October 2011, several adolescent girls at a high school in the town of Leroy, New York (pop. 7641), spontaneously developed facial tics, muscle twitching and garbled speech. By early January 2012, it was revealed that the New York State Health Department had diagnosed the students (by now, 14 women and 1 man) with conversion disorder. News of the ‘mass hysteria’ diagnosis has been vigorously challenged by parents who have formed their own advocacy group. Several victims have appeared on national television to denounce the diagnosis; celebrities have tweeted support for the students and expressed scepticism over its psychogenic origin, while some physicians have publicly suggested alternative explanations. This case has dominated headlines in the USA and continues to generate anxiety and controversy. A common folk theory attributes the symptoms to exposure from a nearby toxic dump, prompting environmental activist Erin Brockovich to challenge the diagnosis and open an independent investigation to determine the ‘real’ cause. There is increasing recognition that mass psychogenic illness (MPI) is underappreciated, under-reported and poses a significant health and social problem.1,2 The financial impact includes the cost of testing to eliminate environmental and organic causes, and the response by emergency services and public health specialists who expend precious time and resources. Schools and factories may temporarily close, resulting in lost production and income, and educational outcomes may be disrupted. When the diagnosis is challenged, students and workers may refuse to enter the premises and erode public confidence in the health system. Ongoing anxiety over the possible existence of a toxic agent may contribute to a variety of stress-related illnesses. The financial burden can be enormous. In 1999, an MPI outbreak in the Belgian school system over the suspected contamination of Coca-Cola products prompted a recall costing the company an estimated US$250 million.3 In 2007, a fainting episode among a group of anxious Australian schoolgirls who had received inoculations for the human papillomavirus, resulted in AU$1 billion being wiped from the stock market value of the corporation producing the Gardasil vaccine.4 Disputed diagnoses surrounding vaccination programmes have resulted in social protests and parents refusing to inoculate their children, placing them at unnecessary risk for preventable diseases.5 Finally, victims can get trapped in wider social arguments and conflicts, especially when the veracity of their symptoms is challenged, impeding their recovery. There are two main types of MPI. The most common in Western countries (anxiety hysteria) is triggered by extreme, sudden stress within a close-knit group. It is usually triggered by a foul or unfamiliar odour that is perceived to be harmful. Symptoms are transient, benign and typically include dizziness, headache, fainting and over-breathing. Most victims recover within 24 hours and there is an absence of pre-existing tension within the group. A second type (motor hysteria) arises from long-term anxiety and features motor agitation. Common symptoms include twitching, shaking, trouble walking, uncontrollable laughing and weeping, communication difficulties and trance states. Symptoms appear slowly over weeks or months under exposure to longstanding stress, and typically take weeks or months to subside, after the stress has been reduced or eliminated.6

A Novel Method for Measuring Tension Generated in Stress Fibers by Applying External Forces

The distribution of contractile forces generated in cytoskeletal stress fibers (SFs) contributes to cellular dynamic functions such as migration and mechanotransduction. Here we describe a novel (to our knowledge) method for measuring local tensions in SFs based on the following procedure: 1), known forces of different magnitudes are applied to an SF in the direction perpendicular to its longitudinal axis; 2), force balance equations are used to calculate the resulting tensions in the SF from changes in the SF angle; and 3), the relationship between tension and applied force thus established is extrapolated to an applied force of zero to determine the preexisting tension in the SF. In this study, we measured tensions in SFs by attaching magnetic particles to them and applying known forces with an electromagnetic needle. Fluorescence microscopy was used to capture images of SFs fluorescently labeled with myosin II antibodies, and analysis of these images allowed the tension in the SFs to be measured. The average tension measured in this study was comparable to previous reports, which indicates that this method may become a powerful tool for elucidating the mechanisms by which cytoskeletal tensions affect cellular functions.

Computational modeling of reconstructive surgery: The effects of the natural tension on skin wrinkling

A computational model is presented for the simulation of procedures of reconstructive surgery characterized by the excision of a cutaneous defect and the closure and suture of the wound edges. The skin is modeled as a plane membrane with zero flexural stiffness. The membrane undergoes large deformations and is characterized by a Fung type constitutive response in biaxial tension. Skin wrinkling, which is a typical outcome of the surgery in the form of extrusion of the wound edges and dog-ears, is considered through a modification of the elastic potential as originally proposed by Pipkin's Relaxed Energy Density theory [A.C. Pipkin, The relaxed energy density for isotropic elastic membranes, IMA J. Appl. Math. 36 (1986) 85–99; A.C. Pipkin, Relaxed energy density for large deformations of membranes, IMA J. Appl. Math. 52 (1994) 197–308]. The post-buckling analysis of a stretched annular membrane performed by Geminard et al. [Wrinkle formations in axi-symmetrically stretched membranes, Eur. Phys. J. E 15 (2004) 117–126] is used to validate the model under conditions similar to those of the surgery and to discuss the influence of a pre-existing tension in the membrane on the extension of the wrinkled regions. The model is applied to simulate different surgical procedures and investigate the effects of the natural state of the skin and the shape and size of the excisions. The results explain and validate current practice.

The dynamics of specific and diffuse support for the U.S. Supreme Court: A panel study

Prior inconsistencies in studies regarding specific and diffuse support for the U.S. Supreme Court have largely resulted from confusing two related yet distinct concepts: the level of diffuse support at a given moment, and change in the level of diffuse support over time. The results of a panel study show that specific support is related to both concepts but in different ways. Overall approval of the Supreme Court positively influences the level of diffuse support at a given moment. However, an individual's reaction to a particular Court decision is mediated by pre-existing ideological tension between the individual and the Court, and can cause a sudden change in that individual's diffuse support level. Post-stimulus diffuse support regeneration within an individual is related to support for democratic norms, awareness of the Court, and satisfaction with other governmental institutions.

Rebound-withdrawal headache (medication overuse headache)

Rebound-withdrawal headache (medication overuse headache) is a problem that affects 1% of the population or perhaps more. Work from many countries has shown this to be a worldwide problem. It appears that the rebound-withdrawal headache often occurs on the background of pre-existing migraine or tension headache and may assume the phenotype of chronic migraine or chronic tension-type headache. The key feature of this entity is that the patient initially uses a symptomatic treatment for headache with good result. Use of this medication may increase over time, but as the use increases to more than 10 to 15 days per month, headache frequency may also increase, reaching a point where metabolic processing of the medication and removal from the system triggers another headache. The patient then finds that as use of the medication increases, the frequency and intensity of the headaches also increases, and the overall headache worsens. Once this pattern is established, therapy requires removal of the medication in order for the rebounding process to be terminated. Preventative antimigraine medications will not work in the presence of the rebound phenomenon. Once the rebound-withdrawal headache is established, it is difficult to treat. After withdrawal of the medication, there is often a high relapse rate of using the medication again with redevelopment of the rebound-withdrawal headache. Even in patients who do not relapse to drug use, headache usually remains a major problem. Recognition and treatment of rebound headache are key factors in management of these patients. Perhaps more important in regard to this entity is recognizing its existence and preventing patients from entering a pattern of rebound withdrawal, which can be achieved by early attention to their use of analgesic narcotic or migraine-abortive medications. Overall, it is likely that this will continue to be an increasing worldwide problem in managing patients with headache.

Intracellular stress transmission through actin stress fiber network in adherent vascular cells.

Intracellular stress transmission through subcellular structural components has been proposed to affect activation of localized mechano-sensing sites such as focal adhesions in adherent cells. Previous studies reported that physiological extracellular forces produced heterogeneous spatial distributions of cytoplasmic strain. However, mechanical signaling pathway involved in intracellular force transmission through basal actin stress fibers (SFs), a mechano-responsive cytoskeletal structure, remains elusive. In the present study, we investigated force balance within the basal SFs of cultured smooth muscle cells and endothelial cells by (i) removing the cell membrane and cytoplasmic constituents except for materials physically attaching to the substrate (i.e., SF-focal adhesion complexities) or (ii) dislodging either mechanically or chemically the cell processes of the cells expressing fluorescent proteins-labeled actin and focal adhesions in order, to examine stress-release-induced deformation of the basal SFs. The result showed that a removal of mechanical restrictions for SFs resulted in a decrease in the length of the remaining SFs, which means SFs bear tension. In addition, a release of the preexisting tension in a single SF was transmitted to another SF physically linked to the former, but not transmitted to the other ones physically independent of the former, suggesting that the prestress is balanced in tensed SF networks. These results support a hypothesis regarding cell structural architecture that physiological extracellular forces can produce in the basal SF network a directional intracellular stress or strain distribution. Therefore, consideration of the coexistence of the directional stretching strain along the axial direction of SFs and the heterogeneous strain in the other cytoplasmic region will be essential for understanding intracellular stress transmission in the adherent cells.

Evaluation of tension in actin bundle of endothelial cells based on preexisting strain and tensile properties measurements.

Actin bundles in vascular endothelial cells (ECs) play a critical role in transmitting intracellular forces between separate focal adhesion sites. However, quantitative descriptions of tension level in single actin bundles in a physiological condition are still poorly studied. Here, we evaluated magnitude of preexisting tension in a single actin bundle of ECs on the basis of measurements of its preexisting stretching strain and tensile properties. Cultured ECs expressing fluorescently-labeled actin were treated with detergents to extract acin bundles. One end of an actin bundle was then dislodged from the substrate by using a microneedle, resulting in a shortening of the actin bundle due to a release of preexisting tension. Assuming the shortened actin bundle reached its non-stress state, preexisting stretching strain was determined to be 0.24 on average. A tensile test of the dislodged single acin bundle was conducted with a pair of cantilevers to measure the force required for stretching it up to the original length, yielding an estimate of preexisting tension in the actin bundle. The magnitude of the preexisting tension, 4 nN on average, was comparable to previously reported data of the traction force generated by adherent cells at single adhesion sites to keep cell integrity. The Young's modulus of the isolated actin bundle was estimated to be approximately 300 kPa from the tensile tests together with evaluation of average diameter of the isolated actin bundle based on transmission electron microscopy. These data will contribute to better understanding of intracellular stress transmission mechanism in ECs.

Effects of cytoskeletal prestress on cell rheological behavior

Normal tissue development requires that cells alter their mechanical behavior in different microenvironments to carry out their diverse functions. During cell spreading, migration, invasion and mitosis, cells exhibit a high degree of deformability, exhibiting almost a fluid-like behavior, whereas within quiescent differentiated tissues, cells must behave like an elastic solid to maintain their structural integrity in the face of an applied mechanical stress. A growing body of experimental evidence suggests that rheological properties of adherent cells depend on pre-existing tensional stress (“prestress”) borne by the cytoskeleton. This prestress results from the action of tensional forces borne by actin microfilaments, transmitted over intermediate filaments and resisted by both extracellular matrix adhesions and internal microtubules. Observations that the prestress influences mechanical properties of the cell are intimately related to the cellular tensegrity model. This model depicts the cytoskeleton as an interconnected network of cables that carry pre-existing tension that is balanced by compression-bearing struts and by anchoring forces of the substrate. This paper offers a brief survey of the basic concept of cellular tensegrity model, comparison of model predictions with experimental data obtained from rheological measurements on living cells, and comparison with other models that have been used in studies of rheology of cells.

Protean nature of mass sociogenic illness: from possessed nuns to chemical and biological terrorism fears.

Episodes of mass sociogenic illness are becoming increasingly recognised as a significant health and social problem that is more common than is presently reported. To provide historical continuity with contemporary episodes of mass sociogenic illness in order to gain a broader transcultural and transhistorical understanding of this complex, protean phenomenon. Literature survey to identify historical trends. Mass sociogenic illness mirrors prominent social concerns, changing in relation to context and circumstance. Prior to 1900, reports are dominated by episodes of motor symptoms typified by dissociation, histrionics and psychomotor agitation incubated in an environment of preexisting tension. Twentieth-century reports feature anxiety symptoms that are triggered by sudden exposure to an anxiety-generating agent, most commonly an innocuous odour or food poisoning rumours. From the early 1980s to the present there has been an increasing presence of chemical and biological terrorism themes, climaxing in a sudden shift since the 11 September 2001 terrorist attacks in the USA. A broad understanding of the history of mass sociogenic illness and a knowledge of episode characteristics are useful in the more rapid recognition and treatment of outbreaks.

Occupational Mass Psychogenic Illness: A Transcultural Perspective

Reports of occupational mass psychogenic illness (OMPI) in the scientific literature were examined to describe underlying presentation patterns and explain their sporadic appearance in the literature. Three distinct patterns were identified: (i) mass anxiety hysteria is precipitated by the sudden appearance of an anxiety-generating stimulus following the redefinition of an innocuous or imaginary odour or agent that is perceived as an immediate threat; (ii) mass motor hysteria is characterized by internalized conflict which fosters dissociation, histrionics and psychomotor agitation. Episodes are typified by an atmosphere of pre-existing tension and employee dissatisfaction with restrictive management practices coupled with inhibited negotiation channels; (iii) a third presentation pattern involves the relabelling of endemic symptoms and the occasional appearance of conversion reactions, which are reinforced by a hypervigilant medical community and exacerbating factors. Social factors may explain the irregular appearance of reports.

Opposing views on tensegrity as a structural framework for understanding cell mechanics.

Donald E. Ingber: Important new theories in science often ignite heated debates. If they do not, they are probably of little significance. Thus a strong argument in support of the importance of the tensegrity model of cell and tissue architecture first proposed almost 20 years ago ([23][1], [24][2

A quantitative model of cellular elasticity based on tensegrity.

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.