Calibration of beam deflection produced by cellular forces in the 10−9–10−6 gram range

An experimental procedure and method of analysis are presented for calibration of a thin-beam force transducer. The beam transducer can be produced and calibrated with a minimum coefficient of 10 ng (10⁻⁵ dyne) force per micron (10⁻⁴ cm) deflection, i.e.,k _B∼0.1 dyne/cm. Since beam deflections on the order of 0.1 μm can be detected, forces of a few nanograms can be resolved. Such forces are common in mechanical experiments on microscopic bodies, e.g., biological cells, artificial membrane capsules, droplets, etc.     

FORCE EXERTED BY THE CLEAVAGE FURROW OF SEA URCHIN EGGS

A drop of ferrofluid injected into the center of a dividing sea urchin egg is deformed into the shape of an hourglass when the cleavage furrow advances. The force applied to the drop is determined from the deformation of the drop and the interfacial tension between the ferrofluid and the protoplasm. The interfacial tension is determined from the deformation of a spherical drop in the protoplasm when a magnetic field is applied, and the force applied to the drop, which is estimated from the deformation by magnetic field of a similar drop in 2 per cent aqueous solution of Triton X-100 and the interfacial tension between the ferrofluid and this solution.
The force applied to the drop in the dividing egg increases during an early stage of cleavage and decreases during a later stage. The force attained a maximum of 9 × 10⁻³ dyne in an egg of Temnopleurus toreumaticus which pinched the drop into two when it divided. Smaller maximum forces, 3.9 × 10⁻³ dyne in the eggs of Temno-pleurus toreumaticus and 2.0 × 10⁻³ dyne in the eggs of Clypeaster japonicus (mean values), were obtained when the furrowing was arrested by the drop. The magnitude of the maximum tension developed in the contractile element located in the furrow cortex is discussed.     

TENSION AT THE HIGHLY STRETCHED SURFACE OF SEA-URCHIN EGGS*

Unfertilized eggs of the sea urchin, Paracentrotus lividus, were placed between two parallel plates and flattened by a definite force to 20% of their original diameter, with two-fold increase in their surface area. The resulting tension at their surface was calculated from the relation of force and deformation. In spite of this extensive stretching, the tension was found to be not more than 0.2 dyne/cm, while under conditions involving mild stretching (3%) the tension still amounted to 0.12 dyne/cm. These results do not support Mela's theory (7, 8), which predicts a transition of the mechanical properties of the egg surface from a ‘subelastic’ to ‘elastic’ state when the surface is stretched to beyond 34% of its initial area.     

Calibration of beam deflection produced by cellular forces in the 10(-9)--10(-6) gram range

An experimental procedure and method of analysis are presented for calibration of a thin-beam force transducer. The beam transducer can be produced and calibrated with a minimum coefficient of 10 ng (10(-5) dyne) force per micron (10(-4) cm) deflection, i.e., kB approximately 0.1 dyne/cm. Since beam deflections on the order of 0.1 micron can be detected, forces of a few nanograms can be resolved. Such forces are common in mechanical experiments on microscopic bodies, e.g., biological cells, artificial membrane capsules, droplets, etc.     

Experimental control of the site of embryonic axis formation in Xenopus laevis eggs centrifuged before first cleavage

In Xenopus laevis, the dorsal structures normally develop from regions of the egg opposite the side of sperm entry. Gravity is known to affect this topographic relationship in eggs inclined obliquely from their normal vertical orientation in the period before first cleavage. This effect has been explored in detail, making use of low-speed centrifugation (10-50 g) for short durations (4 min). Eggs were immobilized in gelatin and oriented with their animal-vegetal axes 90 degrees to the force vector, with the sperm entry point (SEP) side of the egg either toward or away from the center of the rotor. It has been found that the egg shows three distinct periods of response to centrifugal force in the interval from fertilization to first cleavage: Prior to 0.4 (40% of the first cleavage interval), the egg is very sensitive to centrifugal force and develops dorsal structures from its centrifugal side, regardless of the position of the SEP in the centrifugal field. Thus, the dorsal structures of the embryo are reversed from normal in eggs centrifuged with the SEP away from the center of the rotor. In the period 0.4 to 0.7, the egg is still very sensitive to centrifugal force and develops dorsal structures from its centripetal side, regardless of the position of the SEP in the centrifugal field. Thus, the dorsal structures of the embryo are reversed from normal in eggs centrifuged with the SEP toward the center of the rotor. In the period 0.7-1.0, the egg becomes increasingly resistant to centrifugal force and forms dorsal structures at the normal position opposite the SEP side. This resistance can be overcome in some egg clutches by 50 g centrifugation followed by prolonged 90 degrees off-axis inclination at 1g. Midway in the second cell cycle, there is a brief period of sensitivity to centrifugal force. These These results are discussed in terms of the types of cytoplasmic rearrangements occurring in the egg at different times of the cell cycle, and in terms of the process of cytoplasmic localization of determinants of dorsal axial development.     

Measurement of the motive force of the migrating slug ofDictyostelium discoideum by a centrifuge method

Summary The motive force of the migrating slug of the cellular slime mouldDictyostelium discoideum was measured by the use of centrifugal force. Changes in shape of the slugs due to the use of centrifugal force were prevented by letting them migrate in an agar capillary. The motive force thus obtained was proportional to the slug volume, the value per unit volume being 5.8×10⁶ dyne/cm³ (58 N/cm³). This is in good agreement with the value measured by the use of hydrostatic pressure.     

Mechanical properties of the surface of the sea urchin egg at fertilization and during cleavage

1. 1. Changes in stiffness of the cell surface at fertilization and during cleavage in sea urchin eggs were determined by the magnetic particle method.

2. 2. The stiffness of the cell surface increased at fertilization, reached a maximum after about 1.5 min, then decreased and reached a minimum about 4 min after insemination, followed by a gradual increase, in the eggs of Temnopleurus toreumaticus at 25.5 to 26.5 °C.

3. 3. The stiffness of the cell surface increased during the diaster stage, reached a maximum 2 to 3 min before the onset of cleavage, then decreased to a minimum about 1 min before the onset of cleavage, increased again, reached a maximum during cleavage and then diminished, in the eggs of Temnopleurus toreumaticus at 25.5 to 26.5 °C. A similar stiffness change was observed in the eggs of Hemicentrotus pulcherrimus at 17 to 19 °C, occurring almost in parallel in both the equatorial and polar surfaces.

     

MECHANICAL PROPERTIES OF SEA URCHIN EGGS III. VISCO-ELASTICITY OF THE CELL SURFACE

When a sea urchin egg was compressed between two parallel plates, the force required to keep the distance between the plates constant gradually decreased with time. The contours of the compressed egg were different from the contours expected from the assumption that the surface forces are uniform over the entire surface. The surface forces of the egg without deformation computed from the area of the cell surface in contact with the substratum, the density of the egg and its size were 0.02–0.04 dynes/cm in Hemicentrotus pulcherrimus. Larger values were obtained in eggs during compression. Surface forces, which were computed from measurements of the form of the egg and the applied force when the egg was deformed by a rod and a plate supporting the egg, increased as the deformation increased.
From these results, it was concluded that the cell surface is visco-elastic in sea urchin eggs.     

INDUCTION OF A FURROW-LIKE DENT ON THE SURFACE OF THE NEWT EGG BEFORE THE ONSET OF CLEAVAGE*

Sawai (2) found in the amphibian egg that furrow-inducing cytoplasmic component (FIC) was localized along the cleavage furrow, which could induce a furrow on the polar surface of cleaving egg under which FIC was injected. But this procedure failed on the surface of uncleaved fertilized egg. In the present experiments, an attempt was made to induce a cleavage furrow on the surface of uncleaved egg of the newt, Cynops pyrrhogaster. A piece of the cortex was cut from the uncleaved egg, which was transplanted to the egg just before or just after the onset of the cleavage, using a fine glass needle. After the transplantation FIC was injected beneath the graft with a capillary. The graft reacted to FIC and a furrow-like dent was induced at the position. Besides, stiffness of the graft increased during the cleavage of the host egg. In contrast to the cortical grafting, a large amount of the cytoplasm excluding FIC was injected under the cortex of an uncleaved egg. After several minutes FIC was deposited at the site. A furrow-like dent was formed there in many cases.     

Bipolar segregation of mitochondria,actin network,and surface in the Tubifex egg: Role of cortical polarity

The role of the cortex in ooplasmic segregation of the yolky eggs of Tubifex has been studied by epifluorescence microscopy. Living eggs labeled with rhodamine 123 and fine carbon particles placed on the surface showed that, following the second polar body formation, the egg surface cosegregates with subcortical mitochondria in a bipolar fashion, viz. toward the animal and vegetal poles in the animal and vegetal hemispheres, respectively. The egg surface of each pole moves spirally while the equatorial surface appears to remain stationary during this process. The rhodamine-phalloidin staining of whole eggs reveals that actin networks cosegregate with mitochondria. Isolated cortices which were stained with rhodamine-phalloidin demonstrated that cortical actin is organized bipolarly and that, during ooplasmic segregation, it undergoes reorganization directed toward both poles of the egg. The cortical polarity expressed as actin organization is not disrupted by centrifugal force sufficient to stratify the egg cytoplasm into five layers. The surface of a centrifuged egg moves according to the original cortical polarity. This surface movement is accompanied by the reorganization of cortical actin which appears to be identical to that in intact eggs. Other centrifugation experiments have demonstrated that the connection of the subcortical cytoplasm to the cortex is resistant to a centrifugal force of up to 650g. The nature of cortical polarity and its role in ooplasmic segregation are discussed in the light of the present results.     

The introduction and recovery in the United States ofAnaphes diana [Hym.: Mymaridae], an egg parasite ofSitona weevils [Col.: Curculionidae]

Anaphes diana (Girault) (=Patasson lameerei Debauche), a mymarid egg parasite ofSitona spp., was introduced from Europe beginning in 1976 and is now tentatively established in the United States. Techniques are described for the separation of eggs ofSitona spp. from soil, using a series of fine-mesh sieves, water, and a saturated salt solution. Data from 9 years of sampling in an alfalfa field at Newark, Del. (>19,300 host eggs extracted), showed that the mean peak density of viable overwintering eggs ofSitona hispidulus (F.) was 14.6 per 100 cm³ of 1 cm deep surface soil. At the study site,Sitona egg densities consistently increased during the fall as a result of oviposition, peaked during January and February and decreased during the spring as a result of egg hatch. Although the incidence of parasitism byA. diana remained surprisingly low (0.29%), the fact that the species was recovered during 3 years and up to 7 years after the last release, indicates that it has colonized at the Delaware release site.      

Prediction of upper extremity impact forces during falls on the outstretched hand

Among the most common causes of upper extremity fracture is a fall on the outstretched hand. Yet few data exist on the biomechanical factors which affect injury risk during this event. In this study, we measured impact forces during low-height (0–5 cm), forward falls onto the outstretched hand, and found that these are governed by an initial high-frequency peak and a subsequent, lower-frequency oscillation. This behavior was well-simulated by a two-degree-of-freedom, lumped-parameter mathematical model. Increases in body mass caused greater increases in the peak magnitude of the low-frequency component (F_max2) than the high-frequency component (F_max1). However, increases in fall height more strongly influenced F_max1, which exceeded F_max2 for all but very low fall heights. Model predictions suggest that fall heights greater than 0.6 m carry significant risk for wrist fracture, since above this height, peak forces surpass the average fracture force of the distal radius. Finally, while the shoulder experiences lower peak force than the wrist (since F_max1 is not transmitted proximally), it undergoes considerably greater deflection, and thereby absorbs the majority of impact energy during a fall.     

Studies of excitable membrane formed on the surface of protoplasmic drops isolated from Nitella II. Tension at the surface of protoplasmic drops

A protoplasmic drop isolated from an internodal cell of Nitella became electrically excitable in a solution containing 0.5 mM NaCl, 0.5 mM KNO₃, 1mM Ca(NO₃)₂ and 2mM Mg(NO₃)₂. A thermodynamic property of the excitable membrane was characterized in terms of tension at the surface of the protoplasmic drop. This was determined by the compression method and/or by the sessile-drop method. The surface tension of the membrane was obtained as a function of the composition of the salts in the external solution, and the time during the formative period of the excitable surface membrane. The results are summarized as follows:

1. 1. The surface of the protoplasmic drop increased with time starting from 0.003 dyne/cm and approached a steady value of about 0.1 dyne/cm within 1 h after the drop was placed in the test solution described above. The membrane became electrically excitable when the surface tension attained the steady value.

2. 2. Increase of concentration of either Na⁺ or K⁺ in the solution induced a sudden decrease of the surface tension, which followed a suppression of the excitability. The critical concentration of Na⁺ or K⁺ was about 10 mM.

3. 3. The surface tension remained constant at about 0.1 dyne/cm in a Ca²⁺ concentration ranging between about 0.1 and 10 mM. At this concentration the drop was excitable. Below and above this range of Ca²⁺ concentration, the surface tension changed sharply with concentration, and the excitability disappeared. At about 0.1 mM Ca²⁺ concentration a discrete variation of the surface tension was observed.

4. 4. The surface tension of the drop stayed constant at 0.1 dyne/cm in the range between 1 and 10 mM of Mg²⁺ concentration. Above and below this range of Mg²⁺ concentration, the surface tension increased sharply with the variation of Mg²⁺ concentration.

These results indicate that the protoplasmic drop retains its excitability in a limited range of salt composition in the external solution. This implies that the excitable membrane of the drop must be very labile in its structure against external perturbations such as electrical stimulus and/or slight variation of salt composition in the solution.     

Orientation of the photosynthetic flagellate,Peridinium gatunense,in hypergravity

The photosynthetic freshwater flagellate,Peridinium gatunense, uses both positive phototaxis and negative gravitaxis to move upwards in the water column. At higher fluence rates approaching those at the surface of their habitat, the cells tend to become unoriented and thus stop their upward movement. Orientation and motility ofPeridinium gatunense has been studied in the slow rotating centrifuge microscope (NIZEMI), which allows observation of swimming behavior during centrifugation acceleration between 1g and 5g. The movement vectors were analyzed by real time image analysis capable of tracking many cells simultaneously. At 1g the orientation was not very precise, but the degree of orientation increased significantly at higher acceleration forces up to about 3g. Most cells were capable of swimming even against an acceleration vector of 3.8g; at higher acceleration forces the cells were not able to cope with the centrifugal force. The linear velocity of cells swimming against 1g was about 20% lower than that of cells moving in other directions. The velocity decreased even more in cells swimming against higher acceleration forces.     

Analysis of force vector field during centrifugation for optimizing cell sheet adhesion

A three-dimensional tissue was fabricated by layering cell sheets with centrifugation. In this system, an optimal centrifugal force promoted the adhesion between (a) a cell sheet and a culture dish, and (b) layered cell sheets, resulting in a significant decrease in the fabrication time of the tissue. However, negative effects like sliding/significant deformation of cell sheets were observed upon high rotational speed use. These negative effects inhibit the further shortening of the fabrication time. The sliding/deformation suggests that the centrifugal forces were applied on the cell sheets in unwanted directions. Studies on the force vector field applied to the object placed on the plate during centrifugation are not available, and thus, the reason for the occurrence of such negative effects is unclear. Here, we theoretically derived the spatial distribution of acceleration applied on a plate during centrifugation. Using this theory, we found that the negative effects were triggered by the centrifugal force in the direction parallel to the plate surface, which appeared due to an inclination of the plate surface against a horizontal plane. Therefore, by adding weights on the plate edge to maintain the plate surface in a horizontal position, we succeeded in eliminating the negative effects and in increasing the rotational speed, with the minimum risk of sliding/deformation of cell sheets. We succeeded in reducing the time to establish tight adhesion between a mouse myoblast sheet and a culture dish, and layered cell sheets by increasing the centrifugal force from 5 min to 1 min without significant cytotoxicity.     

An expression for the rate of return of an egg after artificial deformation

The forces which may be involved in the restoration of a deformed cell to its normal shape are considered. Estimates of the order of magnitude of the forces suggest that the most important forces are those due to surface tension, membrane elasticity and viscosity. An approximate expression is then derived for the rate of return of an elongated or compressed egg. The former expression is compared with data on eggs ofArbacia by E. N. Harvey and H. Shapiro, and it is found to agree sufficiently well with the data. The initial surface force is too low compared with that given by K. S. Cole but various factors are discussed which could contribute to this discrepancy. The value for the net viscosity of the egg is about twice the value arrived at by L. V. Heilbrunn for the egg protoplasm.     

Fluid flow through a high cell density fluidized‐bed during centrifugal bioreactor culture

An increasing demand for products such as tissues, proteins, and antibodies from mammalian cell suspension cultures is driving interest in increasing production through high‐cell density bioreactors. The centrifugal bioreactor (CCBR) retains cells by balancing settling forces with surface drag forces due to medium throughput and is capable of maintaining cell densities above 10⁸ cells/mL. This article builds on a previous study where the fluid mechanics of an empty CCBR were investigated showing fluid flow is nonuniform and dominated by Coriolis forces, raising concerns about nutrient and cell distribution. In this article, we demonstrate that the previously reported Coriolis forces are still present in the CCBR, but masked by the presence of cells. Experimental dye injection observations during culture of 15 μm hybridoma cells show a continual uniform darkening of the cell bed, indicating the region of the reactor containing cells is well mixed. Simulation results also indicate the cell bed is well mixed during culture of mammalian cells ranging in size from 10 to 20 μm. However, simulations also allow for a slight concentration gradient to be identified and attributed to Coriolis forces. Experimental results show cell density increases from 0.16 to 0.26 when centrifugal force is doubled by increasing RPM from 650 to 920 at a constant inlet velocity of 6.5 cm/s; an effect also observed in the simulation. Results presented in this article indicate cells maintained in the CCBR behave as a high‐density fluidized bed of cells providing a homogeneous environment to ensure optimal growth conditions. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Electrical Characteristics of Triturus Egg Cells during Cleavage

The membrane potential in the blastomeres of dividing Triturus egg cells increases progressively from the first cleavage to the late morula stages. Both the animal and vegetal poles show the same increasing trend in potential; there is no significant potential difference between them. Upon first cell cleavage, the total resistance of the egg cell surface in contact with the exterior decreases to about one-tenth of its value before cleavage, and then remains rather constant up to the late morula stage. The specific resistance of this membrane surface drops rather abruptly upon first cleavage, and rises progressively during the morula stage. The resistance of the junctional membrane surface of the blastomeres, that is, the membrane formed at the former planes of cleavage, is small in relation to that of the cell surface in contact with the exterior. As a result, the blastomeres are electrically coupled throughout all stages of embryonic development examined.     

Kinetics of leaping primates: Influence of substrate orientation and compliance

Our current knowledge about the forces leapers generate and absorb is very limited and based exclusively on rigid force platform measurements. In their natural environments, however, leapers take off and land on branches and tree trunks, and these may be compliant. We evaluated the influence of substrate properties on leaping kinetics in prosimian leapers by using a combined field and laboratory approach. Tree sway and the timing of takeoffs relative to the movements of trees were documented for animals under natural conditions in Madagascar. Field data collected on three species (Indriindri, Propithecus diadema, Propithecus verreauxi) indicate that in the majority of takeoffs, the substrate sways and the animals takeoff before the elastic rebound of the substrate. This implies that force is “wasted” to deform supports. Takeoff and landing forces were measured in an experimental setting with a compliant force pole at the Duke University Primate Center. Forces were recorded for 2 Propithecus verreauxi and 3 Hapalemur griseus. Peak takeoff forces were 9.6 (P. verreauxi) and 10.3 (H. griseus) times body weight, whereas peak landing forces were 6.7 (P. verreauxi) and 8.4 (H. griseus) times body weight. As part of the impulse generated does not translate into leaping distance but is used to deform the pole, greater effort is required to reach a given target substrate, and, consequently, takeoff forces are high. The landing forces, on the other hand, are damped by the pole/substrate yield that increases the time available for deceleration. Our results contrast with previous studies of leaping forces recorded with rigid platform measuring systems that usually report higher landing than takeoff forces. We conclude that 1) Leapers generate and are exposed to exceptionally high locomotory forces. The takeoff forces are higher than the landing forces when using compliant supports, indicating that the takeoff rather than the landing may be critical in interpreting leaping behavior and related aspects of muscu-loskeletal design. 2) Large-bodied vertical clingers and leapers do not usually take advantage of the elastic energy stored in substrates. Rather, force (and energy) is wasted to deform compliant supports. 3) A compliant force pole approximates the conditions faced by large-bodied vertical clingers and leapers in the wild more closely than do rigid force platforms. © 1995 Wiley-Liss, Inc.     

PREFURROW BEHAVIOR OF THE EQUATORIAL SURFACE IN ARBACIA LIXULA EGGS*

Study of equatorial surface activity occurring immediately before furrowing in Arbacia lixula (=pustulosa) eggs was undertaken to learn more about the establishment of the cleavage mechanism. Behavior of echinochrome granules in the egg surface, observed and recorded with a Nikon AFM camera, was used as the indicator of surface events. An hour after fertilization A. lixula eggs were slightly flattened and periodically photographed until the furrow appeared. By measuring regional changes in the concentration of echinochrome granules, we found that a band of equatorial surface approximately 22 μm wide, which comprises about 32% of the uncleaved egg surface, shrinks about 34% and forms a densely pigmented band averaging 15 μm wide. This contraction in the equatorial zone is accompanied by expansion or stretching in the subequatorial surfaces. The possible relation between these events and formation of the microfilamentous contractile ring is discussed.