Postoperative Complications of Minimally Invasive Intramedullary Nail Fixation Versus Plate Fixation for Distal Fibular Fractures in Elderly Patients: A Retrospective Double Cohort Study in a Geriatric Trauma Unit in the Netherlands

Intramedullary fixation using a fibular nail is a minimally invasive alternative to conventional plate fixation that provides superior biomechanical strength and allows immediate full weightbearing postoperatively. The study aim was to compare the postoperative complications of minimally invasive intramedullary fibular nail fixation to plate fixation for Lauge-Hansen supination external rotation type 4 (Weber B) fractures in patients aged 65 years or older treated in a single geriatric trauma unit in the Netherlands. A retrospective cohort study was performed including patients aged 65 years or older with a Lauge-Hansen supination external rotation type 4 (Weber B) fracture treated with either intramedullary fibular fixation or plate fixation between January 2017 and January 2019. A total number of 58 patients were included with a mean age of 73.9 years (range 65-95). The intramedullary fixation-cohort (n = 13) had a significantly higher mean age (82.5 vs 71.4 years, p = .002) and Charlson Co-morbidity Index (4.7 vs 3.6, p = .005) compared to the plate fixation-cohort (n = 45). The total number of postoperative complications was lower after intramedullary fixation (n = 2, 15%) compared to plate fixation (n = 15, 33%), although this relative difference was not significant (p = .307). All 2 complications observed after intramedullary fixation were wound infections demanding no debridement or implant removal. No implant related complications, hospital-acquired complications or mortality were observed after intramedullary fixation. Despite the higher mean age and co-morbidity status of patients treated with minimally invasive intramedullary fibular nailing, the total number of postoperative complications was lower after intramedullary fixation compared to plate fixation. This technique might be a promising alternative in selected patients.

Impact of Comorbidities on the Cause of Death by Necrotizing Soft Tissue Infections

Background: The aim of this study was to identify the cause of death in patients with necrotizing soft tissue infections (NSTIs) stratified by patient's pre-existing comorbidities (American Society of Anesthesiologists [ASA] classification 3/4 vs. ASA 1/2). Differences in clinical presentation, mortality rate, and factors associated with mortality between those two comorbidity groups were investigated. Patients and Methods: A retrospective multicenter study of patients with NSTIs between 2010 and 2020 was conducted. The primary outcome was the cause of death within the first 30 days. Furthermore, factors associated with mortality were identified. All analysis were stratified by severity of comorbidities (ASA 1/2 or ASA 3/4). Results: Of the 187 patients, 39 patients (21%) died within 30 days. American Society of Anesthesiologists 1/2 patients (overall mortality rate, 11%) died more often as direct result of the infection compared with ASA 3/4 patients (overall mortality rate, 33%) (ASA 1/2 group: 92% vs. ASA 3/4 group: 48%; p = 0.013). American Society of Anesthesiologists 3/4 patients died more often due to withdrawal of life-sustaining therapies based on assumed poor outcome after severe critical illness (ASA 1/2 group: 52% vs. ASA 3/4 group: 8%; p = 0.013). Conclusions: Mortality rates of patients with NSTIs varied from 11% in previously healthy patients to 33% in patients with multiple or severe comorbidities. The predominant cause of mortality was overwhelming infection and associated sepsis in healthy patients whereas in patients with multiple or severe pre-existing medical disease, death most often occurred after treatment limitations based on patient's wishes and prognosis.

The impact of operative time on the outcomes of necrotizing soft tissue infections: a multicenter cohort study

Background

The primary aim of this study was to identify if there is an association between the operative time of the initial debridement for necrotizing soft tissue infections (NSTIs) and the mortality corrected for disease severity.

Methods

A retrospective multicenter study was conducted of all patients with NSTIs undergoing surgical debridement. The primary outcome was the 30-day mortality. The secondary outcomes were days until death, length of intensive care unit (ICU) stay, length of hospital stay, number of surgeries within first 30 days, amputations and days until definitive wound closure.

Results

A total of 160 patients underwent surgery for NSTIs and were eligible for inclusion. Twenty-two patients (14%) died within 30 days and 21 patients (13%) underwent an amputation. The median operative time of the initial debridement was 59 min (IQR 35–90). In a multivariable analyses, corrected for sepsis just prior to the initial surgery, estimated total body surface (TBSA) area affected and the American Society for Anesthesiologists (ASA) classification, a prolonged operative time (per 20 min) was associated with a prolonged ICU (β 1.43, 95% CI 0.46–2.40; p = 0.004) and hospital stay (β 3.25, 95% CI 0.23–6.27; p = 0.035), but not with 30-day mortality. Operative times were significantly prolonged in case of NSTIs of the trunk (p = 0.044), in case of greater estimated TBSA affected (p = 0.006) or if frozen sections and/or Gram stains were assessed intra-operatively (p < 0.001).

Conclusions

Prolonged initial surgery did not result in a higher mortality rate, possible because of a short duration of surgery in most studied patients. However, a prolonged operative time was associated with a prolonged ICU and hospital stay, regardless of the estimated TBSA affected, presence of sepsis prior to surgery and the ASA classification. As such, keeping operative times as limited as possible might be beneficial for NSTI patients.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12893-021-01456-0.

Incidence and mortality of necrotizing fasciitis in The Netherlands: the impact of group A Streptococcus

BACKGROUND

Little is known about the exact incidence of necrotizing soft tissue infections. The few incidences reported in international literature are not directly relatable to the Netherlands, or other European countries, due to geographic heterogeneity in causative micro-organisms involved. This resulted in the aim of this study to map the incidence, mortality rate and hospital course of necrotizing fasciitis infections in the Netherlands to gain insight in the incidence of necrotizing fasciitis in the Netherlands and the associated mortality and health care burden.

METHODS

This nationwide retrospective database study used three distinct data sources to map the incidence of necrotizing fasciitis in the Netherlands between 2014 and 2019, being data from the Dutch Hospital Data (DHD) foundation, data from Osiris-AIZ, which is a database of notifiable diseases managed by regional Public Health Services (GGD) and the National Institute for Public Health and the Environment (RIVM), and previously published studies on necrotizing fasciitis conducted in the Netherlands.

RESULTS

The incidence of necrotizing fasciitis in the Netherlands is estimated to be approximately 1.1 to 1.4 cases per 100,000 person years, which corresponds to 193-238 patients per year. Of all necrotizing fasciitis infections, 34 to 42% are caused by the group A Streptococcus. Annually, 56 patients die as a result of a necrotizing fasciitis infection (mortality of 23-29%) and 26 patients undergo an amputation for source control (11-14%). Patients stay a mean of 6 to 7 days at the intensive care unit and have a mean hospital length of stay of 24 to 30 days.

CONCLUSION

The combination of nationwide databases provides reliable insight in the epidemiology of low-incidence and heterogenic diseases. In the Netherlands, necrotizing fasciitis is a rare disease with group A Streptococcus being the most common causative micro-organism of necrotizing fasciitis. The prior Dutch cohort studies on necrotizing fasciitis report slightly higher sample mortality rates, compared to the population mortality. However, necrotizing fasciitis remain associated with substantial morbidity and mortality, risk at amputation and health care burden characterized by prolonged ICU and hospital stay.

Delayed Extension Block Pinning in 27 Patients With Mallet Fracture

Background: Untreated bony mallet fingers can cause an array of problems; therefore, adequate treatment is essential. The primary aim of this study was to determine the patient-reported functional outcome of delayed surgical intervention of bony mallet fingers. The secondary aim was to determine the complication rate of delayed surgical intervention. Methods: In this single-center retrospective cohort study, all consecutive patients treated between 2010 and 2016 at our level 2 regional teaching hospital were included. Inclusion criterion was a bony mallet finger injury (excluding the thumb), presenting >21 days after injury, treated with extension block pinning. Indications for surgery were >2 mm fragment displacement or volar subluxation of the distal interphalangeal joint. Six to 82 months postoperatively, patients completed the Patient-Rated Wrist and Hand Evaluation (PRWHE) by phone. Complications were extracted by chart review. Results: Twenty-seven patients were included, and all completed the PRWHE. Median time to surgery was 35 days (interquartile range [IQR] = 29-42; range = 22-61). Reasons for delay in surgical treatment were patient/physician delay in 24 cases and failed conservative treatment in 3 cases. The median PRWHE score was 0 (IQR = 0-5; range = 0-22.5). After retrospective assessment of the outpatient charts, no early symptoms of malunion or nonunion were found. One patient had a loss of Kirschner-wire fixation, which was corrected. Three patients had an infection that required antibiotic treatment. Conclusions: Delayed surgical management of bony mallet fingers demonstrated adequate functional outcome with minimal complications when compared with prior literature.

Retrograde intramedullary nailing for humeral midshaft fractures : a retrospective cohort study

This study evaluates the patient-reported functional outcome, clinical functional outcome and frequency of complications of simple oblique and transverse humeral midshaft fractures treated with a retrograde expert humeral nail. A retrospective cohort study of humeral midshaft fractures (AO 12-A2, 12-A3) treated with retrograde nailing between January 2010 and February 2018 in a level II trauma center was performed. Patients' perception of functional outcome was measured using the Disabilities of the Arm, Shoulder and Hand (DASH) scores. Thirteen patients with a median age of 20-years were treated with a retrograde nail. The median DASH score, administered 29 months (IQR 74) after surgery, was 7.9 (IQR 15.9). There were no perioperative frac- tures and the frequency of complications was 8%, being one nonunion. Retrograde nailing for humeral midshaft fractures is a safe technique, with excellent patient reported and clinical functional outcome. No iatrogenic peri- operative fractures occurred and the frequency of complications was low. We recommend the retrograde technique, if surgical fixation of humeral midshaft fractures is needed, especially in younger patients for who rotator cuff associated injuries will have a major impact on quality of life.

Finding the match between healthcare worker and expert for optimal audit and feedback on antimicrobial resistance prevention measures

Background

The potentials of audit and feedback (AF) to improve healthcare are currently not exploited. To unlock the potentials of AF, this study focused on the process of making sense of audit data and translating data into actionable feedback by studying a specific AF-case: limiting antimicrobial resistance (AMR). This was done via audit and feedback of AMR prevention measures (APM) that are executed by healthcare workers (HCW) in their day-to-day contact with patients. This study’s aim was to counterbalance the current predominantly top-down, expert-driven audit and feedback approach for APM, with needs and expectations of HCW.

Methods

Qualitative semi-structured interviews were held with sixteen HCW (i.e. physicians, residents and nurses) from high-risk AMR departments at a regional hospital in The Netherlands. Deductive coding was succeeded by open and axial coding to establish main codes, subcodes and variations within codes.

Results

HCW demand insights from audits into all facets of APM in their working routines (i.e. diagnostics, treatment and infection control), preferably in the form of simple and actionable feedback that invites interdisciplinary discussions, so that substantiated actions for improvement can be implemented. AF should not be seen as an isolated ad-hoc intervention, but as a recurrent, long-term, and organic improvement strategy that balances the primary aims of HCW (i.e. improving quality and safety of care for individual patients and HCW) and AMR-experts (i.e. reducing the burden of AMR).

Conclusions

To unlock the learning and improvement potentials of audit and feedback, HCW’ and AMR-experts’ perspectives should be balanced throughout the whole AF-loop (incl. data collection, analysis, visualization, feedback and planning, implementing and monitoring actions). APM-AF should be flexible, so that both audit (incl. collecting and combining the right data in an efficient and transparent manner) and feedback (incl. persuasive and actionable feedback) can be tailored to the needs of various target groups. To balance HCW’ and AMR-experts’ perspectives a participatory holistic AF development approach is advocated.

Surgical treatment of acute and chronic AC joint dislocations: Five-year experience with conventional and modified LARS fixation by a single surgeon

BACKGROUND

Different surgical fixation methods are available for the treatment of acromioclavicular (AC) joint dislocations. The aim of this study was to present the results of five years of experience with the Ligament Augmentation and Reconstruction System (LARS) fixation technique by a single surgeon.

METHODS

A single-center retrospective cohort study was performed. All patients treated for an AC joint dislocation with LARS fixation by the same surgeon between 2012 and 2016 (n = 20) were eligible for inclusion. All these dislocations were unstable injuries, Rockwood type-III or higher, requiring acute or chronic repair. The primary outcome was the QuickDASH score. Secondary outcomes were the Subjective Shoulder Value (SSV), Numerical Rating Scale (NRS) pain score, return to work, complications, and implant removal.

RESULTS

17 patients (85%) were available for final follow-up. The median follow-up was 23 months (IQR; 17─34). The median QuickDASH score was 7 (IQR; 2-18), the median SSV was 90 (IQR; 80-90), and the median NRS pain score was 2 (IQR; 1-3). Patients returned to work after a median of 8 weeks (IQR; 6-12). There was no significant difference in functional outcome scores between acute and chronic repair, or between the conventional and modified LARS fixation groups. There were two major complications requiring revision surgery, one ruptured LARS ligament and one case of deep wound infection. Implant removal was performed in one patient.

CONCLUSIONS

The LARS ligament fixation technique seems to be effective for the treatment of AC joint dislocations, resulting in good short- and mid-term patient-reported functional outcome. LARS fixation might also be an acceptable treatment option for active patients with symptomatic chronic AC dislocations.

LEVEL OF EVIDENCE

Level III, Retrospective Comparative Study, Treatment Study.

Nonunion of the Capitate due to Delayed Diagnosis of an Isolated Fracture: A Case Report

CASE

A 14-year-old girl was diagnosed with nonunion of an isolated capitate fracture 5 months after she first presented to the emergency department. The fracture of the capitate was treated by cancellous proximal bone graft and screw fixation. This current case provides details of the surgical fixation method and long-term functional outcome after nonunion of an isolated capitate fracture after a follow-up of 18 months following fixation.

CONCLUSIONS

Persisting localized tenderness over the capitate should be an indication to perform an additional computed tomography or magnetic resonance imaging scan. Nonunion of isolated capitate fractures can be treated by means of open reduction and internal fixation, with autologous bone grafting.

Cross-border comparison of antimicrobial resistance (AMR) and AMR prevention measures: the healthcare workers' perspective

Background

Cross-border healthcare may promote the spread of multidrug-resistant microorganisms (MDRO) and is challenging due to heterogeneous antimicrobial resistance (AMR) prevention measures (APM). The aim of this article is to compare healthcare workers (HCW) from Germany (DE) and The Netherlands (NL) on how they perceive and experience AMR and APM, which is important for safe patient exchange and effective cross-border APM cooperation.

Methods

A survey was conducted amongst HCW (n = 574) in hospitals in DE (n = 305) and NL (n = 269), using an online self-administered survey between June 2017 and July 2018. Mann-Whitney U tests were used to analyse differences between answers of German and Dutch physicians (n = 177) and German and Dutch nurses (n = 397) on 5-point Likert Items and Scales.

Results

Similarities between DE and NL were a high awareness about the AMR problem and the perception that the possibility to cope with AMR is limited (30% respondents perceive their contribution to limit AMR as insufficient). Especially Dutch nurses scored significantly lower than German nurses on their contribution to limit AMR (means 2.6 vs. 3.1, p ≤ 0.001). German HCW were more optimistic about their potential role in coping with AMR (p ≤ 0.001), and scored higher on feeling sufficiently equipped to perform APM (p ≤ 0.003), although the mean scores did not differ much between German and Dutch respondents.

Conclusions

Although both German and Dutch HCW are aware of the AMR problem, they should be more empowered to contribute to limiting AMR through APM (i.e. screening diagnostics, infection diagnosis, treatment and infection control) in their daily working routines. The observed differences reflect differences in local, national and cross-border structures, and differences in needs of HCW, that need to be considered for safe patient exchange and effective cross-border APM.

Excellent functional recovery after Kirschner-wire extension blocking technique for displaced closed bony mallet finger injuries; results of 36 cases

Bony mallet finger injuries comprise 30% of all mallet injuries. Operative treatment of bony mallet fingers injuries still remains controversial. The aim of this study was to describe the k-wire extension blocking technique and the functional results using the PRWHE questionnaire. A single center retrospective observational cohort of 36 patients was defined between January 2010 and December 2015. Inclusion criteria for this study were acute fractures with 1) persistent displacement of more than 3 mm in extension splint, 2) palmar subluxation of the distal phalanx or 3) fracture fragments consisting of more than one third of the joint surface. According to the PRWHE questionnaire, excellent results were observed with a mean follow up period of 32 months of all patients. Two patients developed a clinically relevant superficial wound infection and one patient developed a nail deformity. In conclusion, the k-wire extension blocking technique is safe and results in excellent mid-term functional outcome.

Intramedullary screw fixation for simple displaced olecranon fractures

Purpose

Olecranon fractures are common and typically require surgical fixation due to displacement generated by the pull of the triceps muscle. The most common techniques for repairing olecranon fractures are tension-band wiring or plate fixation, but these methods are associated with high rates of implant-related soft-tissue irritation. Another treatment option is fixation with an intramedullary screw, but less is known about surgical results using this strategy. Thus, the purpose of this study was to report the clinical and functional outcomes of olecranon fractures treated with an intramedullary cannulated screw.

Methods

We identified 15 patients (average age at index procedure 44 years, range 16–83) with a Mayo type I or IIA olecranon fracture who were treated with an intramedullary cannulated screw at a single level 2 trauma center between 2012 and 2017. The medical record was reviewed to assess radiographic union, postoperative range of motion and complications (including hardware removal). Patient-reported outcome was evaluated using the Disabilities of the Arm, Shoulder and Hand (DASH) score. Average follow-up was 22 months (range 8–36 months).

Results

By the 6th month post-operative visit, 14 patients had complete union of their fracture and 1 patient had an asymptomatic non-union that did not require further intervention. Average flexion was 145° (range 135–160) and the average extension lag was 11° (range 0–30). Implants were removed in 5 patients due to soft-tissue irritation. Average DASH score (± standard deviation) by final follow-up was 16 ± 10.

Conclusions

Fixation of simple olecranon fractures with an intramedullary screw is a safe and easy fixation method in young patients, leading to good functional and radiological results. Compared to available data, less hardware removal is necessary than with tension-band wiring or plate fixation.

Antegrade intramedullary Kirschner-wire fixation of displaced metacarpal shaft fractures

PURPOSE

The objective of this study was to analyze complications and patient-related functional outcome after antegrade intramedullary Kirschner-wire fixation of metacarpal shaft fractures.

METHODS

All consecutive patients treated from January 2010 until December 2015 were retrospectively analyzed using patient logs and radiographic images. Indications for operative fixation were angulation > 40°, shortening > 2 mm, or rotational deficit. Complications were registered from the patient logs. Functional outcome was assessed with the Patient-rated wrist/hand evaluation (PRWHE) and Disabilities of the Arm, Shoulder, and Hand score (DASH) questionnaire both ranging from 1 to 100 after a minimum follow-up of 6 months.

RESULTS

During the study period, 34 fractures of 27 patients could be included. Mean outpatient follow-up was 11 weeks (range 4-24 weeks). The mean interval for functional assessment was 30 months (range 8-62 months) and 19 patients (70%) responded to the questionnaires. During outpatient follow-up, all fractures proceeded to union with no signs of secondary fracture dislocation or implant migration. One re-fracture after a new adequate trauma was seen and one patient underwent tenolysis due to persistent pain and impaired function. In 26 cases (81%), the K-wires were removed of which 23 (68%) were planned removals. Functional outcome was excellent with mean PRWHE and DASH scores of 7 and 5 points, respectively.

CONCLUSIONS

If surgical treatment for metacarpal shaft fractures is considered, we recommend antegrade intramedullary K-wire fixation. This technique results in low complication rates and excellent functional outcome.

[Complete triceps tendon rupture; a rare tendon injury]

Only 1% of all tendon injuries affect the triceps tendon, making triceps ruptures very rare. An acute rupture can therefore easily be missed due to a low degree of suspicion. A palpable gap, inability to flex the elbow against resistance and a positive modified Thompson test are indicative for a complete triceps tendon rupture. The mechanism of injury is most commonly a sudden eccentric muscle contraction. We present the case of a 48-year-old man with an acute complete triceps tendon rupture, after a fall from an unstable chair while performing a one arm push-up. The rupture was surgically treated with Krackow sutures tunneled through drill holes in the olecranon. Postoperative treatment consisted of gradually increasing elbow flexion for six weeks with a brace. Three months following the operation, 150 degree flexion was possible with a 5 degree extension limitation. The Disabilities of the Arm, Shoulder and Hand score was 10.5. We demonstrate that early diagnosis and treatment facilitate excellent functional outcome.

THERMOREVERSIBLE CROSS-LINKING OF RUBBER COMPOUNDS: FROM PROOF-OF-CONCEPT TOWARD AN INDUSTRIAL PROCESS

It is demonstrated that the concept of thermoreversible cross-linking of functionalized maleic anhydride grafted ethylene–propylene (EPM-g-MA) rubber using Diels–Alder chemistry is limited neither to laboratory scale using a solvent route nor to gum rubber. The use of an internal mixer is the first step toward an industrial process, since it greatly reduces the processing time and allows for a solventless process for the furan-functionalization and subsequent bismaleimide cross-linking of EPM rubber. Practical rubber compounds were prepared by mixing thermoreversibly cross-linked EPM with carbon black and mineral oil in the same batch mixer. This resulted in reinforcement of the rubber without affecting the thermoreversible character of the cross-linking. The pendant furan groups of the (non)cross-linked EPM-g-furan interact with the carbon black filler. Finally, crystalline EPM rubber compounds were prepared, which show excellent material properties and property retention over multiple reprocessing cycles.

Paediatric forearm fracture with a twist: a proximal radioulnar translocation combined with radial head fracture

A 10-year-old girl presented to the emergency department with proximal radioulnar translocation and radial head fracture, after fall onto an outstretched hand. Open reduction was used to reduce and stabilise the elbow joint after which the radial head was fixated by Kirschner wires. Three months after surgery, full range of motion was regained and union of the radial head was achieved. Proximal radioulnar translocation is a rare injury which is often missed on initial radiographs. Persistent restriction of forearm rotation with seemingly normal elbow configuration must trigger to take a closer look at the relationship between the ulna, radius and distal humerus. We show that early diagnosis and treatment of a proximal radioulnar translocation associated with a radial head fracture results in an excellent functional outcome.

Lateral subtalar dislocation: Case report and review of the literature

A case of complicated lateral subtalar dislocation is presented and the literature concerning this injury is reviewed. Subtalar joint dislocations are rare and often the result of a high-energy trauma. Complications include avascular necrosis of the talus, infection, posttraumatic osteoarthritis requiring arthrodesis and chronic subtalar instability. Negative prognostic factors include lateral and complicated dislocations, total talar extrusions, and associated fractures. A literature search was performed to identify studies describing outcome after lateral subtalar joint dislocation. Eight studies including fifty patients could be included, thirty out of 50 patients suffered a complicated injury. Mean follow-up was fifty-five months. Ankle function was reported as good in all patients with closed lateral subtalar dislocation. Thirteen out of thirty patients with complicated lateral subtalar joint dislocation developed a complication. Avascular necrosis was present in nine patients with complicated injury. Four patients with complicated lateral subtalar dislocation suffered deep infection requiring treatment with antibiotics. In case of uncomplicated lateral subtalar joint dislocation, excellent functional outcome after closed reduction and immobilization can be expected. In case of complicated lateral subtalar joint dislocation immediate reduction, wound debridement and if necessary (external) stabilisation are critical. Up to fifty percent of patients suffering complicated injury are at risk of developing complications such as avascular talar necrosis and infection.

Ulnar styloid process nonunion and outcome in patients with a distal radius fracture: a meta-analysis of comparative clinical trials

PURPOSE

There is no consensus on the relation between ulnar styloid process nonunion and outcome in patients with distal radius fractures. The aim of this study was to analyze whether patient-reported outcome is influenced by the nonunion of the accompanying ulnar styloid fracture in distal radius fracture patients.

METHODS

A meta-analysis of published studies comparing outcomes after distal radius fractures with a united versus a non-united ulnar styloid process was performed. In addition, if provided by the authors, the raw data of these studies were pooled and analysed as one study. The outcome measures of the analyses included patient-reported outcome, functional outcome, grip-strength, pain, and distal radioulnar joint (DRUJ) instability.

RESULTS

Data from six comparative studies were included, concerning 365 patients with a distal radius fracture. One hundred and thirty-five patients with an ulnar styloid union were compared with 230 patients with a nonunion of the ulnar styloid. No significant differences were found between groups regarding any outcome measure.

CONCLUSION

Based on this meta-analysis, there is no relation between the nonunion of the ulnar styloid process and function in patients with a distal radius fracture.

Qualms regarding the range of validity of the glansdorff-prigogine criterion for stability of non-equilibrium States

Doubt is raised concerning the range of validity of a stability criterion for non-equilibrium states which has been proposed by Glansdorff and Prigogine. In the case of a particular autocatalytic reaction, the stability analysis presented by Glansdorff and Prigogine, and by Eigen and by Katchalsky in their reviews of this problem, does not agree with our analysis, which is based upon exact solution of the relevant rate equations. We also find disagreement between the analysis based upon the Glansdorff-Prigogine criterion and our analysis of a second example which involves non-equilibrium steady states. The situation is quite delicate because seemingly innocent approximations (e.g., the use of specialized conditions in the autocatalytic reaction X + Y right arrow over left arrow 2X discussed in the sequel) may lead to the impression that the scope of validity of the criterion is wider than it actually is. By considering the stability of the equilibrium state, we conclude that the second differential of the entropy, which is at the heart of the Glansdorff-Prigogine criterion, is likely to be relevant for stability questions close to equilibrium only.

Maxwell-type constructions for multiple nonequilibrium steady states

A stochastic analysis is used to obtain Maxwell-type constructions for multiple nonequilibrium steady states in homogeneous systems. The stochastic theory shows that homogeneous molecular fluctuations can nucleate the Maxwell construction only on a time scale that is the order of a Poincaré recurrence time and indicates that hysteresis should be observed. The nonrelevance of homogeneous fluctuations for systems that undergo phase separation or in which spatial structures occur is discussed.

On the mechanism of oscillations in the "beating mercury heart"

The discovery of a class of electrochemical-mechanical oscillators-similar to the beating mercury heart -are reported and characterized. Chemical and physical effects on the voltage-time oscillations in these systems have been measured and a mechanism consistent with these effects is given. Interesting cross-catalytic effects involving the electrocapillarity of mercury are proposed to be the origin of the oscillations in these systems.

Modeling temporal behavior of postnatal cat retinal ganglion cells

During development, mammalian retinal ganglion cells (RGCs) go through marked ontogenetic changes with respect to their excitable membrane properties. Voltage-clamp studies conducted in our laboratory have shown that the amplitude, voltage-dependence and kinetics of activation and inactivation (where present) of Na(+), K(+) and Ca(2+) conductances all exhibit developmental changes during a time when the firing patterns of mammalian ganglion cells shift from being transient to being predominantly sustained in nature. In order to better understand the contribution of each conductance to the generation of spikes and spiking patterns, we have developed a model based on our experimental data. For simplicity, we have initially used experimental data obtained from postnatal ganglion cells. At this age the ontogenetic changes observed in the characteristics of the various ionic currents are complete. Utilizing the methods adopted by Hodgkin and Huxley for the giant squid axon, we have determined rate equations for the activation and inactivation properties of the I(A), I(K dr), I(Na), I(Ca L), I(Ca N), and I(leak) currents in postnatal cat RGCs. Combining these with a simplified model of the calcium-activated potassium current (I(KCa)), we have solved and analysed the resulting differential equations. While spikes and spiking patterns resembling experimental data could be obtained from a model in which [Ca(2+)i] was averaged across the whole cell, more accurate simulations were obtained when the diffusion of intracellular Ca(2+) was modeled spatially. The resulting spatial calcium gradients were more effective in gating I(KCa), and our simulations more accurately matched the recorded amplitude and shape of individual spikes as well as the frequency of maintained discharges observed in mammalian postnatal RGCs.

Fire-diffuse-fire model of dynamics of intracellular calcium waves

When Ca2+ is released from internal stores in living cells, the resulting wave of increased concentration can travel without deformation (continuous propagation) or with burst-like behavior (saltatory propagation). We analyze the "fire-diffuse-fire" model in order to illuminate the differences between these two modes of propagation. We show that the Ca2+ release wave in immature Xenopus oocytes and cardiac myocytes is saltatory, whereas the fertilization wave in the mature oocyte is continuous.

Simulation of the fertilization Ca2+ wave in Xenopus laevis eggs

In the preceding paper Fontanilla and Nuccitelli (Biophysical Journal 75:2079-2087 (1998)) present detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we develop here a computational technique based on the finite element method that allows us to carry out realistic simulations of the fertilization wave. Our simulations support the hypothesis that the physiological state of the mature egg is bistable, i.e., that its cytoplasm can accommodate two alternative physiological Ca2+ concentrations: a low concentration characteristic of the prefertilization state and a greatly elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and re-uptake properties of the endoplasmic reticulum (ER) as determined by inositol trisphosphate (IP3) receptor/Ca2+ channels and sarcoendoplasmic reticulum calcium ATPase (SERCA) pumps. When combined with buffered diffusion of Ca2+ in the cytoplasm, our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with an elevated IP3 concentration near the plasma membrane in the unfertilized egg that is augmented significantly near the site of fertilization. These gradients are essential in determining the concave shape of the Ca2+ fertilization wave front.

Saltatory propagation of Ca2+ waves by Ca2+ sparks

Punctate releases of Ca2+, called Ca2+ sparks, originate at the regular array of t-tubules in cardiac myocytes and skeletal muscle. During Ca2+ overload sparks serve as sites for the initiation and propagation of Ca2+ waves in myocytes. Computer simulations of spark-mediated waves are performed with model release sites that reproduce the adaptive Ca2+ release observed for the ryanodine receptor. The speed of these waves is proportional to the diffusion constant of Ca2+, D, rather than D, as is true for reaction-diffusion equations in a continuous excitable medium. A simplified "fire-diffuse-fire" model that mimics the properties of Ca2+-induced Ca2+ release (CICR) from isolated sites is used to explain this saltatory mode of wave propagation. Saltatory and continuous wave propagation can be differentiated by the temperature and Ca2+ buffer dependence of wave speed.

Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes

Using a modular approach, in which kinetic models of various mechanisms of calcium handling in cells are fine-tuned to in vivo and in vitro measurements before combining them into whole-cell models, three distinct modes of transmission of calcium waves in mature and immature frog eggs have been defined. Two modes of transmission are found in immature eggs, where the inositol 1,4,5-trisphosphate receptor (IP3R) controls release of calcium from the endoplasmic reticulum (ER). The first mode corresponds to an excitable physiological state of the cytoplasm and results in solitary waves that can appear as circular or spiral waves in two dimensions with the wave speed proportional to the square root of the diffusion constant of calcium. A second mode occurs when the state of the cytoplasm is oscillatory and because of the small size of the buffered diffusion constant for calcium, the wave speed can appear to be weakly dependent on diffusion. In the mature frog egg, where the sperm-induced Ca2+ fertilization wave is a propagating front, the cytoplasm appears to be bistable and in this mode the wave speed is also proportional to the square root of the diffusion constant. Here we investigate a fourth mode of propagation for cardiac myocytes, in which calcium release from the sarcoplasmic reticulum (SR) is dominated by clusters of ryanodine receptors spaced at regular intervals. In myocytes a stochastically excitable myoplasm leads to the spontaneous production of calcium 'sparks' that under certain conditions can merge into saltatory waves with a speed proportional to the diffusion constant.

Initial high anti-emetic efficacy of granisetron with dexamethasone is not maintained over repeated cycles

We have reported previously that the anti-emetic efficacy of single agent 5HT3 antagonists is not maintained when analysed with the measurement of cumulative probabilities. Presently, the most effective anti-emetic regimen is a combination of a 5HT3 antagonist plus dexamethasone. We, therefore, assessed the sustainment of efficacy of such a combination in 125 patients, scheduled to receive cisplatin > or = 70 mg m(-2) either alone or in combination with other cytotoxic drugs. Anti-emetic therapy was initiated with 10 mg of dexamethasone and 3 mg of granisetron intravenously, before cisplatin. On days 1-6, patients received 8 mg of dexamethasone and 1 mg of granisetron twice daily by oral administration. Protection was assessed during all cycles and calculated based on cumulative probability analyses using the method of Kaplan-Meier and a model for transitional probabilities. Irrespective of the type of analysis used, the anti-emetic efficacy of granisetron/dexamethasone decreased over cycles. The initial complete acute emesis protection rate of 66% decreased to 30% according to the method of Kaplan-Meier and to 39% using the model for transitional probabilities. For delayed emesis, the initial complete protection rate of 52% decreased to 21% (Kaplan-Meier) and to 43% (transitional probabilities). In addition, we observed that protection failure in the delayed emesis period adversely influenced the acute emesis protection in the next cycle. We conclude that the anti-emetic efficacy of a 5HT3 antagonist plus dexamethasone is not maintained over multiple cycles of highly emetogenic chemotherapy, and that the acute emesis protection is adversely influenced by protection failure in the delayed emesis phase.

Model of beta-cell mitochondrial calcium handling and electrical activity. II. Mitochondrial variables

In the preceding article [Am. J. Physiol. 274 (Cell Physiol. 43): C1158-C1173, 1998], we describe the development of a kinetic model for the interaction of mitochondrial Ca2+ handling and electrical activity in the pancreatic beta-cell. Here we describe further results of those simulations, focusing on mitochondrial variables, the rate of respiration, and fluxes of metabolic intermediates as a function of D-glucose concentration. Our simulations predict relatively smooth increases of O2 consumption, adenine nucleotide transport, oxidative phosphorylation, and ATP production by the tricarboxylic acid cycle as D-glucose concentrations are increased from basal to 20 mM. On the other hand, we find that the active fraction of pyruvate dehydrogenase saturates, due to increases in matrix Ca2+, near the onset of bursting electrical activity and that the NADH/NAD+ ratio in the mitochondria increases by roughly an order of magnitude as glucose concentrations are increased. The mitochondrial ATP/ADP ratio increases by factor of < 2 between the D-glucose threshold for bursting and continuous spiking. According to our simulations, relatively small changes in mitochondrial membrane potential (approximately 1 mV) caused by uptake of Ca2+ are sufficient to alter the cytoplasmic ATP/ADP ratio and influence ATP-sensitive K+ channels in the plasma membrane. In the simulations, these cyclic changes in the mitochondrial membrane potential are due to synchronization of futile cycle of Ca2+ from the cytoplasm through mitochondria via Ca2+ uniporters and Na+/Ca2+ exchange. Our simulations predict steady mitochondrial Ca2+ concentrations on the order of 0.1 microM at low glucose concentrations that become oscillatory with an amplitude on the order of 0.5 microM during bursting. Abrupt increases in mitochondrial Ca2+ concentration > 5 microM may occur during continuous electrical activity.

Model of beta-cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables

We continue our development of a kinetic model of bursting electrical activity in the pancreatic beta-cell (J. Keizer and G. Magnus. Biophys. J. 56: 229-242, 1989), including the influence of Ca2+ handling by the mitochondria. Our minimal model of mitochondrial Ca2+ handling [G. Magnus and J. Keizer. Am. J. Physiol. 273 (Cell Physiol. 42): C717-C733, 1997] is expanded to include the D-glucose dependence of the rate of production of mitochondrial reducing equivalents. The Ca2+ dependence of the mitochondrial dehydrogenases, which is also included in the model, plays only a small role in the simulations, since the dehydrogenases appear to be maximally activated when D-glucose concentrations are sufficient to produce bursting. A previous model of ionic currents in the plasma membrane is updated using a recent experimental characterization of the dependence of the conductance of the ATP-sensitive K+ (KATP) current on adenine nucleotides. The resulting whole cell model is complex, involving 12 dynamic variables that couple Ca2+ handling in the cytoplasm and the mitochondria with electrical activity in the plasma and inner mitochondrial membranes. Simulations with the whole cell model give rise to bursting electrical activity similar to that seen in pancreatic islets and clusters of pancreatic beta-cells. The full D-glucose dose response of electrical activity is obtained if the cytosolic rate of ATP hydrolysis is a sigmoidal function of glucose. The simulations give the correct shape, period, and phase of the associated oscillations in cytosolic Ca2+, predict that the conductance of the KATP current oscillates out of phase with electrical activity [as recently observed in ob/ob mice (O. Larsson, H. Kindmark, R. Bränstrom, B. Fredholm, and P.-O. Berggren. Proc. Natl. Acad. Sci. USA 93: 5161-5165, 1996)], and make other novel predictions. In this model, bursting results because Ca2+ uptake into mitochondria during the active phase reduces the mitochondrial inner membrane potential, reducing the rate of production of ATP, which in turn activates the KATP current and repolarizes the plasma membrane.

A fluorometric method for estimating the calcium content of internal stores

The concentration of Ca2+ in intracellular stores is an important factor in many aspects of Ca2+ signaling, including the generation of Ca2+ spikes, oscillations and waves, control of mitochondrial respiration, and activation of store-operated Ca2+ channels. Here we describe a consistent method for estimating the content of stores, based on the release of stored Ca2+ by thapsigargin (TG) or ionomycin (IO). Once released from stores, Ca2+ elevates [Ca2+]i transiently before it is pumped across the plasma membrane. If the dependence of the pump rate on [Ca2+]i is known, then the kinetics and amplitude of the Ca2+ transient allows the total amount of releasable Ca2+ to be estimated. We develop this quantitative approach and validate its use in human T cells, in which the Ca2+ clearance rate is an approximately linear function of [Ca2+]i. Our results support the assumption that the ER Ca2+ leak in resting T cells is unregulated, i.e. its rate is proportional to luminal [Ca2+]. The characteristic time constant for basal Ca2+ release is 110-140 s, comparable to that for activation of Ca2+ release-activated Ca2+ (CRAC) channels by TG and consistent with the dependence of ICRAC on store depletion. This method for estimating store content may be useful for quantifying the overlap between functionally distinct stores and for defining the relation between store content and cellular responses.

Agonist-induced calcium waves in oscillatory cells: a biological example of Burgers' equation

Oscillations in cytosolic Ca2+ concentrations in living cells are often a manifestation of propagating waves of Ca2+. Numerical simulations with a realistic model of inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ wave trains lead to wave speeds that increase linearly at long times when (a) IP3 levels are in the range for Ca2+ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP3, and (c) IP3 concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP3 receptor that includes the influence of Ca2+ buffers. For concentrations of IP3 in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca2+ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca2+. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca2+. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.

Minimal model of beta-cell mitochondrial Ca2+ handling

We develop a simplified, but useful, mathematical model to describe Ca2+ handling by mitochondria in the pancreatic beta-cell. The model includes the following six transport mechanisms in the inner mitochondrial membrane: proton pumping via respiration and proton uptake by way of the F1Fzero-ATPase (adapted from D. Pietrobon and S. Caplan. Biochemistry 24: 5764-5778, 1985), a proton leak, adenine nucleotide exchange, the Ca2+ uniporter, and Na+/Ca2+ exchange. Each mechanism is developed separately into a kinetic model for the rate of transport, with parameters taken from experiments on isolated mitochondrial preparations. These mechanisms are combined in a modular fashion first to describe state 4 (nonphosphorylating) and state 3 (phosphorylating) mitochondria with mitochondrial NADH and Ca2+ concentrations as fixed parameters and then to describe Ca2+ handling with variable mitochondrial Ca2+ concentration. Simulations are compared to experimental measurements and agree well with the threshold for Ca2+ uptake, measured mitochondrial Ca2+ levels, and the influence of Ca2+ on oxygen uptake. In the absence of Ca2+ activation of mitochondrial dehydrogenases, the simulations predict a significant reduction in the rate of production of ATP that involves a "short circuit" via Ca2+ uptake through the uniporter. This effect suggests a potential role for mitochondrial Ca2+ handling in determining the ATP-ADP ratio in the pancreatic beta-cell.

Sensing and refilling calcium stores in an excitable cell

Inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ mobilization leads to depletion of the endoplasmic reticulum (ER) and an increase in Ca2+ entry. We show here for the gonadotroph, an excitable endocrine cell, that sensing of ER Ca2+ content can occur without the Ca2+ release-activated Ca2+ current (Icrac), but rather through the coupling of IP3-induced Ca2+ oscillations to plasma membrane voltage spikes that gate Ca2+ entry. Thus we demonstrate that capacitative Ca2+ entry is accomplished through Ca(2+)-controlled Ca2+ entry. We develop a comprehensive model, with parameter values constrained by available experimental data, to simulate the spatiotemporal behavior of agonist-induced Ca2+ signals in both the cytosol and ER lumen of gonadotrophs. The model combines two previously developed models, one for ER-mediated Ca2+ oscillations and another for plasma membrane potential-driven Ca2+ oscillations. Simulations show agreement with existing experimental records of store content, cytosolic Ca2+ concentration ([Ca2+]i), and electrical activity, and make a variety of new, experimentally testable predictions. In particular, computations with the model suggest that [Ca2+]i in the vicinity of the plasma membrane acts as a messenger for ER content via Ca(2+)-activated K+ channels and Ca2+ pumps in the plasma membrane. We conclude that, in excitable cells that do not express Icrac, [Ca2+]i profiles provide a sensitive mechanism for regulating net calcium flux through the plasma membrane during both store depletion and refilling.

Ryanodine receptor adaptation and Ca2+(-)induced Ca2+ release-dependent Ca2+ oscillations

A simplified mechanism that mimics "adaptation" of the ryanodine receptor (RyR) has been developed and its significance for Ca2+(-)induced Ca2+ release and Ca2+ oscillations investigated. For parameters that reproduce experimental data for the RyR from cardiac cells, adaptation of the RyR in combination with sarco/endoplasmic reticulum Ca2+ ATPase Ca2+ pumps in the internal stores can give rise to either low [Cai2+] steady states or Ca2+ oscillations coexisting with unphysiologically high [Cai2+] steady states. In this closed-cell-type model rapid, adaptation-dependent Ca2+ oscillations occur only in limited ranges of parameters. In the presence of Ca2+ influx and efflux from outside the cell (open-cell model) Ca2+ oscillations occur for a wide range of physiological parameter values and have a period that is determined by the rate of Ca2+ refilling of the stores. Although the rate of adaptation of the RyR has a role in determining the shape and the period of the Ca2+ spike, it is not essential for their existence. This is in marked contrast with what is observed for the inositol 1,4,5-trisphosphate receptor for which the biphasic activation and inhibition of its activity by Ca2+ are sufficient to produce oscillations. Results for this model are compared with those based on Ca2+(-)induced Ca2+ release alone in the bullfrog sympathetic neuron. This kinetic model should be suitable for analyzing phenomena associated with "Ca2+ sparks," including their merger into Ca2+ waves in cardiac myocytes.

Modeling plasma membrane and endoplasmic reticulum excitability in pituitary cells

The response of gonadotrophs to secretagogues involves dose-dependent, complex dynamic patterns of electrical activity and inositol 1,4,5-trisphosphate (InsP(3))-induced Ca(2+) mobilization, including pulsatility and oscillations on multiple time scales from milliseconds to minutes. Detailed in vitro experiments have enabled the identification of key mechanisms that underlie the plasma membrane (PM) electrical excitability and endoplasmic reticulum (ER) calcium excitability. We summarize these findings and review computer simulations of a biophysical model that resynthesizes and couples these components and that reproduces quantitatively the observed time courses and dose-response characteristics, as well as effects of various pharamacological manipulations. The theory suggests that cytosolic calcium is the primary messenger in coordinating the PM and ER regenerative behaviors during ER depletion and refilling.

Validity of the rapid buffering approximation near a point source of calcium ions

In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ channel or a cluster of channels. Using a point source and performing numerical simulations of different durations, we quantify the error of the rapid buffering approximation as a function of buffer and source parameters as well as the time and spatial scale set by the resolution of confocal microscopic measurements. We carry out simulations of Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid or EGTA. In this regime, where the rapid buffering approximation is poor. Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adjacent to the pore.

Effect of Ca2+ influx on intracellular free Ca2+ responses in antigen-stimulated RBL-2H3 cells

We undertake a quantitative investigation of changes in intracellular free Ca2+ concentration ([Ca2+]i) in antigen-stimulated rat basophilic leukemia (RBL-2H3) cells, which include contributions of both Ca2+ store release and Ca2+ influx from the medium. Following Keizer and De Young (J. Keizer and G. De Young. Biophys. J. 61: 649-660, 1992), we develop a highly constrained mathematical model for [Ca2+]i oscillations in RBL-2H3 cells, which includes activation of the inositol trisphosphate receptor (IP3R) by inositol 1,4,5-trisphospate, indirect Ca2+ activation of the IP3R via Ca2+ -dependent activity of phospholipase C-gamma, slow inhibition of the IP3R by cytosolic Ca2+, refilling of Ca2+ stores by a Ca2+ -ATPase (SERCA)-type pump, and a simple representation of the dependence of plasma membrane (PM) fluxes on experimental conditions. Using this full (open cell) model, we simulate [Ca2+]i responses for protocols in which antigen concentration and external Ca2+ are manipulated and compare out calculations with experimental data. In protocol A, cells are stimulated in the presence of external Ca2+, in protocols B and C, cells are stimulated in the absence of external Ca2+, with external Ca2+ later reapplied in protocol C. We are able to reproduce quantitatively the important features of all three protocols, including the dose response of protocol B, the [Ca2+]i response to thapsigargin, and lag time results, and we provide qualitative explanations for the responses derived from our calculations. We also develop a simplified (closed cell) version of the model in which PM fluxes are neglected and total free Ca2+ concentration ([Ca2+]T) is a slowly varying parameter. This permits us to explain in a simple graphical fashion how PM fluxes may influence [Ca2+]i responses in RBH-2H3 cells through modulation of [Ca2+]T.

Mechanisms of calcium oscillations and waves: a quantitative analysis

Oscillations and waves of increased intracellular free calcium concentration ([Ca2+]i) are observed in a wide range of cell types. Because of their inherent nonlinear nature and the consequent unreliability of intuitive approaches, mathematical modeling has an important role to play in the study of these phenomena. One important class of oscillations and waves is dependent on the presence of inositol (1,4,5)-trisphosphate (IP3), which releases Ca2+ from internal stores via the IP3 receptor/Ca2+ channel. With the minimum possible mathematical formalism, we review mechanistic models for IP3-dependent Ca2+ oscillations and waves. These models are based on the regulation of the IP3 receptor by both IP3 and Ca2+, and incorporate experimental data on the steady-state and kinetic properties of the receptor. The extension of the models to describe intracellular and intercellular Ca2+ waves is considered.

Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations

Recent research dealing with experiments and theoretical models of Ca2+ excitability of the endoplasmic reticulum (ER) membrane induced by inositol 1,4,5-trisphosphate (IP3) is reviewed. Ca2+ excitability refers to the ability of a small increment of cytoplasmic Ca2+ concentration ([Ca2+]i) to trigger a large [Ca2+]i pulse or oscillations. Such nonlinear regenerative behavior is conferred by the existence of IP3 channels and Ca(2+)-ATPase transporters on the ER membrane, which extends throughout the cytoplasm. Ca2+ excitability resembles the plasma membrane electrical excitability of neurons and other cells: it is driven by the ionic concentration gradient across the ER membrane (higher Ca2+ concentration inside the ER); each [Ca2+]i spike partially consumes the prestored energy that is reestablished through ATP-dependent active transport; and [Ca2+]i, the excitation variable, controls the nonlinear dynamic release rate of ER Ca2+. This review focuses on the kinetic models based on these features and on experiments dealing with the kinetic properties of [Ca2+]i-dependent gating of the IP3 receptor channel. We summarize evidence in favor of two roles for [Ca2+]i in gating the channel's opening: activation at a rapid time scale and inactivation on a slower time scale. Exploiting an analogy to the well-known Hodgkin-Huxley model for neuronal electrical excitability, we show how Ca2+ excitability of the ER membrane can be explained by these gating properties combined with the ER Ca2+ pump activity. The theory's ability to predict is illustrated by comparing calculated with experimental [Ca2+]i responses for pituitary gonadotrophs under various stimulus conditions.

On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves

We have investigated the effects of Ca2+ diffusion, mobile and stationary Ca2+ buffers in the cytosol, and Ca2+ handling by the endoplasmic reticulum on inositol 1,4,5-trisphosphate-induced Ca2+ wave propagation. Rapid equilibration of free and bound Ca2+ is used to describe Ca2+ sequestration by buffers in both the cytosol and endoplasmic reticulum (ER) lumen. Cytosolic Ca2+ regulation is based on a kinetic model of the inositol 1,4,5-trisphosphate (IP3) receptor of De Young and Keizer that includes activation and inhibition of the IP3 receptor Ca2+ channel in the ER membrane and SERCA Ca2+ pumps in the ER. Diffusion of Ca2+ in the cytosol and the ER and the breakdown and diffusion of IP3 are also included in our calculations. Although Ca2+ diffusion is severely limited because of buffering, when conditions are chosen just below the threshold for Ca2+ oscillations, a pulse of IP3 or Ca2+ results in a solitary trigger wave that requires diffusion of Ca2+ for its propagation. In the oscillatory regime repetitive wave trains are observed, but for this type of wave neither the wave shape nor the speed is strongly dependent on the diffusion of Ca2+. Local phase differences lead to waves that are predominately kinematic in nature, so that the wave speed (c) is related to the wavelength (lambda) and the period of the oscillations (tau) approximately by the formula c = lambda/tau. The period is determined by features that control the oscillations, including [IP3] and pump activity, which are related to recent experiments. Both solitary waves and wave trains are accompanied by a Ca2+ depletion wave in the ER lumen, similar to that observed in cortical preparations from sea urchin eggs. We explore the effect of endogenous and exogenous Ca2+ buffers on wave speed and wave shape, which can be explained in terms of three distinct effects of buffering, and show that exogenous buffers or Ca2+ dyes can have considerable influence on the amplitude and width of the waves.

Enzymological differences of AChE and diazinon hepatic metabolism: correlation of in vitro data with the selective toxicity of diazinon to fish species

The in vitro hepatic metabolism of diazinon, as well as the sensitivity of the brain acetylcholine esterase, to diazoxon inhibitory action have been studied in order to explain the different toxicity of diazinon to Oncorhynchus mykiss (rainbow trout), Poecilia reticulata (guppy), Brachydanio rerio (zebra fish) and Cyprinus carpio (carp). In spite of a very sensitive acetylcholine esterase the carp is very resistant to diazinon toxicity because of its very low rate of bioactivation and relatively high activity of detoxicating enzymes. The trout is very sensitive towards diazinon in spite of its low activity of bioactivation, because of its lack of detoxicating enzymes and a very sensitive acetylcholine esterase. Diazinon is very toxic for the guppy, because this fish combines a relatively sensitive acetylcholine esterase with a high rate of bioactivation. The zebra fish has the most insensitive acetylcholine esterase, associated with a limited activation rate, thus resulting a rather resistant species. The results obtained indicate that diazinon toxicity differences among the fish species studied can largely be explained in relation to metabolic balances in the liver and with the features of the target enzyme.

InsP3-induced Ca2+ excitability of the endoplasmic reticulum

Oscillations in intracellular Ca2+ can be induced by a variety of cellular signalling processes (Woods et al., 1986; Berridge 1988; Jacob et al., 1988) and appear to play a role in secretion (Stojilković et al., 1994), fertilization (Miyazaki et al., 1993), and smooth muscle contraction (Iino and Tsukioka, 1994). Recently, great progress has been made in understanding the mechanisms involved in a particular class of Ca2+ oscillation, associated with the second messenger inositol 1,4,5-trisphosphate (InsP3) (Berridge, 1993). Working in concert with intracellular Ca2+, InsP3 controls Ca2+ release via the InsP3 receptor in the endoplasmic reticulum (ER) (Berridge and Irvine, 1989). The IP3 receptor is regulated by its coagonists InsP3 and Ca2+, which both activate and inhibit Ca2+ release (Finch et al., 1991; Bezprozvanny et al., 1991; De Young and Keizer, 1992). These processes, together with the periodic activation of Ca2+ uptake into the ER, have been identified as key features in the mechanism of InsP3-induced Ca2+ oscillations in pituitary gonadotrophs (Li et al., 1994), Xenopus laevis oocytes (Lechleiter and Clapham, 1992; Atri et al., 1993), and other cell types (Keizer and De Young, 1993). Earlier discussions and models of InsP3-induced Ca2+ oscillations focused on the nature and number of internal releasable pools of Ca2+ (Goldbeter et al., 1990; Swillens and Mercan, 1990; Somogyi and Stucki, 1991), the importance of oscillations in InsP3 (Meyer and Stryer, 1988), and other issues not based on detailed experimental findings in specific cells types.

Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells

Oscillatory secretion of insulin has been observed in many different experimental preparations ranging from pancreatic islets to the whole pancreas. Here we examine the mathematical features underlying a possible model for oscillatory secretion from the perifused, insulin-secreting cell line, HIT-15. The model includes the kinetics of uptake of glucose by GLUT transporters, the rate of glucose metabolism within the cell, and the effect of glucose on the rate of insulin secretion. Putative feedback by insulin on the rate of glucose transport into the cells is treated phenomenologically and leads to insulin oscillations similar to those observed experimentally in HIT cells. The resulting set of ordinary differential equations is simplified by time-scale analysis to a two-variable set of ordinary differential equations. Because of this simplification we can explore, in great detail, the characteristics of the oscillations and their sensitivity to parameter variation using phase plane analysis.

Analysis of possible mechanisms for in vitro oscillations of insulin secretion

We explore possible kinetic mechanisms responsible for the oscillatory (pulsatile) secretion of insulin observed in vitro when pancreatic islets or islet-derived cells are perifused with glucose. Three primary processes are included: 1) glucose stimulation of insulin secretion, controlled by glucokinase; 2) uptake of glucose through GLUT transporters; and 3) glucose metabolism. Perifusion is approximated as a limiting case of a chemical flow reactor. Using experimentally determined rate laws for the three processes, we examine the effects of exogenous insulin as a phenomenological activator and inhibitor of secretion. The resulting differential equations support oscillations using either direct or indirect inhibition by insulin. The oscillations have many of the characteristics observed in vitro, although the indirect model is in better overall agreement with experiment. We conclude that the mechanisms explored here may help explain insulin oscillations for HIT cells, but not for islets, and predict that oscillations can be modulated by including insulin in the perifusion medium.

Diffusion of inositol 1,4,5-trisphosphate but not Ca2+ is necessary for a class of inositol 1,4,5-trisphosphate-induced Ca2+ waves

Combining a realistic model of inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ oscillations with the diffusion of IP3 and buffered diffusion of Ca2+, we have found that diffusion of Ca2+ plays only a minor role in a class of agonist-induced Ca2+ wave trains. These waves are primarily kinematic in nature, with variable wavelengths and speeds that depend primarily on the phase differences between oscillators at different spatial points. The period is set by the steady-state value of IP3, while the wave speed approximately equals the wavelength/period. Ca2+ diffusion, which is much slower than that of IP3 because of endogenous buffers, is shown to have only a small effect on the wave trains and not to be necessary for the apparent wave propagation. Diffusion of IP3 sets the phase gradient responsible for these wave trains, which consist primarily of localized cycles of Ca2+ uptake and release. Our results imply a possible previously undisclosed role for IP3 in cell signaling.