The sinus node as a nonlinear dynamic system

The Sinus Node (SN) of the heart is the natural pacemaker driving electrical impulses into the atria, an ordinary excitable medium. In order to avoid wave interference, the SN operation must be of such a nature that no reflections from the atria should occur. It is shown that such a behavior is achieved when the SN operates in a nonlinear dynamical regime situated away from relaxation.

Combination therapy with low dose sirolimus and tacrolimus is synergistic in preventing spontaneous and recurrent autoimmune diabetes in non-obese diabetic mice

AIMS/HYPOTHESIS

Sirolimus and tacrolimus are immunosuppressive drugs that prevent rejection of pancreatic islet allografts transplanted into patients with Type I (insulin-dependent) diabetes mellitus. This study aimed to determine whether sirolimus and tacrolimus can prevent autoimmune beta-cell destruction, and if so, what the mechanisms of action are.

METHODS

Sirolimus and tacrolimus were given separately and together to female non-obese diabetic (NOD) mice from age 12 to 35 weeks. Diabetes incidence was determined and pancreatic insulitis and insulin content were measured. Sirolimus and tacrolimus were also given separately and together to diabetic NOD mice from the time of syngeneic islet transplantation until the reappearance of hyperglycaemia. Islet grafts were examined by RT-PCR assay for expression of interferon (IFN)- gamma, interleukin (IL)-2, IL-4, IL-10 and transforming growth factor (TGF)- beta1.

RESULTS

Low doses of sirolimus (0.1 mg/kg) and tacrolimus (0.1 mg/kg) were synergistic in reducing insulitis, preserving pancreatic insulin content and preventing diabetes in female NOD mice (8 % diabetes incidence at 35 weeks vs 66 % in vehicle-treated mice). Also, the combination of sirolimus and tacrolimus prolonged syngeneic islet graft survival (median 34 days vs 13 days for vehicle-treated mice). Islet grafts from sirolimus plus tacrolimus-treated mice expressed significantly decreased mRNA contents of Th1-type cytokines (IFN- gamma and IL-2) and the highest ratio of TGF- beta1/IFN- gamma mRNA.

CONCLUSION/INTERPRETATION

These findings suggest that combination therapy with sirolimus and tacrolimus prevent autoimmune beta-cell destruction by upregulating expression of the immunoregulatory cytokine, TGF- beta1 and reducing Th1 cytokines (IFN- gamma and IL-2) expressed in the islets. Low-dose sirolimus and tacrolimus combination therapy could warrant consideration for prevention or early treatment of human Type I diabetes.

Gutenberg-Richter-type relation for laboratory fracture-induced electromagnetic radiation

The fractal nature of electromagnetic radiation induced by uniaxial and triaxial rock fracture is considered. Both the well-known Gutenberg-Richter-type and the Benioff strain-release relationship, for earthquakes and starquakes, are shown to extend to the microscale (millimeters-centimeters). Results show that both the b value of the Gutenberg-Richter-type law and the slope of the Benioff strain-release relationship of the electromagnetic radiation signals are similar to values known for earthquakes. These results imply that a common mechanism is acting at all scales.

Peroxynitrite is a mediator of cytokine-induced destruction of human pancreatic islet beta cells

The proinflammatory cytokines, interleukin-1beta (IL-1beta), tumor necrosis factor alpha (TNFalpha), and interferon gamma (IFNgamma), are cytotoxic to pancreatic islet beta cells, possibly by inducing nitric oxide and/or oxygen radical production in the beta cells. Peroxynitrite, the reaction product of nitric oxide and the superoxide radical, is a strong oxidant and cytotoxic mediator; therefore, we hypothesized that peroxynitrite might be a mediator of cytokine-induced islet beta-cell destruction. To test this hypothesis we incubated islets isolated from human pancreata with the cytokine combination of IL-1beta, TNFalpha, and IFNgamma. We found that these cytokines induced significant increases in nitrotyrosine, a marker of peroxynitrite, in islet beta cells, and the increase in nitrotyrosine preceded islet-cell destruction. Peroxynitrite mimicked the effects of cytokines on nitrotyrosine formation and islet beta-cell destruction. L-N(G)-monomethyl arginine, an inhibitor of nitric oxide synthase, prevented cytokine-induced nitric oxide production but not hydrogen peroxide production, nitrotyrosine formation, or islet beta-cell destruction. In contrast, guanidinoethyldisulphide, an inhibitor of inducible nitric oxide synthase and scavenger of peroxynitrite, prevented cytokine-induced nitric oxide and hydrogen peroxide production, nitrotyrosine formation, and islet beta-cell destruction. These results suggest that cytokine-induced peroxynitrite formation is dependent upon increased generation of superoxide (measured as hydrogen peroxide) and that peroxynitrite is a mediator of cytokine-induced destruction of human pancreatic islet beta cells.

Inwards propagating waves in a limit cycle medium

The existence of a novel inwards propagating wave motion is demonstrated in a limit-cycle medium both for the FitzHugh-Nagumo and for modified Chernyak-Starobin-Cohen reaction-diffusion systems. The waves (pulses) are seen to be moving "backwards," that is, towards the point where the triggering pulse was initiated, instead of the regular propagation away from the origin. The feasibility of the phenomenon and some of its features are analyzed.

Expression of calbindin-D(28k) in a pancreatic islet beta-cell line protects against cytokine-induced apoptosis and necrosis

Cytokines produced by immune system cells that infiltrate pancreatic islets are candidate mediators of islet beta-cell destruction in autoimmune (type 1) diabetes mellitus. Because the calcium binding protein, calbindin-D(28k), can prevent apoptotic cell death in different cell types, we investigated the possibility that calbindin-D(28k) may prevent cytokine-mediated islet beta-cell destruction. Using the expression vector BSRalpha, rat calbindin-D(28k) was stably expressed in the pancreatic islet beta-cell line, betaTC-3. Calbindin-D(28k) expression resulted in increased cell survival in the presence of the cytotoxic combination of the cytokines IL-1beta (30 U/ml), TNFalpha (10(3) U/ml), and interferon gamma (10(3) U/ml). The greatest protection was observed in the betaTC-3 cell clone expressing the highest concentration of calbindin-D(28k). Apoptotic cell death was detected by annexin V staining and by the TdT-mediated dUTP-X nick end labeling assay in vector-transfected betaTC-3 cells incubated with cytokines (14-15% apoptotic cells). The number of apoptotic cells was significantly decreased in calbindin-D(28k)-overexpressing betaTC-3 cells incubated with cytokines (5-6% apoptotic cells). To address the mechanism of the antiapoptotic effects of calbindin, studies were done to examine whether calbindin inhibits free radical formation. The stimulatory effects of the cytokines on lipid hydroperoxide, nitric oxide, and peroxynitrite production were significantly decreased in the calbindin-D(28k)-expressing betaTC-3 cells. Our findings indicate that calbindin-D(28k), by inhibiting free radical formation, can protect against cytokine-mediated apoptosis and destruction of beta-cells. These findings suggest that calbindin-D(28k) may be an important regulator of cell death that can protect pancreatic islet beta-cells from autoimmune destruction in type 1 diabetes.

Inhibition of poly (ADP-ribose) synthetase by gene disruption or inhibition with 5-iodo-6-amino-1,2-benzopyrone protects mice from multiple-low-dose-streptozotocin-induced diabetes

Activation of poly(ADP-ribose) synthetase (PARS, also termed polyADP-ribose polymerase or PARP) has been proposed as a major mechanism contributing to beta-cell destruction in type I diabetes. In the present study, we have investigated the role of PARS in mediating the induction of diabetes and beta-cell death in the multiple-low-dose-streptozotocin (MLDS) model of type I diabetes. Mice genetically deficient in PARS were found to be less sensitive to MLDS than wild type mice, with a lower incidence of diabetes and reduced hyperglycemia. A potent inhibitor of PARS, 5-iodo-6-amino-1,2-benzopyrone (INH(2)BP), was also found to protect mice from MLDS and prevent beta-cell loss, in a dose-dependent manner. Paradoxically, in the PARS deficient mice, the compound increased the onset of diabetes. In vitro the cytokine combination; interleukin-1beta, tumor necrosis factor-alpha and interferon-gamma inhibited glucose-stimulated insulin secretion from isolated rat islets of Langerhans and decreased RIN-5F cell viability. The PARS inhibitor, INH(2)BP, protected both the rat islets and the beta-cell line, RIN-5F, from these cytokine-mediated effects. These protective effects were not mediated by inhibition of cytokine-induced nitric oxide formation. Inhibition of PARS by INH(2)BP was unable to protect rat islet cells from cytokine-mediated apoptosis. Cytokines, peroxynitrite and streptozotocin were all shown to induce PARS activation in RIN-5F cells, an effect suppressed by INH(2)BP. The present study provides evidence for in vivo PARS activation contributing to beta-cell damage and death in the MLDS model of diabetes, and indicates a role for PARS activation in cytokine-mediated depression of insulin secretion and cell viability in vitro.

An inhibitor of inducible nitric oxide synthase and scavenger of peroxynitrite prevents diabetes development in NOD mice

Peroxynitrite (ONOO(-)) is a highly reactive oxidant produced by the interaction of the free radicals superoxide (O*-2) and nitric oxide (NO(*)). In a previous study, we found that peroxynitrite is formed in islet beta-cells of nonobese diabetic (NOD) mice. Here, we report that guanidinoethyldisulphide (GED), a selective inhibitor of inducible nitric oxide synthase (iNOS) and scavenger of peroxynitrite prevents diabetes in NOD mice. GED treatment of female NOD mice, starting at age 5 weeks, delayed diabetes onset (from age 12 to 22 weeks) and significantly decreased diabetes incidence at 30 weeks (from 80% to 17%). GED did not prevent pancreatic islet infiltration by leukocytes; however, beta-cells that stained positive for nitrotyrosine (a marker of peroxynitrite) were significantly decreased in islets of GED-treated mice (1+/-1%) compared with vehicle-treated mice (30+/-9%). In addition, GED significantly inhibited nitric oxide and nitrotyrosine formation and decreased destruction of beta-cells in NOD mouse islets incubated in vitro with the combination of proinflammatory cytokines interleukin 1-beta (IL-1beta), tumour necrosis factor-alpha (TNF-alpha) and interferon-gamma (IFN-gamma). These findings indicate that both superoxide and nitric oxide radicals contribute to islet beta-cell destruction in autoimmune diabetes via peroxynitrite formation in the beta-cells.

Clinical outcomes and insulin secretion after islet transplantation with the Edmonton protocol

Islet transplantation offers the prospect of good glycemic control without major surgical risks. After our initial report of successful islet transplantation, we now provide further data on 12 type 1 diabetic patients with brittle diabetes or problems with hypoglycemia previous to 1 November 2000. Details of metabolic control, acute complications associated with islet transplantation, and long-term complications related to immunosuppression therapy and diabetes were noted. Insulin secretion, both acute and over 30 min, was determined after intravenous glucose tolerance tests (IVGTTs). The median follow-up was 10.2 months (CI 6.5-17.4), and the longest was 20 months. Glucose control was stable, with pretransplant fasting and meal tolerance-stimulated glucose levels of 12.5+/-1.9 and 20.0+/-2.7 mmol/l, respectively, but decreased significantly, with posttransplant levels of 6.3+/-0.3 and 7.5+/-0.6 mmol/l, respectively (P < 0.006). All patients have sustained insulin production, as evidenced by the most current baseline C-peptide levels 0.66+/-0.06 nmol/l, increasing to 1.29+/-0.25 nmol/l 90 min after the meal-tolerance test. The mean HbA1c level decreased from 8.3+/-0.5% to the current level of 5.8+/-0.1% (P < 0.001). Presently, four patients have normal glucose tolerance, five have impaired glucose tolerance, and three have post-islet transplant diabetes (two of whom need oral hypoglycemic agents and low-dose insulin (<10 U/day). Three patients had a temporary increase in their liver-function tests. One patient had a thrombosis of a peripheral branch of the right portal vein, and two of the early patients had bleeding from the hepatic needle puncture site; but these technical problems were resolved. Two patients had transient vitreous hemorrhages. The two patients with elevated creatinine levels pretransplant had a significant increase in serum creatinine in the long term, although the mean serum creatinine of the group was unchanged. The cholesterol increased in five patients, and lipid-lowering therapy was required for three patients. No patient has developed cytomegalovirus infection or disease, posttransplant lymphoproliferative disorder, malignancies, or serious infection to date. None of the patients have been sensitized to donor antigen. In 11 of the 12 patients, insulin independence was achieved after 9,000 islet equivalents (IEs) per kilogram were transplanted. The acute insulin response and the insulin area under the curve (AUC) after IVGTT were consistently maintained over time. The insulin AUC from the IVGTT correlated to the number of islets transplanted, but more closely correlated when the cold ischemia time was taken into consideration (r = 0.83, P < 0.001). Islet transplantation has successfully corrected labile type 1 diabetes and problems with hypoglycemia, and our results show persistent insulin secretion. After a minimum of 9,000 IEs per kilogram are provided, insulin independence is usually attained. An elevation of creatinine appears to be a contraindication to this immunosuppressive regimen. For the subjects who had labile type 1 diabetes that was difficult to control, the risk-to-benefit ratio is in favor of islet transplantation.

Th1 to Th2 cytokine shifts in nonobese diabetic mice: sometimes an outcome, rather than the cause, of diabetes resistance elicited by immunostimulation

Numerous immunostimulatory protocols inhibit the development of T cell-mediated autoimmune insulin-dependent diabetes mellitus (IDDM) in the nonobese diabetic (NOD) mouse model. Many of these protocols, including treatment with the nonspecific immunostimulatory agents CFA or bacillus Calmette-Guérin (BCG) vaccine, have been reported to mediate protection by skewing the pattern of cytokines produced by pancreatic beta-cell autoreactive T cells from a Th1 (IFN-gamma) to a Th2 (IL-4 and IL-10) profile. However, most of these studies have documented associations between such cytokine shifts and disease protection rather than a cause/effect relationship. To partially address this issue we produced NOD mice genetically deficient in IFN-gamma, IL-4, or IL-10. Elimination of any of these cytokines did not significantly alter the rate of spontaneous IDDM development. Additional experiments using these mice confirmed that CFA- or BCG-elicited diabetes protection is associated with a decreased IFN-gamma to IL-4 mRNA ratio within T cell-infiltrated pancreatic islets, but this is a secondary consequence rather than the cause of disease resistance. Unexpectedly, we also found that the ability of BCG and, to a lesser extent, CFA to inhibit IDDM development in standard NOD mice is actually dependent upon the presence of the Th1 cytokine, IFN-gamma. Collectively, our studies demonstrate that while Th1 and Th2 cytokine shifts may occur among beta-cell autoreactive T cells of NOD mice protected from overt IDDM by various immunomodulatory therapies, it cannot automatically be assumed that this is the cause of their disease resistance.

Intranet-based quality improvement documentation at the Veterans Affairs Maryland Health Care System

The Pathology and Laboratory Medicine Service of the Veterans Affairs Maryland Health Care System is inspected biannually by the College of American Pathologists (CAP). As of the year 2000, all documentation in the Anatomic Pathology Section is available to all staff through the VA Intranet. Signed, supporting paper documents are on file in the office of the department chair. For the year 2000 CAP inspection, inspectors conducted their document review by use of these Web-based documents, in which each CAP question had a hyperlink to the corresponding section of the procedure manual. Thus inspectors were able to locate the documents relevant to each question quickly and efficiently. The procedure manuals consist of 87 procedures for surgical pathology, 52 procedures for cytopathology, and 25 procedures for autopsy pathology. Each CAP question requiring documentation had from one to three hyperlinks to the corresponding section of the procedure manual. Intranet documentation allows for easier sharing among decentralized institutions and for centralized updates of the laboratory documentation. These documents can be upgraded to allow for multimedia presentations, including text search for key words, hyperlinks to other documents, and images, audio, and video. Use of Web-based documents can improve the efficiency of the inspection process.

Testicular sertoli cells protect islet beta-cells from autoimmune destruction in NOD mice by a transforming growth factor-beta1-dependent mechanism

Testicular Sertoli cells protect pancreatic islet grafts from allo- and autoimmune destruction; however, the mechanism(s) of protection is unclear. The aim of this study was to determine whether Fas ligand (FasL) and/or transforming growth factor (TGF)-beta, immunoregulatory proteins produced by Sertoli cells, might mediate the protective effects of these cells against autoimmune destruction of islet beta-cells. Sertoli cells were purified from testes of NOD mice and implanted under the right renal capsule of diabetic NOD mice, whereas NOD islets were implanted under the left renal capsule. Of the mice that received islet and Sertoli cells grafts, 64% (9 of 14) remained normoglycemic at 60 days posttransplantation compared with 0% (0 of 6) of the mice that received islet grafts alone. Immunohistochemical examination of Sertoli cell grafts in normoglycemic mice revealed that TGF-beta1 expression by Sertoli cells remained high, whereas FasL expression by Sertoli cells decreased progressively posttransplantation. Also, plasma levels of TGF-beta1 were significantly elevated in mice that received Sertoli cells and islet grafts, and anti-TGF-beta1 antibody administration completely abrogated the protective effect of Sertoli cells on islet graft survival, whereas anti-FasL antibody did not. Islet graft destruction in anti-TGF-beta1-treated mice was associated with increases in interferon (IFN)-gamma-producing cells and decreases in interleukin (IL)-4-producing cells in the islet grafts. We conclude that 1) Sertoli cell production of TGF-beta1, not FasL, protects islet beta-cells from autoimmune destruction and 2) TGF-beta1 diverts islet-infiltrating cells from a beta-cell-destructive (IFN-gamma+) phenotype to a nondestructive (IL-4+) phenotype.

Fas ligand-mediated mechanisms are involved in autoimmune destruction of islet beta cells in non-obese diabetic mice

AIMS/HYPOTHESIS

A mechanism implicated in pancreatic islet beta-cell destruction in autoimmune diabetes is the binding of the Fas ligand (FasL) on T cells to Fas receptors on beta cells, causing their destruction. Evidence for this mechanism is, however, controversial. The aim of this study was to find whether the Fas ligand contributes to beta-cell death in autoimmune diabetes.

METHODS

We transplanted syngeneic islets under the renal capsule in non-obese diabetic (NOD) mice and treated the mice with a neutralizing monoclonal antibody to the Fas ligand. Survival of beta cells in islet grafts and phenotypes of graft-infiltrating cells were investigated.

RESULTS

We found 58% (7 of 12) of mice treated with anti-Fas ligand antibody were normoglycaemic at 30 days after islet transplantation compared with none (0 of 9) of the mice treated with control antibody. Immunohistochemical analysis of islet grafts showed that infiltration of leucocytes (CD4+ T cells, CD8+ T cells, macrophages and neutrophils) and apoptosis of beta cells in the grafts was significantly decreased in mice treated with anti-Fas ligand antibody. Expression of proinflammatory cytokines (interleukin 1 alpha, tumour necrosis factor alpha and interferon gamma) was not different in islet grafts of mice treated with anti-Fas ligand and control antibodies.

CONCLUSION/INTERPRETATION

These findings indicate that Fas ligand-mediated mechanisms play a major part in promoting leucocytic infiltration of islets and beta-cell destruction in autoimmune diabetes.

Testicular Sertoli cells exert both protective and destructive effects on syngeneic islet grafts in non-obese diabetic mice

AIMS/HYPOTHESIS

Testicular Sertoli cells protect allogeneic islet grafts from rejection after transplantation into animals with chemically induced diabetes. The aims of this study were to determine whether Sertoli cells can protect syngeneic islets from autoimmune destruction after transplantation into non-obese diabetic (NOD) mice and, if so, whether protection is due to Sertoli cell expression of Fas ligand (FasL), believed to be the mechanism that protects against allograft rejection.

METHODS

We compared the survival of syngeneic islets transplanted under the renal capsule of nonobese diabetic mice, alone and together with purified Sertoli cells prepared from testes of newborn nonobese diabetic mice. Additionally, we examined the composition of the islet and Sertoli cell co-transplants by immunohistochemistry to determine whether islet graft survival correlated with Sertoli cell expression of Fas ligand.

RESULTS

Sertoli cell doses of 1, 2 and 4 x 10(6) cells produced a dose-dependent prolongation of median islet graft survival from 11 days (islets alone) to 32 days (islets + 4 x 10(6) Sertoli cells); addition of 8 x 10(6) Sertoli cells to the islet grafts decreased, however, median survival to 8 days. Immunohistochemical analysis of the islet and Sertoli cell co-transplants showed a correlation between Fas ligand expression by Sertoli cells and graft infiltration by neutrophilic leucocytes, leading to islet beta-cell destruction and diabetes recurrence.

CONCLUSION/INTERPRETATION

Sertoli cells exert opposing effects on survival of syngeneic islet grafts in nonobese diabetic mice: Fas ligand-dependent neutrophil infiltration and graft destruction, and Fas ligand-independent protection of the graft from autoimmune destruction.

Exhibition of intrinsic properties of certain systems in response to external disturbances

Two systems, which are models of biological processes, are considered. These systems are notable for responding to different external actions nearly alike. This is associated with the fact that an external action excites only their natural intrinsic motions. Two kinds of external actions, harmonic and random, are studied. It is shown that each of them induces a transition to a new state that can be treated as a peculiar kind of phase transitions. Characteristics of these phase transitions are found.

Bacterial lysis by phage--a theoretical model

The similarity to materials corrosion is invoked to develop a model for phage-infected bacterial lysis based on the statistics of extremes. The importance of cell size, envelope thickness and lysozyme eclipse time on the final probability distribution of lysis is considered. Experiments are suggested to test the model.

Threshold, excitability and isochrones in the Bonhoeffer-van der Pol system

Some new insight is obtained for the structure of the Bonhoeffer-van der Pol system. The problems of excitability and threshold are discussed for all three types of the system classified according to the existing attractors: a focus only, a limit cycle only and a limit cycle together with a focus. These problems can be treated by the T-repellers and the T-attractors of the system which are mutually reciprocal under time inversion. The threshold depends on the structure of the T-repeller (unstable part of integral manifold). This structure is then used to understand the behavior and the properties of the two different types of isochrones: Winfree isochrones (W-isochrones) and regular isochrones. Winfree's description of a W-isochrone is extended to excitable systems. Both W-isochrones and regular isochrones are calculated for the Bonhoeffer-van der Pol system in its limit cycle and excitable regimes. The important role of the T-repeller as an asymptotic limit for both types of isochrones is manifested. (c) 1999 American Institute of Physics.

Transfection of human pancreatic islets with an anti-apoptotic gene (bcl-2) protects beta-cells from cytokine-induced destruction

Apoptosis has been identified as a mechanism of pancreatic islet beta-cell death in autoimmune diabetes. Proinflammatory cytokines are candidate mediators of beta-cell death in autoimmune diabetes, and these cytokines can induce beta-cell death by apoptosis. In the present study, we examined whether transfection of human islet beta-cells with an anti-apoptotic gene, bcl-2, can prevent cytokine-induced beta-cell destruction. Human islet beta-cells were transfected by a replication-defective herpes simplex virus (HSV) amplicon vector that expressed the bcl-2 gene (HSVbcl-2) and, as a control, the same HSV vector that expressed a beta-galactosidase reporter gene (HSVlac). Two-color immunohistochemical staining revealed that 95+/-3% of beta-cells transfected with HSVbcl-2 expressed Bcl-2 protein compared with 14+/-3% of beta-cells transfected with HSVlac and 19+/-4% of nontransfected beta-cells. The bcl-2-transfected beta-cells were fully protected from impaired insulin secretion and destruction resulting from incubation for 5 days with the cytokine combination of interleukin (IL)-1beta, tumor necrosis factor (TNF)-alpha, and interferon (IFN)-gamma. In addition, the bcl-2-transfected islet cells were significantly protected from cytokine-induced lipid peroxidation and DNA fragmentation. These results demonstrate that cytokine-induced beta-cell dysfunction and death involve mechanisms subject to regulation by an anti-apoptotic protein, Bcl-2. Therefore, bcl-2 gene therapy has the potential to protect human beta-cells in pancreatic islets, or islet grafts, from immune-mediated damage in type 1 diabetes.

Model for bacteriophage T4 development in Escherichia coli

Mathematical relations for the number of mature T4 bacteriophages, both inside and after lysis of an Escherichia coli cell, as a function of time after infection by a single phage were obtained, with the following five parameters: delay time until the first T4 is completed inside the bacterium (eclipse period, nu) and its standard deviation (sigma), the rate at which the number of ripe T4 increases inside the bacterium during the rise period (alpha), and the time when the bacterium bursts (mu) and its standard deviation (beta). Burst size [B = alpha(mu - nu)], the number of phages released from an infected bacterium, is thus a dependent parameter. A least-squares program was used to derive the values of the parameters for a variety of experimental results obtained with wild-type T4 in E. coli B/r under different growth conditions and manipulations (H. Hadas, M. Einav, I. Fishov, and A. Zaritsky, Microbiology 143:179-185, 1997). A "destruction parameter" (zeta) was added to take care of the adverse effect of chloroform on phage survival. The overall agreement between the model and the experiment is quite good. The dependence of the derived parameters on growth conditions can be used to predict phage development under other experimental manipulations.