The circulation stage of the metastatic cascade: A mathematical description and its clinical implications.

Metastatic cascade is a multi-stage process that starts with separation of a cancer cell from the primary tumor and ends with the emergence of a detectable metastasis. In the process the initiator cancer cell enters the circulatory system (intravasates), flows with the blood, and exits the circulation (extravasates) into an organ or tissue. The time period between intravasation and extravasation constitutes the circulation stage of the metastatic cascade. This stage is unique in that it lends itself naturally to various non-invasive observations and measurements in an individual cancer patient. This creates an opportunity for gaining insight into metastasis, its mathematical modeling, and designing diagnostic/prognostic tools and new cancer therapies. Although mechanisms of intravasation, survival and extravasation of circulating tumor cells (CTCs) are very complex and largely unknown, mathematical modeling of the circulation stage of the metastatic cascade is facilitated by two inter-related factors: a relative simplicity of the circulatory network and the cyclic nature of blood flow. The article presents a single-subject stochastic model of CTC dynamics that leads to simple formulas, applicable to any homogeneous CTC population, for organ-specific extravasation probabilities, the distribution and expected value of the number, X, of circulation cycles completed by a CTC prior to extravasation, and the average circulation time. In particular, we found that the distribution of random variable X is geometric G(x), where parameter x is measurable, at least in principle, in an individual subject. We also discuss implications of our results for cancer research and treatment.

Tumor control probability in hypofractionated radiotherapy as a function of total and hypoxic tumor volumes.

Clinical studies in the hypofractionated stereotactic body radiotherapy (SBRT) have shown a reduction in the probability of local tumor control with increasing initial tumor volume. In our earlier work, we obtained and tested an analytical dependence of the tumor control probability (TCP) on the total and hypoxic tumor volumes using conventional radiotherapy model with the linear-quadratic (LQ) cell survival. In this work, this approach is further refined and tested against clinical observations for hypofractionated radiotherapy treatment schedules. Compared to radiotherapy with conventional fractionation schedules, simulations of hypofractionated radiotherapy may require different models for cell survival and the oxygen enhancement ratio (OER). Our TCP simulations in hypofractionated radiotherapy are based on the LQ model and the universal survival curve (USC) developed for the high doses used in SBRT. The predicted trends in local control as a function of the initial tumor volume were evaluated in SBRT for non-small cell lung cancer (NSCLC). Our results show that both LQ and USC based models cannot describe the TCP reduction for larger tumor volumes observed in the clinical studies if the tumor is considered completely oxygenated. The TCP calculations are in agreement with the clinical data if the subpopulation of radio-resistant hypoxic cells is considered with the volume that increases as initial tumor volume increases. There are two conclusions which follow from our simulations. First, the extent of hypoxia is likely a primary reason of the TCP reduction with increasing the initial tumor volume in SBRT for NSCLC. Second, the LQ model can be an acceptable approximation for the TCP calculations in hypofractionated radiotherapy if the tumor response is defined primarily by the hypoxic fraction. The larger value of OER in the hypofractionated radiotherapy compared to the conventional radiotherapy effectively extends the applicability of the LQ model to larger doses.

The natural history of renal cell carcinoma with pulmonary metastases illuminated through mathematical modeling.

The goal of this study is to uncover some unobservable aspects of the individual-patient natural history of metastatic renal cell carcinoma (RCC) through mathematical modeling. We analyzed four clear cell RCC patients who at the time of primary tumor resection already had pulmonary metastases. Our description of the natural history of cancer in these patients was based on a parameterized version of a previously proposed very general mathematical model adjusted to these clinical cases. For each patient, identifiable model parameters were estimated by the method of maximum likelihood from the volumes of lung metastases computed from CT scans taken at or around the time of surgery. The model-based distribution of the volumes of lung metastases with likelihood maximizing parameters provided an excellent fit to the data for all patients analyzed. We found that, according to the model, the most likely scenario in all four patients had the following clinically important features: (1) duration of metastatic latency was very small compared to the growth period; (2) seeding of the first lung metastasis occurred before primary tumor reached detectable size, which implies that early cancer detection would not have prevented metastasis; (3) primary tumor contained a relatively fast growing subpopulation of metastasis-producing cells, which is consistent with the observed aggressive course of the disease; and (4) the volume of the primary tumor at the time of metastasis survey does not seem to be correlated with such characteristics of the metastatic burden as the number of detected lung metastases, their total volume, and the volume of the largest detected lung metastasis.

Suppression of Metastasis by Primary Tumor and Acceleration of Metastasis Following Primary Tumor Resection: A Natural Law?

We study metastatic cancer progression through an extremely general individual-patient mathematical model that is rooted in the contemporary understanding of the underlying biomedical processes yet is essentially free of specific biological assumptions of mechanistic nature. The model accounts for primary tumor growth and resection, shedding of metastases off the primary tumor and their selection, dormancy and growth in a given secondary site. However, functional parameters descriptive of these processes are assumed to be essentially arbitrary. In spite of such generality, the model allows for computing the distribution of site-specific sizes of detectable metastases in closed form. Under the assumption of exponential growth of metastases before and after primary tumor resection, we showed that, regardless of other model parameters and for every set of site-specific volumes of detected metastases, the model-based likelihood-maximizing scenario is always the same: complete suppression of metastatic growth before primary tumor resection followed by an abrupt growth acceleration after surgery. This scenario is commonly observed in clinical practice and is supported by a wealth of experimental and clinical studies conducted over the last 110 years. Furthermore, several biological mechanisms have been identified that could bring about suppression of metastasis by the primary tumor and accelerated vascularization and growth of metastases after primary tumor resection. To the best of our knowledge, the methodology for uncovering general biomedical principles developed in this work is new.

Why statistical inference from clinical trials is likely to generate false and irreproducible results.

One area of biomedical research where the replication crisis is most visible and consequential is clinical trials. Why do outcomes of so many clinical trials contradict each other? Why is the effectiveness of many drugs and other medical interventions so low? Why have prescription medications become the third leading cause of death in the US and Europe after cardiovascular diseases and cancer? In answering these questions, the main culprits identified so far have been various biases and conflicts of interest in planning, execution and analysis of clinical trials as well as reporting their outcomes. In this work, we take an in-depth look at statistical methodology used in planning clinical trials and analyzing trial data. We argue that this methodology is based on various questionable and empirically untestable assumptions, dubious approximations and arbitrary thresholds, and that it is deficient in many other respects. The most objectionable among these assumptions is that of distributional homogeneity of subjects' responses to medical interventions. We analyze this and other assumptions both theoretically and through clinical examples. Our main conclusion is that even a totally unbiased, perfectly randomized, reliably blinded, and faithfully executed clinical trial may still generate false and irreproducible results. We also formulate a few recommendations for the improvement of the design and statistical methodology of clinical trials informed by our analysis.

A quantitative insight into metastatic relapse of breast cancer.

BACKGROUND: Metastatic relapse is the principal source of breast cancer mortality. This work seeks to uncover unobservable, yet clinically important, aspects of post-surgery metastatic relapse of breast cancer and to quantify effects of surgery on metastatic progression. METHODS: We classified metastases into three categories: (1) solitary cancer cells that were formed before or during surgery and either circulate in blood or are lodged at various secondary sites; (2) dormant or slowly growing avascular metastases; and (3) vascular secondary tumors. We developed a general mathematical model aimed at describing post-surgery dynamics of these three metastatic states. One parametric version of the model assumed that sojourn times of metastases in the three states are exponentially distributed while another was based on Erlang distribution. Model parameters were estimated from a sample of metastatic relapse or censoring times for 673 breast cancer patients treated with surgery. RESULTS: We estimated the expected number of metastases at surgery and mean sojourn times for the three states and found that both are decreasing with state number. We also computed the probability that metastatic relapse resulted from a metastasis in a given state at surgery. The values of these attribution probabilities suggest that under the Erlang model all three states have a considerable effect on metastatic relapse while in the case of exponential model this is true for states 1 and 2 only. CONCLUSIONS: (1) In some patients metastasis occurred before surgery; (2) our results confirm significance of metastatic dormancy; (3) according to the model surgery stimulates escape from dormancy, promotes angiogenesis and accelerates metastatic growth in a fraction of breast cancer patients. Taken summarily, these findings call into question the benefits of primary tumor resection for certain categories of breast cancer patients.

A "universal" model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases.

We develop a methodology for estimating unobservable characteristics of the individual natural history of metastatic cancer from the volume of the primary tumor and site-specific volumes of metastases measured before, or shortly after, the start of treatment. In particular, we address the question as to what information about natural history of cancer can and cannot be gained from this type of data. Estimation of the natural history of cancer is based on parameterization of a very general mathematical model of cancer progression accounting for primary tumor growth, shedding of metastases, their selection, latency and growth in a given secondary site. This parameterization assumes Gompertz (and, as a limiting case, exponential) growth of the primary tumor, exponential growth of metastases, and exponential distribution of metastasis latency times. We find identifiable parameters of this model and give a rigorous proof of their identifiability. As an illustration, we analyze a clinical case of renal cancer patient who developed 55 lung metastases whose volumes were measured through laborious reading of CT images. The model with maximum likelihood parameters provided an excellent fit to this data. We uncovered many aspects of this patient's cancer natural history and showed that, according to the model, onset of metastasis occurred long before primary tumor became clinically detectable.

Uncovering the natural history of cancer from post-mortem cross-sectional diameters of hepatic metastases.

We develop a mathematical and statistical methodology for estimation of important unobservable characteristics of the individual natural history of cancer from a sample of cross-sectional diameters of liver metastases measured at autopsy. Estimation of the natural history of cancer is based on a previously proposed stochastic model of cancer progression tailored to this type of observations. The model accounts for primary tumour growth, shedding of metastases, their selection, latency and growth in a given secondary site. The model was applied to the aforementioned data on 428 liver metastases detected in one untreated small cell lung cancer patient. Identifiable model parameters were estimated by the method of maximum likelihood and through minimizing the [Formula: see text] distance between theoretical and empirical cumulative distribution functions. The model with optimal parameters provided an excellent fit to the data. Results of data analysis support, if only indirectly, the hypothesis of the existence of stem-like cancer cells in the case of small cell lung carcinoma and point to the possibility of suppression of metastatic growth by a large primary tumour. They also lead to determination of the lower and upper bounds for the age of cancer onset and expected duration of metastatic latency. Finally, model-based inference on the patient's natural history of cancer allowed us to conclude that resection of the primary tumour would most likely not have had a curative effect.

Optimal schedules of fractionated radiation therapy by way of the greedy principle: biologically-based adaptive boosting.

We revisit a long-standing problem of optimization of fractionated radiotherapy and solve it in considerable generality under the following three assumptions only: (1) repopulation of clonogenic cancer cells between radiation exposures follows linear birth-and-death Markov process; (2) clonogenic cancer cells do not interact with each other; and (3) the dose response function s(D) is decreasing and logarithmically concave. Optimal schedules of fractionated radiation identified in this work can be described by the following 'greedy' principle: give the maximum possible dose as soon as possible. This means that upper bounds on the total dose and the dose per fraction reflecting limitations on the damage to normal tissue, along with a lower bound on the time between successive fractions of radiation, determine the optimal radiation schedules completely. Results of this work lead to a new paradigm of dose delivery which we term optimal biologically-based adaptive boosting (OBBAB). It amounts to (a) subdividing the target into regions that are homogeneous with respect to the maximum total dose and maximum dose per fraction allowed by the anatomy and biological properties of the normal tissue within (or adjacent to) the region in question and (b) treating each region with an individual optimal schedule determined by these constraints. The fact that different regions may be treated to different total dose and dose per fraction mean that the number of fractions may also vary between regions. Numerical evidence suggests that OBBAB produces significantly larger tumor control probability than the corresponding conventional treatments.

On the probability of cure for heavy-ion radiotherapy.

The probability of a cure in radiation therapy (RT)-viewed as the probability of eventual extinction of all cancer cells-is unobservable, and the only way to compute it is through modeling the dynamics of cancer cell population during and post-treatment. The conundrum at the heart of biophysical models aimed at such prospective calculations is the absence of information on the initial size of the subpopulation of clonogenic cancer cells (also called stem-like cancer cells), that largely determines the outcome of RT, both in an individual and population settings. Other relevant parameters (e.g. potential doubling time, cell loss factor and survival probability as a function of dose) are, at least in principle, amenable to empirical determination. In this article we demonstrate that, for heavy-ion RT, microdosimetric considerations (justifiably ignored in conventional RT) combined with an expression for the clone extinction probability obtained from a mechanistic model of radiation cell survival lead to useful upper bounds on the size of the pre-treatment population of clonogenic cancer cells as well as upper and lower bounds on the cure probability. The main practical impact of these limiting values is the ability to make predictions about the probability of a cure for a given population of patients treated to newer, still unexplored treatment modalities from the empirically determined probability of a cure for the same or similar population resulting from conventional low linear energy transfer (typically photon/electron) RT. We also propose that the current trend to deliver a lower total dose in a smaller number of fractions with larger-than-conventional doses per fraction has physical limits that must be understood before embarking on a particular treatment schedule.

Dynamics of pathologic clot formation: a mathematical model.

Recent studies have provided evidence of a significant role of the Hageman factor in pathologic clot formation. Since auto-activation of the Hageman factor triggers the intrinsic coagulation pathway, we study the dynamics of pathologic clot formation considering the intrinsic pathway as the predominant mechanism of this process. Our methodological approach to studying the dynamics of clot formation is based on mathematical modelling. Activation of the blood coagulation cascade, particularly its intrinsic pathway, is known to involve platelets. Therefore, equations accounting for the effects of activated platelets on the intrinsic pathway activation are included in our model. This brings about a considerable increase in the values of kinetic constants involved in the model of the principal biochemical processes resulting in clot formation. The purpose of this study is to elucidate the mechanism of pathologic clot formation. Since the time window of thrombolysis is 3-6h, we hypothesize that in many cases the rate of pathologic clot formation is much lower than that of haemostatic clot. This assumption is used to simplify the mathematical model and to estimate kinetic constants of biochemical reactions that initiate pathologic clot formation. The insights we gained from our mathematical model may lead to new approaches to the prophylaxis of pathologic clot formation. We believe that one of the most efficient ways to prevent pathologic clot formation is simultaneous inhibition of activated factors ХII and ХI.

Reconstruction of the natural history of metastatic cancer and assessment of the effects of surgery: Gompertzian growth of the primary tumor.

This work deals with retrospective reconstruction of the individual natural history of solid cancer and assessment of the effects of treatment on metastatic progression. This is achieved through a mathematical model of cancer progression accounting for the growth of the primary tumor, shedding of metastases, their dormancy and growth at secondary sites. To describe dynamics of the primary tumor, we used the Gompertz law, a parsimonious model of tumor growth accounting for its saturation. Parameters of the model were estimated from the age and volume of the primary tumor at surgery and volumes of detectable bone metastases collected from one breast cancer patient and one prostate cancer patient. This allowed us to estimate, for each patient, the ages at cancer onset and inception of all detected metastases, the expected metastasis latency time, parameters of the Gompertzian growth of the primary tumor, and the rates of growth of metastases before and after surgery. We found that for both patients: (1) onset of metastasis occurred when primary tumor was undetectable; (2) inception of all surveyed metastases except one occurred before surgery; and most importantly, (3) resection of the primary tumor led to a dramatic increase in the rate of growth of metastases. The model provides an excellent fit to the observed volumes of bone metastases in both patients. Our results agree well with those obtained previously based on exponential growth of the primary tumor, which serves as model validation. Our findings support the notion of metastatic dormancy and indirectly confirm the existence of stem-like cancer cells in breast and prostate tumors. We also explored the logistic law of primary tumor growth; however, it degenerated into the exponential law for both patients analyzed. The conclusions of this work are supported by a vast body of experimental, clinical and epidemiological knowledge accumulated over the last century.

A mechanistic description of radiation-induced damage to normal tissue and its healing kinetics.

We introduce a novel mechanistic model of the yield of tissue damage at the end of radiation treatment and of the subsequent healing kinetics. We find explicit expressions for the total number of functional proliferating cells as well as doomed (functional but non-proliferating) cells as a function of time post treatment. This leads to the possibility of estimating-for any given cohort of patients undergoing radiation therapy-the probability distribution of those kinetic parameters (e.g. proliferation rates) that determine times to injury onset and ensuing resolution. The model is suitable for tissues with simple duplication organization, meaning that functionally competent cells are also responsible for tissue renewal or regeneration following injury. An extension of the model to arbitrary temporal patterns of dose rate is presented. To illustrate the practical utility of the model, as well as its limitations, we apply it to data on the time course of urethral toxicity following fractionated radiation treatment and brachytherapy for prostate cancer.

Optimal screening schedules for prevention of metastatic cancer.

We develop methodological, mathematical, statistical, and computational approaches to constructing schedules of cancer screening that maximize the probability that by the time of primary tumor detection it has not yet metastasized. Solving this problem is based on a comprehensive mechanistic model of cancer progression. We apply the model with realistic parameters and the screening optimization methodology to mammographic screening for breast cancer within the American female population. We uncover some general patterns of optimal screening schedules. We show that optimization of screening regimens leads to a significant reduction in the probability of detecting breast cancer that has already disseminated.

Seeing the invisible: how mathematical models uncover tumor dormancy, reconstruct the natural history of cancer, and assess the effects of treatment.

The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.In this primarily methodological work, we discuss critically important, yet largely unobservable, aspects of the natural history of cancer, such as (1) early metastatic dissemination; (2) dormancy of secondary tumors; (3) treatment-related interruption of metastatic dormancy, induction of angiogenesis, and acceleration of the growth of vascular metastases; and (4) the existence of cancer stem cells. The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.We focus on the unique role played by very general mathematical models of the individual natural history of cancer that are entirely mechanistic yet, somewhat paradoxically, essentially free of assumptions about specific nature of the underlying biological processes. These models make it possible to reconstruct in considerable detail the individual natural history of cancer and retrospectively assess the effects of treatment. Thus, the models can be used as a tool for generation and validation of biomedical hypotheses related to carcinogenesis, primary tumor growth, its metastatic dissemination, growth of metastases, and the effects of various treatment modalities. We discuss in detail one such general model and review the conclusions relevant to the aforementioned aspects of cancer progression that were drawn from fitting a parametric version of the model to data on the volumes of bone metastases in one breast cancer patient and 12 prostate cancer patients.

Tumor control probability in radiation treatment.

Patients undergoing radiation therapy (and their physicians alike) are concerned with the probability of cure (long-term recurrence-free survival, meaning the absence of a detectable or symptomatic tumor). This is not what current practice categorizes as "tumor control (TC);" instead, TC is taken to mean the extinction of clonogenic tumor cells at the end of treatment, a sufficient but not necessary condition for cure. In this review, we argue that TC thus defined has significant deficiencies. Most importantly, (1) it is an unobservable event and (2) elimination of all malignant clonogenic cells is, in some cases, unnecessary. In effect, within the existing biomedical paradigm, centered on the evolution of clonogenic malignant cells, full information about the long-term treatment outcome is contained in the distribution Pm(T) of the number of malignant cells m that remain clonogenic at the end of treatment and the birth and death rates of surviving tumor cells after treatment. Accordingly, plausible definitions of tumor control are invariably traceable to Pm(T). Many primary cancers, such as breast and prostate cancer, are not lethal per se; they kill through metastases. Therefore, an object of tumor control in such cases should be the prevention of metastatic spread of the disease. Our claim, accordingly, is that improvements in radiation therapy outcomes require a twofold approach: (a) Establish a link between survival time, where the events of interest are local recurrence or distant (metastatic) failure (cancer-free survival) or death (cancer-specific survival), and the distribution Pm(T) and (b) link Pm(T) to treatment planning (modality, total dose, and schedule of radiation) and tumor-specific parameters (initial number of clonogens, birth and spontaneous death rates during the treatment period, and parameters of the dose-response function). The biomedical, mathematical, and practical aspects of implementing this program are discussed.

Why victory in the war on cancer remains elusive: biomedical hypotheses and mathematical models.

We discuss philosophical, methodological, and biomedical grounds for the traditional paradigm of cancer and some of its critical flaws. We also review some potentially fruitful approaches to understanding cancer and its treatment. This includes the new paradigm of cancer that was developed over the last 15 years by Michael Retsky, Michael Baum, Romano Demicheli, Isaac Gukas, William Hrushesky and their colleagues on the basis of earlier pioneering work of Bernard Fisher and Judah Folkman. Next, we highlight the unique and pivotal role of mathematical modeling in testing biomedical hypotheses about the natural history of cancer and the effects of its treatment, elaborate on model selection criteria, and mention some methodological pitfalls. Finally, we describe a specific mathematical model of cancer progression that supports all the main postulates of the new paradigm of cancer when applied to the natural history of a particular breast cancer patient and fit to the observables.

Effects of Surgery and Chemotherapy on Metastatic Progression of Prostate Cancer: Evidence from the Natural History of the Disease Reconstructed through Mathematical Modeling.

This article brings mathematical modeling to bear on the reconstruction of the natural history of prostate cancer and assessment of the effects of treatment on metastatic progression. We present a comprehensive, entirely mechanistic mathematical model of cancer progression accounting for primary tumor latency, shedding of metastases, their dormancy and growth at secondary sites. Parameters of the model were estimated from the following data collected from 12 prostate cancer patients: (1) age and volume of the primary tumor at presentation; and (2) volumes of detectable bone metastases surveyed at a later time. This allowed us to estimate, for each patient, the age at cancer onset and inception of the first metastasis, the expected metastasis latency time and the rates of growth of the primary tumor and metastases before and after the start of treatment. We found that for all patients: (1) inception of the first metastasis occurred when the primary tumor was undetectable; (2) inception of all or most of the surveyed metastases occurred before the start of treatment; (3) the rate of metastasis shedding is essentially constant in time regardless of the size of the primary tumor and so it is only marginally affected by treatment; and most importantly, (4) surgery, chemotherapy and possibly radiation bring about a dramatic increase (by dozens or hundred times for most patients) in the average rate of growth of metastases. Our analysis supports the notion of metastasis dormancy and the existence of prostate cancer stem cells. The model is applicable to all metastatic solid cancers, and our conclusions agree well with the results of a similar analysis based on a simpler model applied to a case of metastatic breast cancer.

Does extirpation of the primary breast tumor give boost to growth of metastases? Evidence revealed by mathematical modeling.

A comprehensive mechanistic model of cancer natural history was utilized to obtain an explicit formula for the distribution of volumes of detectable metastases in a given secondary site at any time post-diagnosis. This model provided an excellent fit to the volumes of n=31, 20 and 15 bone metastases observed in three breast cancer patients 8 years, 5.5 years and 9 months after primary diagnosis, respectively. The model with optimal parameters allowed us to reconstruct the individual natural history of cancer for the first patient. This gave definitive answers, for the patient in question, to the following three questions of major importance in clinical oncology: (1) How early an event is metastatic dissemination of breast cancer? (2) How long is the metastasis latency time? and (3) Does extirpation of the primary breast tumor accelerate the growth of metastases? Specifically, according to the model applied to the first patient, (1) inception of the first metastasis occurred 29.5 years prior to the primary diagnosis; (2) the expected metastasis latency time was about 79.5 years; and (3) resection of the primary tumor was followed by a 32-fold increase in the rate of metastasis growth. The model and our conclusions were validated by the results for the two other patients.

Non-linear dynamics of the complement system activation.

The complement system (CS) plays a prominent role in the immune defense. The goal of this work is to study the dynamics of activation of the classic and alternative CS pathways based on the method of mathematical modeling. The principal difficulty that hinders modeling effort is the absence of the measured values of kinetic constants of many biochemical reactions forming the CS. To surmount this difficulty, an optimization procedure consisting of constrained minimization of the total protein consumption by the CS was designed. The constraints made use of published data on the in vitro kinetics of elimination of the Borrelia burgdorferi bacteria by the CS. Special features of the problem at hand called for a significant modification of the general constrained optimization procedure to include a mathematical model of the bactericidal effect of the CS in the iterative setting. Determination of the unknown kinetic constants of biochemical reactions forming the CS led to a fully specified mathematical model of the dynamics of cell killing induced by the CS. On the basis of the model, effects of the initial concentrations of complements and their inhibitors on the bactericidal action of the CS were studied. Proteins playing a critical role in the regulation of the bactericidal action of the CS were identified. Results obtained in this work serve as an important stepping stone for the study of functioning of the CS as a whole as well as for developing methods for control of pathogenic processes.