Mihajlo D. Mesarovic

Feedback dynamics and cell function: Why systems biology is called Systems Biology

A new paradigm, like Systems Biology, should challenge the way research has been conducted previously. This Opinion article aims to present Systems Biology, not as the application of engineering principles to biology but as a merger of systems- and control theory with molecular- and cell biology. In our view, the central dogma of Systems Biology is that it is system dynamics that gives rise to the functioning and function of cells. The concepts of feedback regulation and control of pathways and the coordination of cell function are emphasized as an important area of Systems Biology research. The hurdles and risks for this area are discussed from the perspective of dynamic pathway modelling. Most of all, the aim of this article is to promote mathematical modelling and simulation as a part of molecular- and cell biology. Systems Biology is a success if it is widely accepted that there is nothing more practical than a good theory.

Systems Theory and Biology­ View of a Theoretician *

There exists a considerable diversity of opinion on what constitutes the systems approach to biology. On one side of the spectrum the systems approach is considered to be the application of techniques and instruments for measurements and signal analysis (so-called bio-instrumentation); further down the line is bio-engineering concerned with the application of the “engineering principles” in the study of the biological problems. On the other side of the spectrum, the systems approach is considered to be a search for some general biological laws which govern the behavior and evolution of living matter in a way analogous to the relation of the physical laws and non-living matter. (Often the latter viewpoint is presented as part of a scientific philosophy1,2.)

On a qualitative theory of satisfactory control

Satisfactory control is defined as a control which yields the performance below a given tolerance limit over the entire range of uncertainties (disturbances). Some results on the existence of a satisfactory control are given and such questions as sensitivity and feedback are considered. Results are applied to the systems described in function spaces and by differential equations.

The role of theorem proving in systems biology

Theorems offer a rarity in biology, a guarantee that something will always be true if certain conditions are met. We show that modeling and theorem proving are distinct while playing mutually supporting roles in understanding cellular phenomena. Using two recently proven theorems from systems biology as examples, we demonstrate that theorems are not an alternative to mechanistic models. Rather, theorem proving, in conjunction with conventional mathematical (mechanistic) modeling, is an essential tool for a deeper understanding in systems biology.

Systems Theoretic Approach to Formal Theory of Problem Solving

Objective of my presentation is to give an outline or rather a “synopsis” for mathematical theory of problem solving based on systems theoretic concepts and viewpoints, in particular what I call (mathematical) general systems theory.

A MEANING OF THE DECOUPLING BY FEEDBACK OF LINEAR FUNCTIONAL TIME SYSTEMS

Abstract The purpose of this paper is to demonstrate how the general method of the mathematical general systems theory is applicable to such a detailed problem as the decoupling of a linear system by giving a new result about the problem. We first define the feedback transformation in a general manner, and consider the feedback invariant properties and the class controllability problem by feedback transformation. Next we consider the decoupling problem by feedback of linear, functional, bijective, causal and time invariantly realizable lime systems which input and output spaces can be represented in terms of the component linear spaces. In conclusion we show that it is an essential fact for the decoupling problem that the range space of linear systems is feedback invariant and so that the functionally output non-cohesiveness plays an important role.

From Networks to Systems to Complex Systems: A Signaling Pathway Coordination Case Study

Networks of Signaling pathways provide a robust mechanism for cells to respond to various biological stimuli. In this paper we demonstrate cell adaptation through the viewpoint of an organizing principle between two interconnected pathways- MAPK and PKC. We use a multi-layered system representation of the pathways to determine the pathway components contributing to the adaptive behavior and coordination. The adaptation can be thought of as being manifested by a change in parameters of the coordinator. In silico experiments are conducted using MAPK/PKC mathematical model in literature to investigate the role of PLA2as a coordinator is reported here. Our results show that varying parameters of the coordinator not only activates the network of pathways where otherwise the pathway activity is very low, but also reveal the ability of the system to activate itself in the absence of the input, indicating relevance of the principle of bounded autonomy.

Realizability and general dynamical systems

Abstract The realizability problem in the dynamical systems theory is concerned with the existence of a family of state transition functions for a given response function (e.g., weighting pattern for the case of linear systems) meaning that the latter can be realized by a dynamical system. The results giving realizability conditions are well known for the continuous differential equations systems [see, e.g., 1, 2]. The objective of this paper is to present a general realization theory which will cover not only nonlinear systems but also those systems that are not necessarily continuous or even defined on the topological spaces. Actually, the results reported represent yet another step in the development of a mathematical theory of general systems following a program outlined earlier [3–5 ]. Consistent with that program the concept of a general dynamical system is introduced using minimal mathematical structure and the realizability theory is developed as such on a general level.

Uncertainties and optimal control approach to feedback control problems

The relevance of the optimal control approach to the solution of automatic feedback control problems is investigated. Some inadequacies of the approach and their causes are presented both analytically and numerically. A formulation of the basic control problem is offered in order to circumvent these difficulties.

Institutional Level Management

This chapter will discuss an adaptive behavior of an organization performed by the institutional level management. In order to get sharp results, the adaptation of this chapter will be particularized as an activity to adapt to a structural change of the external management information input. The adaptation is performed by adjusting a decision parameter of the institutional level. The ultimate outcome is a global goal which is an operationalization of the organizational goal adapting to the external input change. The goal of the adaptation is to sustain a satisfactory activity state (a set point of the institutional level management) of the organization. It should be noticed then that this adaptation concept presumes that the organization is in an acceptable state in an appropriately defined sense before an adaptation activity is requested.