Modeling Complexity in Molecular Systems

Contents

Abstract

Preface

Introduction

Review of the Literature

Chapter 1 The Flow Diagram

Chapter 2 Binary Systems in Biology

Chapter 3 Interlinked Fast and Slow Positive Feedback

Chapter 4 Modeling Systems Biology

Summary

Bibliography

Appendix A

Appendix B

About the Author

Abstract

The dissertation will model interlinked fast and slow positive feedback loops that represent reliable signal transmission to a cell's decision making process. The use of the signal flow diagram will be used to graph an ideal model of this system.

Preface

I have a background in using signal flow diagrams in biology, 1996, 1998 and 2001, and it does not surprise me to see that with the advancement of systems biology to computational data collecting has lead to the introduction of engineering methodologies to the 'natural' sciences. With this 'hybridizing' of the natural sciences with the engineering disciplines, the need for the appropriate use of research 'tools' become paramount.

Such is the case for signal flow diagrams, as opposed to other types of graphing methods, when analyzing a biological process.

As data becomes more cumbersome, in both quality and quantity, to the study of biological systems, the very real need for accurate study and presentation of such data will only increase with time. Current studies have already pointed to the very large collection of data in the natural sciences and will only increase as techniques and computational power grows (Nicholson, 2006: 992).

The nature of this dissertation then is the application of a signal flow diagram to model the communication of a cell, reliable signal transmission of information of a cell's decision. On a secondary level, the dissertation addresses the need for correct application of engineering techniques to the growing field of systems biology.

The financing for the research done for this dissertation was a medical grant from both Advanced Human Design, located in Cupertino, California USA and Tice Pharmaceuticals, that is located in San Jose, California USA.

Citation:

Nicholson, J.K. (2006) "Reviewers peering from under a pile of 'omics' data". Nature, Volume 441, April 2006, pp. 992, Comments section.

Introduction

The growing need for effective modeling of complex systems in the biological sciences expands the traditional areas of graph theory from the physical science's and engineering disciplines to that of systems biology. While the future of modeling biological processes and systems will be automated, by computers, the need for human evaluations of such processes will still fall within the sphere of human perceptions of those processes (Muggleton, 2006: 409-410). Hence, the need for clear and accurate graphing methods. The author has previous experience with flow graphs and has found that the application of such graphing methods to the natural sciences the ideal modeling tool for representations of systems and sub-systems (Tice, 1997a, 1997b, 1997c, 1997d, 1997e, and 1998).

The graphing method to be used in this dissertation will be the signal flow diagram, also called the signal flow graph, that was developed by Mason in 1953 (Mason, 1953). Because the signal flow diagram incorporates the use of cycles and loops to represent a feedback system, they present an ideal graphing method to represent the 'product' flow of a system, in this case, a biological system. An example of current biological research data will be modeled using an interlinked fast and slow positive feedback loops to represent reliable signaling transmission for cell decisions (Brandman, Ferrell, Li, and Meyer, 2005, and Bornholdt, 2005). The model of the system data will use the signal flow diagram.

Review of the Literature

The literature for this dissertation is concise with Mason (1953), Brandman, Ferrell, Li and Meyer (2005), Barnholdt (2005) and Tice (1996) being primary sources. The remaining literature represents secondary sources of research. I have included my further work with signal flow diagrams in Appendix A of this dissertation. The literature is, in essence, the utilization of engineering techniques to natural, biological, processes. The resulting list of literature becomes neat and tidy as a result of the direct aspects of this academic work. Signal flow diagrams are graphs that were invented by Mason in 1953 (Mason, 1953).

The signal flow diagram is a directed graph that may have cycles and loops present that represent feedback in the system.

This type of graph is also considered a network (Busacker and Saaty, 1965: 185-186). While signal flow diagrams are the domain of the engineering disciplines, a growing need for such graphing methods is developing in the physical and natural sciences, especially in the field of systems biology (Barnholdt, 2005:

451). The dissertation will take current research data from the field of systems biology and model interlinked fast and slow positive feedback loops in producing reliable signaling decisions for cells (Brandman, Ferrell, Li, and Meyer, 2005 and Bornholdt, 2005).

Chapter 1 The Flow Diagram

The Flow Diagram

The signal flow diagram is a flow diagram that was developed by Mason in 1953 (Mason, 1953). The signal flow diagram is a directed graph, also known as a digraph, that is a collection of elements known as vertices that when collected in ordered pairs, or arcs, have a direction (Faudree, 1987: 322)

The following is taken from my chemistry dissertation (1996) that describes a signal flow diagram (Tice, 2001: 20-23) .

Signal Flow Diagram

The use of signal flow diagrams are common in fields such as engineering and a practical use of them can be made in the field of pharmacology. The main reason for the use of signal flow diagrams over other diagram systems, formal or block diagrams, are that they are easy to use and permits a solution practically upon visual inspection (Shinners, 1964: 25)1 Signal flow diagrams can solve complex linear, multiloop systems in less time than either block diagrams or equations (Macmillian, Higgins, and Naslin, 1964: 4). A signal flow graph Is a topological representation of a set of linear equations as represented by the following equation

illustration not visible in this excerpt

Branches and nodes are used to represent a set of equations in a signal flow graph. Each node represents a variable in the system, like node i represents variable y in equation 1. Branches represent the different variables such as branch ij relates variable yi to yj where the branch originates at node i and terminates at node j in equation 1 (Shinners, 1964: 25).

The following set of linear equations are represented in the signal flow graph in Figure 1 (Shinners, 1964: 25).

illustration not visible in this excerpt

It is necessary now to define the terms as represented by the signal flow diagram in Figure 1 (Shinners, 1964: 28).

1. The Source is a node having only outgoing branches, as yl in Figure 1.
2. The Sink is a node having only incoming branches, as y5 in Figure 1.
3. The Path is a group of connected branches having the same sense of direction. These are he, adfh, and b in Figure 1.
4. The Forward Paths are paths which originate from a source and terminate at a sink along which no node is encountered more than once, as are eh, adg, and adfh in Figure 1.
5. The Path Gain is the product of the coefficient associated with the branches along the path.
6. The Feedback Loop is a path originating from a node and terminating at the same node. In addition, a node cannot be encountered more than once. They are b and dfc in Figure 1.
7. The Loop Gain is the product of the coefficients associated with the branches forming a feedback loop.

By using a signal flow diagram to represent the variables associated with pharmacological testing, drug delivery, behavior, dosage and time intervals can all be graphed for ease of representation of these complex systems.

Chapter 2 Binary Systems in Biology

The notion of a binary system is simple, whether it is off or it is on. It cannot be both, nor can it be a gradual quality of either. Black and white with no grey. In a biological system the process of communication, the science of signal transmission of information, can be modeled into a binary system of two states, but with the added notion of duration, or time, it takes that signal to be transmitted as a variable.

Previous use of binary arithmetic to questions of biology can be traced back to Shannon's Doctorial work at MIT (1940) (Shannon, 1940). The use of other disciplines 'resources' is not uncommon today as an example Niels K. Jerne upon receiving his 1984 Nobel Prize in Medicine, gave a Noble lecture titled "The Generative Grammar of the Immune System" that seems to bind the study of linguistics with that of processes with in the immune system (Wright, 1988: 84).

Chapter 3 Interlinked Fast and Slow Positive Feedback

An example of interlinked fast and slow positive feedback is taken from a paper by Brandman, Ferrell, Li, and Meyer (2005).

In this paper biological systems, in this case cell communication, is organized into a binary, on or off, system that uses positive feedback as the central method of communication (Brandman, Ferrell, Li, and Meyer, 2005: 496). Multiple positive feedback loops can be composed of both fast and slow rates, the duration or time, it takes the signal to transmit a communication, and that many of these multiple positive feedback loops are interlinked (Brandman, Ferrell, Li, and Meyer, 2005: 496) .

Chapter 4 Modeling Systems Biology

The most important element to keep in decribing a system or process is the integrity must be kept intact of that system or process. Because graphing is the most 'illustrative' use of modeling of the descriptive devices to be used to describe a system or process, the need for an 'ideal' or 'most accurate' graph should be maintained to perserve the nature of the process being described. I have taken an example of interlinked fast and slow positive feedback loops from a paper by Brandman, Ferrell, Li, and Meyer (2005) that describes reliable cell decisions in a schematic manner that makes for an ideal model for the signal flow diagram (Brandman, Ferrell, Li, and Meyer, 2005: 497).

The focus of this example is not to examine the research in this paper but to use the signal flow diagram in place of the schematic model used in the paper. All explinations taken from the paper are to enhance the reason for the presentation of the data in a diagrammatic manner. This dissertation will assume the research from this paper is accurate and viable.

The focus will be on Brandman, Ferrell, Li, and Meyer's paper (2005) titled "Interlinked Fast and Slow Positive Feedback Loops Drive Reliable Cell Decisions" (Brandman, Ferrell, Li, and Meyer, 2005: 496-498). In this paper, I am selecting the schematic model for the establishment of polarity in budding yeast cells (Brandman, Ferrell, Li, and Meyer, 2005: 497). The paper addresses the presence of multiple interlinked positive loops as a question of performance as an advantage of the multiloop design (Brandman, ferrell, Li, and Meyer, 2005: 496-497).

In using previous studies, Brandman, et al., concluded that the slow positive feedback loop was crucial for stability of the polarized "on" state, and the fast loop was crucial for the speed of the transmission between the unpolarized "off" state and polarized "on" state (Brandman, Ferrell, Li, and Meyer, 2005:

497) . The paper concludes that linked slow and fast positive loop systems have advantages over single loop and dual looped systems such as independent timing of activation and deactivation times (Brandman, ferrell, Li, and Meyer, 2005: 497) .

The following is the positive feedback loop data from Table 1 in Brandman, et al. paper for budding yeast polarization (Brandman, Ferrell, Li, and Meyer, 2005: 497). The information flow is from the left to right in both lines of data.

Table 1

Cdc42-Cdc24-Cdc42

Cdc42-actin-Cdc42

The following is a copy of Figure 1 example A from Brandman, et al., paper that is a schematic representation of the data found in Table 1 of the polarization of budding yeast cells from the same paper (Brandman, Ferrell, Li, and Meyer, 2005: 497).

Figure 1 Example A

illustration not visible in this excerpt

In replacing the original schematic found in Brandman, et al, paper with a signal flow diagram the following will result as seen in Figure 2.

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