Basics of Cybernetics, Feedback and Control, and Modelling Biological Systems

Introduction to Cybernetics and Systems Theory

• Cybernetics Definition: The formal study of control and connections across nature, science, and society.

• Core Components of Cybernetics:

  • Organization: Governed by systems theory.

  • Information: Governed by information theory.

  • Control: Governed by control theory.

• Systems Theory: The study of systems in a generalized manner, aiming to uncover principles applicable to:

  • All varieties of systems.

  • All nesting levels (hierarchies).

  • All fields of scientific research.

Organization and Cybernetic Systems

• Organization: Defined as the formation of systems.

• Cybernetic System: A collection of interacting structures and processes combined to execute a common function.

  • Crucially, the function performed by the system is distinct from the individual functions of its separate components.

• General Properties of Cybernetic Systems:

  • Connections: They interact with their environment and with other external systems.

  • Hierarchical Structure: Systems are composed of subsystems and simultaneously function as subsystems within larger systems.

  • Robustness: They preserve their general structure even under changing environmental conditions.

• Types of Functions Describing Systems:

  • Component states.

  • Structure and connections.

  • Transmitted signals.

Classification of Systems

• By Degree of Determinism:

  • Deterministic Systems: Components interact in a predetermined, rigid way, making the system's response entirely predictable. Example: A machine.

  • Probabilistic Systems: The response cannot be predicted with total certainty. Example: The weather.

• By Interaction with the Environment:

  • Closed Systems: Components interact exclusively with each other; there is no interaction with the external environment.

  • Open Systems: Components interact with the environment as well as each other.

• Elements of Interaction:

  • Perception: The acquisition of signals from other systems via sensors or receptors ($\text{e.g., eyes, ears}$).

  • Transmission: The delivery of signals to other systems via effectors ($\text{e.g., organs of speech, gestures}$).

Characteristics of Biological Cybernetic Systems

• Nature of Biological Systems:

  • They possess varying levels of complexity.

  • They are probabilistic due to high component counts and strong external influences.

  • They feature a multi-level hierarchical organization.

• Basic Properties:

  • Self-organization: The internal capability to form or change structure.

  • Self-regulation: The capability to maintain internal stability.

• Complexity Factors:

  • A massive number of individual components.

  • Complex, interrelated connections between these components.

• Two-Way Hierarchy:

  • Each component is viewed as a system of lower-level components.

  • Lower-level components operate independently if they can process all relevant input information.

  • Higher-level components exert control over the lower-level components.

Information Theory and Communication

• Information Definition:

  • Any set of related data.

  • Any meaningful event resulting in an action.

  • The state of a system of interest.

  • Information serves to reduce ambiguity and remove a lack of knowledge.

• Information Theory Scope: The study of information acquisition, transmission, storage/retention, processing, and measurement.

• Communication System Components:

  • Message: The specific information being transmitted.

  • Signal: The physical carrier of the message.

  • Communication Channel: The medium through which the signal propagates.

• Signal-Channel Examples:

  • Sound wave (Signal) through Air (Channel).

  • Light wave (Signal) through Optical Fibre (Channel).

  • Electric signal (Signal) through a Wire in an electronic device (Channel).

Coding, Isomorphism, and Noise

• Alphabet (Code): A set of simple signals utilized to send any message.

• Processes of Coding:

  • Encoding: The transmitter generates a signal using an alphabet to carry a message.

  • Recoding: The process of altering the alphabet used.

  • Decoding: The receiver extracts the message from the signal.

• Isomorphism: Refers to physically different signals that carry the exact same message. Recoding must ensure that the initial and recoded signals remain isomorphic.

• Noise: Disturbances within the communication system that modify the signal.

• Channel Fidelity: Measured by the Signal to Noise Ratio (SNR).

Memory and Information Measurement

• Memory: The system's ability to store and retain information for later recall and use.

• Mechanism of Memorization:

  • Changing the states of system components.

  • Changing the system structure (altering connections between components).

• Mathematical Measurement of Information:

  • If an experiment produces one of a set of $N$ equally likely events, the information received ($I$) is:

  • $I = \log_2(N)$

• The Bit: The basic unit of measurement. One bit is the information received from learning which of $2$ equally likely events occurred ($\text{e.g., tossing a coin}$).

• Information in Human DNA:

  • DNA utilizes $4$ bases. Since a nucleotide contains only one base, information per nucleotide is $2$ bits ($\log_2(4) = 2$).

  • Human sperm chromosomal DNA contains approximately $10^9$ nucleotides.

  • Total information equals $2 \times 10^9$ bits.

Principles of Control and Regulation

• Control: Actions taken to affect a system to reach a specific goal.

• Regulation: A specific form of control aimed at maintaining a particular state or process.

• Cybernetic Control System: A system that is self-contained in monitoring its own performance and applying corrections.

• Logic of Control:

  • Program: The algorithm or set of rules used to control the system.

  • Reference: The law describing how the controlled system must behave.

  • These may be internal to the system or received from a higher hierarchical level.

• Subsystems of Control:

  • Controlling Subsystem: Processes information and generates commands (control messages).

  • Controlled Subsystem: Changes its state based on received messages.

  • Connections: Communication channels between the two.

Loop Architectures: Open vs. Closed

• Open-Loop Control:

  • The execution of commands is not monitored.

  • Utilizes only a forward-coupling connection (transmitting messages from controlling to controlled).

  • Used only when noise is absent and system properties are static.

• Closed-Loop Control:

  • The execution of commands is monitored.

  • Utilizes a back-coupling connection (feedback) to transmit data from the controlled system back to the controller.

  • Used when noise is present or system properties vary.

• Biological Example: The Reflex Arc:

  • Receptors: Transform stimulus into excitation.

  • Afferent (sensory) neurons: Serve as the back-coupling (feedback) channel.

  • Neural center: Functions as the Controlling Subsystem (issues commands).

  • Efferent (motor) neurons: Serve as the forward-coupling channel.

  • Effectors: Respond to commands to produce an action.

Positive Feedback Loops

• Definition: A self-reinforcing loop where control leads to increased divergence in the controlled subsystem.

• Divergence: The difference between the current and preceding states.

• Outcome: The process accelerates until the subsystem reaches its limiting constraints.

• Beneficial Applications:

  • Amplifying vital biological processes.

  • Aiding adaptation by allowing fast transitions to more appropriate states.

  • Example: Food digestion. Digestion products stimulate gastric juice; more juice creates more products; this further increases secretion.

• Detrimental Applications:

  • Aggravating morbid/diseased conditions.

  • Example: Cardiac insufficiency. Reduced blood supply to the heart reduces pumping capacity, which further reduces blood supply, leading to a downward spiral.

  • Example: Stress. Psychological events lead to weight preoccupation and food avoidance. This elevates cortisol, which mobilizes glucose. High blood glucose further suppresses appetite, potentially leading to death without intervention.

Negative Feedback and Homeostasis

• Definition: A self-correcting or balancing loop that leads to the balancing of the controlled subsystem.

• Balancing: Minimizing the difference ($\Delta X$) between the controlled parameter ($X$) and the reference setpoint ($X_0$).

• Significance:

  • Ensures stability, quality, and reliability.

  • Maintains constant values for vital parameters and resistance to external factors.

  • Primary mechanism for Homeostasis, energy/metabolite balance, and population control.

• Control Mechanism:

  • 1. Determine error: $\Delta X = X - X_0$.

  • 2. Generate a control message to reduce $\Delta X$.

• Example: Body Temperature Regulation:

  • If X > X_0 (Overheat): Intesify heat loss (vasodilation, sweating) and reduce heat production (less movement, less food).

  • If X < X_0 (Cold): Reduce heat loss and intensify heat production (shivering, metabolic efficiency).

• Quality of Control: Measured by the Control Area, which is the area between the curves of the reference value and the actual value. Quality is higher when the control area is minimized. Control can be Static or Dynamic.

Scientific Modelling and Simulation

• Model: A simplified physical or mathematical representation of a system used for investigation.

• Modelling: The methods used to study systems via their models.

• Simulation: Represents the operation of a system over time (whereas the model represents the system itself).

• Types of Models:

  • Mathematical Model: Mathematical descriptions and computer algorithms used to generate information about the real system. Example: Modelling blood glucose regulation.

  • Physical Model: A material object that performs similarly to the real system. Example: An electrical circuit representing a nerve fibre.

  • Biological Model: A laboratory animal used to reproduce human body conditions. These require fewer simplifying assumptions than mathematical or physical models. Example: Testing pharmaceuticals, poisons, or infections.

• Training Applications: Medical simulators are used for training in procedures ranging from basic care to laparoscopic surgery and trauma management.