Connecting Living Systems Through Graphs

There are many ways to look at living systems. Because of this, models of life can vary a lot, both in how they look and what they include. To truly grasp what a living system is about, we need to figure out how these different models connect with each other. In previous efforts, we created a framework to compare any kind of physical models. In this work, we introduce a method that zeroes in on a key aspect of living systems-Self-organization. By using graphs, we represent self-organizing processes as cycles, which help us identify how biological models describe these features.

#Understanding Self-Organization

Living systems are constantly changing and adapting. Think of a tree that grows, responds to sunlight, and sheds leaves in autumn. This ability to change and maintain itself is a fundamental characteristic of life. Our new approach uses graphs to map out how different processes in living systems enable one another. This method allows us to see connections and distinctions among various biological theories.

#The Many Theories of Life

Over many years, thinkers have tried to figure out what life is. Some have proposed theories like autopoiesis and Autocatalytic Sets. These theories might differ in details, but they all look at how living systems sustain themselves. The idea is that living organisms must keep creating and maintaining the conditions needed for their existence.

Some people suggest that we can combine the best bits from these theories into one big theory of life. Others argue that we can’t find a single unifying theory until we find life beyond Earth. This quest for a comprehensive theory is tempting, especially since biology can sometimes seem a bit all over the place. However, some scholars believe that expecting one unified theory is unrealistic due to the complexity of life.

Instead, a pluralistic approach is more promising. This means we should appreciate the different ways we can model living systems. Each model has its strengths and weaknesses, and it’s through comparing these models that we gain real insight into life.

#The Need for Dialogue

Creating different models is good, but we need to make sure they talk to each other. Scientists must engage in discussions to see how their models fit together. They should ask questions like: What does your model show that mine misses? How can we make sense of our differences? Instead of looking for a winner or a single truth, we should keep valuable perspectives available. This way, ongoing dialogue can lead to new insights as time goes on.

Many scholars have begun to compare different theories about life. This paper aims to push that spirit of comparison further by using a mathematical method. By expressing different models in a consistent way, we can compare them.

#Moving from Processes to Graphs

Every model emphasizes different aspects. Some might focus on basic biological processes like metabolism, while others might concentrate on ecosystem interactions. We want to take a closer look at the processes that occur in living systems, using directed graphs to represent the relationships between these processes.

A process-enablement graph helps us capture how different processes interact in real time. For example, a tree takes in sunlight to grow, demonstrating a process that enables its survival.

#What Are Enablements?

To see how processes support each other, we define "enablement." In a system, one process enables another if the first one creates the conditions necessary for the second one to occur. If you remove the first process, the second one can’t happen. This is crucial for understanding how processes in a living system influence each other.

#Building the Process-Enablement Graph

Now, let’s build our process-enablement graph, or P-graph. A P-graph is made up of processes happening together within a system. The connections between these processes show how they enable one another. For example, in a simple food chain, plants produce energy from sunlight, which then enables animals to eat those plants.

With our P-graphs, we can represent various biological processes and their interactions in a structured way, allowing for better comparisons and insights.

#The Concept of Organizational Closure

In this context, organizational closure means that we can find cycles in our graphs that show how processes work together to maintain the system. For a living system to be functional, it must ensure that the processes that keep it alive are interconnected in a way that sustains itself.

Cycles in a P-graph indicate that if you follow the processes along the connections, you can loop back to the starting point, demonstrating that the system maintains its internal conditions.

#Differentiating Processes and Constraints

It’s essential to understand the difference between processes (the activities that happen) and constraints (the limits or rules that govern those processes). While processes can create energy and matter, constraints simply limit what can happen.

Understanding both processes and constraints is vital when studying living systems, as it helps clarify how these systems organize themselves.

#Comparing Graphs

Each P-graph offers one perspective of a system. When comparing two different P-graphs, we can analyze how they visualize the same system. For instance, if a biologist studies a bird, they might create one P-graph, while a chemist studying the same bird might create a different one.

To accurately compare these graphs, we look for homomorphisms-these are mappings that highlight the similarities between different P-graphs while maintaining their unique structures.

#Homorheisms

If a mapping reflects closure, we call it a homorheism. This mapping indicates that the vital features of the processes and cycles in the two graphs correspond, suggesting that these perspectives could both be valid representations of the same underlying system.

#Applying Our Framework

With our framework in place, we can analyze different perspectives across the biological landscape. We will explore three examples to illustrate how our P-graphs can help clarify complex processes.

#Autocatalytic Sets

First, let’s look at autocatalytic sets, which are systems of chemical reactions that enable themselves to produce more of their components. Within this framework, we can create P-graphs to visualize these interactions.

When we analyze these graphs, we can see how certain reactions depend on each other, forming cycles that create a closed system. This helps us understand better how life might have emerged from simple chemical processes.

#Autopoiesis

Next, we explore the concept of autopoiesis-systems that maintain themselves by constantly regenerating their components. In this case, we can also create P-graphs to illustrate how various processes within a living system support one another.

By examining the cycles and connections in these graphs, we can gain insights into how living organisms maintain their boundaries and sustain their existence.

#Viruses

Viruses present a unique challenge because they blur the lines between living and non-living systems. They require a host to reproduce but can exhibit life-like behaviors when inside a host. By creating a P-graph for a virus and its interactions with a host cell, we can better understand how viruses can behave like living systems while still lacking certain characteristics.

#Conclusion

In summary, we have developed a method that utilizes process-enablement graphs as a framework to explore and compare different theories of life. By representing biological processes in a structured way, we can analyze how they enable one another, ultimately enhancing our understanding of life itself.

By combining perspectives from different scientific disciplines, we can create a richer understanding of how living systems operate. This approach will help advance our knowledge of biological processes, the boundaries of life, and the interplay between living and non-living systems.

As we move forward, we must continue to embrace the diversity of perspectives within biology, as this pluralistic approach will guide us towards deeper insights into the nature of life.