Relations In Biological Systems Research Articles

Revisiting neural information, computing and linking capacity.

Neural information theory represents a fundamental method to model dynamic relations in biological systems. However, the notion of information, its representation, its content and how it is processed are the subject of fierce debates. Since the limiting capacity of neuronal links strongly depends on how neurons are hypothesized to work, their operating modes are revisited by analyzing the differences between the results of the communication models published during the past seven decades and those of the recently developed generalization of the classical information theory. It is pointed out that the operating mode of neurons is in resemblance with an appropriate combination of the formerly hypothesized analog and digital working modes; furthermore that not only the notion of neural information and its processing must be reinterpreted. Given that the transmission channel is passive in Shannon's model, the active role of the transfer channels (the axons) may introduce further transmission limits in addition to the limits concluded from the information theory. The time-aware operating model enables us to explain why (depending on the researcher's point of view) the operation can be considered either purely analog or purely digital.

A gentle introduction to scaling relations in biological systems

In this paper it is presented a gentle review of empirical and theoretical advances in understanding the role of size in biological organisms. More specifically, it deals with how the energy demand, expressed by the metabolic rate, changes according to the mass of an organism. Empirical evidence suggests a power-law relation between mass and metabolic rate, namely the allometric equation. For vascular organisms, the exponent β of this power-law is smaller than one, which implies scaling economy; that is, the greater the organism is, the lesser energy per cell it demands. However, the numerical value of this exponent is a theme of extensive debate and a central issue in comparative physiology. A historical perspective is shown, beginning with the first empirical insights in the sec. 19 about scaling properties in biology, passing through the two more important theories that explain the scaling properties quantitatively. Firstly, the Rubner model considers organism surface area and heat dissipation to derive β=2/3. Secondly, the West-Brown-Enquist theory explains such scaling properties due to the hierarchical and fractal nutrient distribution network, deriving β=3/4.

Input-output relations in biological systems: measurement, information and the Hill equation

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system’s overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.ReviewersThis article was reviewed by Eugene Koonin, Georg Luebeck and Sergei Maslov.

About the correspondences between dual heyting arrow lattices of a distributive lattice and its sublattices for relational biologic systems

Heyting and dual Heyting arrow operations relating non-comparable elements of finite relatively pseudo-complemented lattices being pseudo-Boolean algebras ( L) gave place to new structures named Heyting arrow ( L F ) and dual Heyting arrow lattices ( L F) (though sometimes they are only posets). They were used for analyzing qualitative relations in biological systems by means of isomorphisms relating the lattice elements with energy states identified through abstract relational concepts describing the system being represented. This paper considers the problem of connecting the poset L F with the posets L F (κ) corresponding to the epimorphic images L κ of a pseudo-Boolean lattice L.

Correspondences between the Heyting arrow lattices of a distributive lattice and its sublattices in relational biologic systems

Qualitative relations in biological systems were studied by means of lattices. The first representations gave place to finite pseudo-Boolean algebras. The Heyting arrow operation relating noncomparable elements of the lattices ( L) allowed the definition of a new one: the Heyting arrow lattice ( L F ). Owing to the fact that the lattice elements are isomorphically related with states of the system being represented, then the Heyting operation is isomorphically related with enhancements of energy. This paper considers the problem of connecting the lattice L F with the lattices L F ( i) corresponding to the epimorphic images L i of L.

The Whitman condition in the Heyting arrow lattice for relational biologic processes

Qualitative relations in biological systems have been studied by means of lattices. The first representations gave place to finite pseudo-Boolean algebras. The Heyting arrow operation relating noncomparable elements of the lattices allowed the definition of a new one: the Heyting arrow lattice. Being the elements of the lattices expressed in energetic terms, enhancements of energy in the systems the represent were associated with the Heyting operation. The requirements of improving the knowledge about the meaning of this arrow in the representations, led to analyze the mathematical properties of the Heyting arrow lattice. The Whitman condition is considered in this paper.

Semidistributivity in the Heyting arrow lattice for relational biologic processes

Lattices have been used to study qualitative relations in biological systems. The resulting lattices are pseudo-Boolean algebras. The Heyting arrow operation between noncomparable elements of the original lattices gives place to a new one named the Heyting arrow lattice L F . The elements of these lattices are considered relational states of the systems being represented and they are expressed in terms of energy. In connection with this, the Heyting arrow has been related to enhancements of energy in the system. In order to know more about the meaning of this type of energetical variations, mathematical properties of L F are being studied. In this paper, the condition of semidistributivity is analyzed.

The dual Heyting arrow lattice for biologic relational processes

Qualitative relations in biological systems were studied by means of lattices. The first main representations gave place to lattices being double pseudo-Boolean algebras. So, close to the poset which defined the lattices, two operations appeared: the Heyting arrow and the dual Heyting arrow. Both are important to relate noncomparable elements in terms of processes concerned with increasing and decreasing energies in the system, as results from the order defining the poset which considers the lattice elements as relational energetic states. The present developments find out mathematical properties of lattice structures satisfying dual Heyting arrow operations between noncomparable elements.

The Heyting arrow lattice for qualitative relations in biological systems

Previous developments to study qualitative relations in biological systems were made by means of lattices, which resulted in pseudo-Boolean algebras. The Heyting arrow operation being obtained is considered particularly useful to study qualitative relations between non-comparable elements of the lattices. This operation involves enhancements of energy in the systems. Accordingly, the lattice built with the results of the Heyting arrow operation between non-comparable elements of pseudo-Boolean algebras is defined. The first properties of this lattice are found, and they are connected with the sets of closed and dense elements of the original algebra.