184,545 research outputs found
Relative Entropy in Biological Systems
In this paper we review various information-theoretic characterizations of
the approach to equilibrium in biological systems. The replicator equation,
evolutionary game theory, Markov processes and chemical reaction networks all
describe the dynamics of a population or probability distribution. Under
suitable assumptions, the distribution will approach an equilibrium with the
passage of time. Relative entropy - that is, the Kullback--Leibler divergence,
or various generalizations of this - provides a quantitative measure of how far
from equilibrium the system is. We explain various theorems that give
conditions under which relative entropy is nonincreasing. In biochemical
applications these results can be seen as versions of the Second Law of
Thermodynamics, stating that free energy can never increase with the passage of
time. In ecological applications, they make precise the notion that a
population gains information from its environment as it approaches equilibrium.Comment: 20 page
Flexible temperature probe for biological systems
Probe is sufficiently flexible so that it can be worn comfortably for long periods of time, but relatively rigid to permit easy insertion. Body and electrical leads of small thermistor are imbedded in flexible fluorosilicone matrix contained in vinyl plastic tubing
Protention and retention in biological systems
This paper proposes an abstract mathematical frame for describing some
features of cognitive and biological time. We focus here on the so called
"extended present" as a result of protentional and retentional activities
(memory and anticipation). Memory, as retention, is treated in some physical
theories (relaxation phenomena, which will inspire our approach), while
protention (or anticipation) seems outside the scope of physics. We then
suggest a simple functional representation of biological protention. This
allows us to introduce the abstract notion of "biological inertia".Comment: This paper was made possible only as part of an extended
collaboration with Francis Bailly (see references), a dear friend and
"ma\^itre \'a penser", who contributed to the key ideas. Francis passed away
in february 2008: we continue here our inspiring discussions and joint wor
Boolean Models of Bistable Biological Systems
This paper presents an algorithm for approximating certain types of dynamical
systems given by a system of ordinary delay differential equations by a Boolean
network model. Often Boolean models are much simpler to understand than complex
differential equations models. The motivation for this work comes from
mathematical systems biology. While Boolean mechanisms do not provide
information about exact concentration rates or time scales, they are often
sufficient to capture steady states and other key dynamics. Due to their
intuitive nature, such models are very appealing to researchers in the life
sciences. This paper is focused on dynamical systems that exhibit bistability
and are desc ribedby delay equations. It is shown that if a certain motif
including a feedback loop is present in the wiring diagram of the system, the
Boolean model captures the bistability of molecular switches. The method is
appl ied to two examples from biology, the lac operon and the phage lambda
lysis/lysogeny switch
Modeling delayed processes in biological systems
Delayed processes are ubiquitous in biological systems and are often
characterized by delay differential equations (DDEs) and their extension to
include stochastic effects. DDEs do not explicitly incorporate intermediate
states associated with a delayed process but instead use an estimated average
delay time. In an effort to examine the validity of this approach, we study
systems with significant delays by explicitly incorporating intermediate steps.
We show by that such explicit models often yield significantly different
equilibrium distributions and transition times as compared to DDEs with
deterministic delay values. Additionally, different explicit models with
qualitatively different dynamics can give rise to the same DDEs revealing
important ambiguities. We also show that DDE-based predictions of oscillatory
behavior may fail for the corresponding explicit model
Formal executable descriptions of biological systems
The similarities between systems of living entities and systems of concurrent processes may support biological experiments in silico. Process calculi offer a formal framework to describe biological systems, as well as to analyse their behaviour, both from a qualitative and a quantitative point of view. A couple of little examples help us in showing how this can be done. We mainly focus our attention on the qualitative and quantitative aspects of the considered biological systems, and briefly illustrate which kinds of analysis are possible. We use a known stochastic calculus for the first example. We then present some statistics collected by repeatedly running the specification, that turn out to agree with those obtained by experiments in vivo. Our second example motivates a richer calculus. Its stochastic extension requires a non trivial machinery to faithfully reflect the real dynamic behaviour of biological systems
Effective simulation techniques for biological systems
In this paper we give an overview of some very recent work on the stochastic simulation of systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the Balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and discuss how novel computing implementations can enhance the performance of these simulations
Entropy and biological systems: experimentally-investigated entropy-driven stacking of plant photosynthetic membranes
According to the Second Law of thermodynamics, an overall increase of entropy contributes to the driving force for any physicochemical process, but entropy has seldom been investigated in biological systems. Here, for the first time, we apply Isothermal Titration Calorimetry (ITC) to investigate the Mg21-induced spontaneous stacking of photosynthetic membranes isolated from spinach leaves. After subtracting a large endothermic interaction of MgCl2 with membranes, unrelated to stacking, we demonstrate that the enthalpy
change (heat change at constant pressure) is zero or marginally positive or negative. This first direct experimental evidence strongly suggests that an entropy increase significantly drives membrane stacking in
this ordered biological structure. Possible mechanisms for the entropy increase include: (i) the attraction between discrete oppositely-charged areas, releasing counterions; (ii) the release of loosely-bound water molecules from the inter-membrane gap; (iii) the increased orientational freedom of previously-aligned
water dipoles; and (iv) the lateral rearrangement of membrane components.This work was supported consecutively by Australian Research Council grants (DP0664719 and DP 1093927)
COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS
The ability to simulate a biological organism by employing a computer is related to the
ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b)
for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)
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