A model of myoglobin self-organization

The self-organization of helical regions of myoglobin into a compact tertiary structure is considered on the basis of the hypothesis on the step-wise mechanism of self-organization of protein molecules. It is assumed that the self-organization begins with the formation of “ centers of crystallization ” and proceeds with the growth of one such center or by a sequential collapse of two or more grown centers.Different pathways of self-organization of myoglobin are considered; the most favourable structures corresponding to the greatest number of dehydrated bulky hydroptiobic groups and to all the strongly hydrophilic groups exposed to water are selected at every stage of the given pathway and the others are neglected. One of the two most favourable structures obtained in such a way coincides in rough resolution with the native tertiary structure of protein.     

Spatial self-organization in a cyclic resource-species model

Biological communities are remarkable in their ability to form cooperative ensembles that lead to coexistence through various types of niche partitioning, usually intimately tied to spatial structure. This is especially true in microbial settings where differential expression and regulation of genes allows members of a given species to alter their lifestyle so as to fill a functional role within the community. The resulting species interactions can involve feedback, as in the case of some bacterial consortia that participate in the cooperative degradation of a given resource in a succession of steps and in such a way that certain "later" species provide catalytic support for the primary degrader. We seek to capture the essential features of such spatially extended biological systems by introducing a lattice-based stochastic spatial model (interacting particle system) with cyclic local dynamics. Here, a given site progresses through a sequence of resource and species states in a prescribed order. Furthermore, this succession of states (at a site) is assumed to form a cyclic pattern due to a natural feedback mechanism. We explore conditions under which all the species are able to coexist and consider the extent to which this coexistence requires the development of spatio-temporal patterns, including spiral waves. This self-organization, if it occurs, results when synchronization of the dynamics at the microscopic level leads to macroscopic patterns. These patterns result in consumer-driven resource fluctuations that generate a form of spatio-temporal niche partitioning. As with most models of this complexity, we employ a mixture of mathematical analysis and simulations to develop an understanding of the resulting dynamics.     

Mathematical model for the self-organization of neural networks

Mutual inhibition between neurons combined with a learning principle similar to that proposed by Hebb is shown to secure a powerful selforganizing property for neural networks. Numerical analysis reveals that the system investigated always organizes itself into the same final state from any arbitrarily chosen initial state.     

The spatial form self-organization in the development of Dictyostelium discoideum

The emergence of the developmental axis within the early aggregate Dictyostelium discoideum is analyzed. Macroscopic parameters of physical continuum such as hydrostatic pressure and surface tension are applied to the cell mass. Cell chemotaxis, differential rate of attractant production by the prestalk and prespore cells and attractant diffusion are shown to be sufficient factors for the Dictyostelium slug morphogenesis.     

Modelling the dynamics of biosystems

The need for a more formal handling of biological information processing with stochastic and mobile process algebras is addressed. Biology can benefit this approach, yielding a better understanding of behavioural properties of cells, and computer science can benefit this approach, obtaining new computational models inspired by nature.     

A model for competing polymers leading to their spatial separation

A model for a prebiotic polymer synthesis in a gradient of monomer is presented. In the absence of mutations the synthesis of the polymer proceeds in the region where the monomer concentration is the highest. However if a favorable mutation occurs, the latter accumulates in the high concentration zone and the initial polymer is restricted to a poorer monomer concentration region.     

On the unlikelihood of non-aqueous biosystems

Theunique ability of the solvent liquid water to form polymorphic, 3-dimensional, H-bonded aggregates and solvation envelopes of widely different character (hydrophilic or coulombic hydration and hydrophobic hydration) is anecessary condition for the realization of the levels of order in form and complexity in function required by carbonaceous biotic systems.Woods Hole Oceanographic Institution Contribution No. 2572.     

Generation of oxy radicals in biosystems

Many recent lines of evidence indicate that endogenous free radicals contribute to spontaneous mutagenesis through the direct induction of DNA damage. However, the mechanisms underlying this process are not yet fully understood. A brief overview of the knowledge that is currently available is provided here, with emphasis on the generation of oxy radicals in biosystems, the reactions of those radicals with biomolecules, and the induction of oxidative DNA base damage that might lead to mutation.     

A continuous migration model with stable demography

A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x–y) where V(x) V(x/)/ ² approaches a delta function, the equilibrium probability of identity vanishes as 0. The asymptotic rate at which this occurs is discussed for mutation rates u u _o > 0 and for Cu , > 0, and u 0.Partially supported by NSF grant MCS79-03472Research was partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Dept. Energy and the University of Washington     

Mathematical model for self-organization of direction columns in the primate middle temporal area

We attempted to reproduce modular structures for direction selectivity characteristic of the primate middle temporal area (MT) based on our thermodynamic model for the activity-dependent self-organization of neural networks. We assumed that excitatory afferent input to MT neurons arises from V1 and/or V2 neurons which are selective to both orientation of a visual stimulus and direction of its motion, and that such input is modifiable and becomes selectively connected through the process of self-organization. By contrast, local circuit connections within MT are unmodifiable and remain nonselectively connected (isotropic). The present simulations reproduced characteristic patterns of organization in the cortex of MT in that: (1) preferred directions of the afferent input gradually shifted, except for singularity lines where direction abruptly changed by 180°; (2) model MT neurons located between the singularity lines responded to unidirectionally moving stimuli, closely reflecting preferred direction of the afferent input; (3) neurons responding to stimuli moving in two opposite directions were located along the singularity lines; and (4) neurons responding to stimuli moving in any direction were clustered at the ends of the singularity lines. When the strength of the lateral inhibition was decreased, direction selectivity of MT neurons was reduced. Therefore, the lateral inhibition, even if isotropic, strengthens the direction selectivity of MT neurons. Expression of singularities changed depending on a parameter that represents the relative dominance of the direction selectivity to the orientation selectivity of the afferent input. When the direction selectivity was predominant, singularity points were formed, while when the orientation selectivity prevailed, the MT was covered by two-dimensional singularity networks. Line singularities similar to those experimentally observed were reproduced when these two types of selectivity were in balance. Received: 15 October 1992/Accepted in revised form: 27 June 1993     

Model of active peristaltic transport in biosystems

A nonlinear distributed mathematical model of a soft vessel with a nonmonotonic static characteristic is proposed and considered. The model describes space-time dynamics of the vascular lumen. Wave phenomena in vessels of different nature and the possibility of peristaltic fluid pumping are discussed and analyzed. The model is quite general in character and represents a broad class of transport phenomena. Lymphatic vessels are considered as an example.     

Time-dependent covariates in the proportional subdistribution hazards model for competing risks

Separate Cox analyses of all cause-specific hazards are the standard technique of choice to study the effect of a covariate in competing risks, but a synopsis of these results in terms of cumulative event probabilities is challenging. This difficulty has led to the development of the proportional subdistribution hazards model. If the covariate is known at baseline, the model allows for a summarizing assessment in terms of the cumulative incidence function. black Mathematically, the model also allows for including random time-dependent covariates, but practical implementation has remained unclear due to a certain risk set peculiarity. We use the intimate relationship of discrete covariates and multistate models to naturally treat time-dependent covariates within the subdistribution hazards framework. The methodology then straightforwardly translates to real-valued time-dependent covariates. As with classical survival analysis, including time-dependent covariates does not result in a model for probability functions anymore. Nevertheless, the proposed methodology provides a useful synthesis of separate cause-specific hazards analyses. We illustrate this with hospital infection data, where time-dependent covariates and competing risks are essential to the subject research question.     

An abstract cell model that describes the self-organization of cell function in living systems

The principal aim of systems biology is to search for general principles that govern living systems. We develop an abstract dynamic model of a cell, rooted in Mesarovi? and Takahara's general systems theory. In this conceptual framework the function of the cell is delineated by the dynamic processes it can realize. We abstract basic cellular processes, i.e., metabolism, signalling, gene expression, into a mapping and consider cell functions, i.e., cell differentiation, proliferation, etc. as processes that determine the basic cellular processes that realize a particular cell function. We then postulate the existence of a 'coordination principle' that determines cell function. These ideas are condensed into a theorem: If basic cellular processes for the control and regulation of cell functions are present, then the coordination of cell functions is realized autonomously from within the system. Inspired by Robert Rosen's notion of closure to efficient causation, introduced as a necessary condition for a natural system to be an organism, we show that for a mathematical model of a self-organizing cell the associated category must be cartesian closed. Although the semantics of our cell model differ from Rosen's (M,R)-systems, the proof of our theorem supports (in parts) Rosen's argument that living cells have non-simulable properties. Whereas models that form cartesian closed categories can capture self-organization (which is a, if not the, fundamental property of living systems), conventional computer simulations of these models (such as virtual cells) cannot. Simulations can mimic living systems, but they are not like living systems.