A crumpled surface having transverse attractive interactions as a simplified model with biological significance.

Using extensive analogical simulations with square sheets of paper we investigate the influence of short-range transverse attractive interactions on the packing properties of a crumpled surface. These interactions are due to transverse connections or local bridges associated with a given number of binding sites localized on the two-dimensional surface and distributed in several patterns in the three-dimensional physical space. Geometrical relations and critical exponents describing the statistical properties of the crumpled surface are obtained as a function of the strength of the attractive interactions. Our model suggests how the presence of short-range interactions as, e.g. van der Waals forces can be important for the geometric plasticity of biological molecules, which in turn is important for biological function. The relevance of our results to the study of molecular conformation of proteins and membranes is discussed, and a comparison is also made between the behavior of the crumpled surface studied here and other important non-equilibrium fractal structures.

Yet another application of the Monte Carlo method for modeling in the field of biomedicine.

By means of Monte Carlo simulations performed in the C programming language, an example of scientific programming for the generation of pseudorandom numbers relevant to both teaching and research in the field of biomedicine is presented. The relatively simple algorithm proposed makes possible the statistical analysis of sequences of random numbers. The following three generators of pseudorandom numbers were used: the rand function contained in the stdlib.h library of the C programming language, Marsaglia's generator, and a chaotic function. The statistical properties of the sequences generated were compared, identical parameter values being adopted for this purpose. The properties of two estimators in finite samples of the pseudorandom numbers were also evaluated and, under suitable conditions, both the maximum-likelihood and method of moments proved to be good estimators. The findings demonstrated that the proposed algorithm appears to be suitable for the analysis of data from random experiments, indicating that it has a large variety of possible applications in the clinical practice.

The dynamic activation of colicin Ia channels in planar bilayer lipid membrane.

Dynamic activation of ion channels formed by colicin Ia incorporated into a planar bilayer lipid membrane (BLM) was investigated by the voltage clamp technique using different step voltage stimuli. We have demonstrated a critical resting interval, Deltat(c), between two identical successive voltage pulses. If the second pulse is applied within Deltat(c), it produces a predictable current response. On the contrary, if the second pulse is applied after Deltat(c), the current response cannot be reliably predicted. Computer simulations based on an idealized mathematical model, developed in this paper, qualitatively reproduce the system's dynamic responses to stimulus trains. The behavior of the ion channels, when the resting period exceeds Deltat(c), may be interpreted as a transient gain or loss or resetting of memory, as revealed by a specific sequence of electrical pulses used for stimulation.

Output of a neuronal population code.

In the population coding framework, we consider how the response distributions affect output distribution. A general theory for the output of neuronal population code is presented when the spike train is a renewal process. Under a given condition on the response distribution, the most probable value of the output distribution is the center of input-preferred values, whereas in the other cases the most improbable value of the output distribution is the center of input-preferred values or there are no most probable states. Depending on the exact form of the response distributions, the variance of the output distributions can either enlarge or reduce the tuning width of the tuning curves.