A simple translation in cortical log-coordinates may account for the pattern of saccadic localization errors

During saccadic eye movements, the visual world shifts rapidly across the retina. Perceptual continuity is thought to be maintained by active neural mechanisms that compensate for this displacement, bringing the presaccadic scene into a postsaccadic reference frame. Because of this active mechanism, objects appearing briefly around the time of the saccade are perceived at erroneous locations, a phenomenon called perisaccadic mislocalization. The position and direction of localization errors can inform us about the different reference frames involved. It has been found, for example, that errors are not simply made in the direction of the saccade but directed toward the saccade target, indicating that the compensatory mechanism involves spatial compression rather than translation. A recent study confirmed that localization errors also occur in the direction orthogonal to saccade direction, but only for eccentricities far from the fovea, beyond the saccade target. This spatially specific pattern of distortion cannot be explained by a simple compression of space around the saccade target. Here I show that a change of reference frames (i.e., translation) in cortical (logarithmic) coordinates, taking into account the cortical magnification factor, can accurately predict these spatial patterns of mislocalization. The flashed object projects onto the cortex in presaccadic (fovea-centered) coordinates but is perceived in postsaccadic (target-centered) coordinates.     

A simple model of dynamic receptor pattern generation

A dynamic pattern generating automaton has been constructed. The rules controlling its function furnish the non-random generation of sub-patterns in consecutive cycles, within a large plane area, covered by four different classes of units of constant mean frequency in each class (standard system). The stabilization of certain specific sub-patterns over 100 subsequent cycles of pattern generation (modified systems) resulted in the modification of the frequency and frequency distribution of the sub-patterns relative to the standard system. Some new types of sub-patterns, not encountered in the standard system, also made appearance in the modified systems. The functioning of the standard and modified systems was analyzed and compared by the methods of mathematical statistics. The automaton was used to model certain features of the cytoplasmic membrane. The latter was regarded as a device by which the cell collects information about its environment. The dynamic generation of sub-patterns was taken as the cell's manner of asking questions, and the complementary chemical structures present in the environment were treated as possible answers to these. The irreversible question-answer interactions were regarded as signals and were modelled by the stabilization of specific sub-patterns. It was found that in a dynamic system like the model presented, it is not necessary to code each possible sub-pattern individually. Precise coding of the relative frequency of units per class and of their possible interactions is sufficient to furnish statistically constant mean frequencies for a given range of sub-patterns. In a dynamic system, the actual range of sub-patterns arisen in a population of identical individuals depends only on the size of the population. If the latter is appropriately large, all possible sub-patterns may be simultaneously present at any time at the average frequencies characteristic of each. Stabilized sub-patterns (signals) seem to modify specifically the frequencies of the other sub-patterns generated by the normal automaton. Some sub-patterns may disappear permanently, while others (new ones) may turn up and persist at given frequencies. Missense signals may definitively put the automaton out of order, i.e. result in the cell's complete misorientation in respect of its relations to the normal tissue structure.Reader of publications in physics, Gondolat Publishing House, Budapest, Hungary     

Tests of the simple model of Lin and Brandts for the folding kinetics of ribonuclease A

L.-N. Lin and J.F. Brandts recently proposed a simple model for the folding kinetics of ribonuclease A in which folding intermediates are not detectable. We have tested the basic assumption of the simple model for the major unfolded species, which is produced by a slow isomerization (the "X in equilibrium Y reaction" according to Lin and Brandts) after unfolding. The simple model assumes that in refolding the slow Y----X reaction must occur before any folding can take place. We have measured the Y----X reaction during folding. Tyrosine-detected folding occurs before the Y----X reaction; the difference in rate between the Y----X reaction and folding monitored by tyrosine absorbance becomes large when the stabilizing salt 0.56 M (NH4)2SO4 is added. The simple model predicts that the kinetic properties of the X in equilibrium Y reaction in unfolded ribonuclease are the same as those of tyrosine-detected folding. We find, however, that the kinetics of the X in equilibrium Y reaction in unfolded ribonuclease are independent of urea concentration, whereas the rate of tyrosine-detected folding decreases almost 100-fold between 0.3 and 5 M urea, as reported by Lin and Brandts. We point out that the kinetic properties of the X in equilibrium Y reaction in unfolded ribonuclease are characteristic of proline isomerization.     

A simple semiempirical model for the effect of molecular confinement upon the rate of protein folding

A simple two-state model for the dependence of the rate of folding of a polypeptide confined within a spherical cavity upon the size of the cavity relative to that of the polypeptide is presented. A general prediction of the model is that decreasing the size of the cavity will increase the rate of refolding until the cavity becomes only slightly larger than the native state of the protein, at which point a further decrease in cavity size decreases the rate of refolding. The model qualitatively accounts for the behavior of several previously published simulations of folding within a cavity, as well as recently reported experimental measurements of the relative rate of refolding of each of five proteins encapsulated within wild-type and mutant GroEL-GroES complexes that have been engineered to provide internal cavities with similar surface composition and varying volume.     

A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition

In a recent paper (D. Gront et al., Journal of Chemical Physics, Vol. 115, pp. 1569, 2001) we applied a simple combination of the Replica Exchange Monte Carlo and the Histogram methods in the computational studies of a simplified protein lattice model containing hydrophobic and polar units and sequence-dependent local stiffness. A well-defined, relatively complex Greek-key topology, ground (native) conformations was found; however, the cooperativity of the folding transition was very low. Here we describe a modified minimal model of the same Greek-key motif for which the folding transition is very cooperative and has all the features of the "all-or-none" transition typical of real globular proteins. It is demonstrated that the all-or-none transition arises from the interplay between local stiffness and properly defined tertiary interactions. The tertiary interactions are directional, mimicking the packing preferences seen in proteins. The model properties are compared with other minimal protein-like models, and we argue that the model presented here captures essential physics of protein folding (structurally well-defined protein-like native conformation and cooperative all-or-none folding transition).     

A partially folded intermediate species of the beta-sheet protein apo-pseudoazurin is trapped during proline-limited folding

The folding of apo-pseudoazurin, a 123-residue, predominantly beta-sheet protein with a complex Greek key topology, has been investigated using several biophysical techniques. Kinetic analysis of refolding using far- and near-ultraviolet circular dichroism (UV CD) shows that the protein folds slowly to the native state with rate constants of 0.04 and 0.03 min(-1), respectively, at pH 7.0 and at 15 degrees C. This process has an activation enthalpy of approximately 90 kJ/mole and is catalyzed by cyclophilin A, indicating that folding is limited by trans-cis proline isomerization, presumably around the Xaa-Pro 20 bond that is in the cis isomer in the native state. Before proline isomerization, an intermediate accumulates during folding. This species has a substantial signal in the far-UV CD, a nonnative signal in the near-UV CD, exposed hydrophobic surfaces (judged by 1-anilino naphthalenesulphonate binding), a noncooperative denaturation transition, and a dynamic structure (revealed by line broadening on the nuclear magnetic resonance time scale). We compare the properties of this intermediate with partially folded states of other proteins and discuss its role in folding of this complex Greek key protein.     

A heteropolymer model study for the mechanism of protein folding

A heteropolymer model of randomly self-interacting chains in two dimensions is studied with numerical simulations in order to elucidate the folding mechanism of protein. We find that the model occasionally shows folding propensity depending on the sequence of random numbers given to the chain. We study the thermodynamic and kinematic roles in the folding mechanism by grouping the local energy minima found in the simulations into clusters according to the similarity of their conformations. It is suggested that the local minima to which some heteropolymers show a folding tendency are always the lowest energy states of the energy spectrum within a cluster, though which cluster is selected depends on the sequence. For the eight random sequences we study, we find that the energy gap between the ground state and excited states is little correlated with folding or nonfolding. We rather find that folding propensities are correlated with the global structure of the average energy surface, implying a dominant kinetic role in the folding mechanism, although thermal factors cannot be ignored as the mechanism of choosing the ground state within a cluster of states connected by small deformations. We suggest that a hierarchical cluster structure plays an important role in selecting a unique folded state out of the huge number of local minima of heteropolymers. © 1997 John Wiley & Sons, Inc.     

Alternatively folded choriogonadotropin analogs. Implications for hormone folding and biological activity

Most heterodimeric proteins are stabilized by intersubunit contacts or disulfide bonds. In contrast, human chorionic gonadotropin (hCG) and other glycoprotein hormones are secured by a strand of their beta-subunits that is wrapped around alpha-subunit loop 2 "like a seatbelt." During studies of hCG synthesis in COS-7 cells, we found that, when the seatbelt was prevented from forming the disulfide that normally "latches" it to the beta-subunit, its carboxyl-terminal end can "scan" the surface of the heterodimer and become latched by a disulfide to cysteines substituted for residues in the alpha-subunit. Analogs in which the seatbelt was latched to residues 35, 37, 41-43, and 56 of alpha-subunit loop 2 had similar lutropin activities to those of hCG; that in which it was latched to residue 92 at the carboxyl terminus had 10-20% the activity of hCG. Attachment of the seatbelt to alpha-subunit residues 45-51, 86, 88, 90, and 91 reduced lutropin activity substantially. These findings show that the heterodimer can form before the beta-subunit has folded completely and support the notions that the carboxyl-terminal end of the seatbelt, portions of alpha-subunit loop 2, and the end of the alpha-subunit carboxyl terminus do not participate in lutropin receptor interactions. They suggest also that several different architectures could have been sampled without disrupting hormone activity as the glycoprotein hormones diverged from other cysteine knot proteins.     

A binocular model for the simple cell

We authors propose a mathematical model for simple cell binocular response. It comprises two Gabor-type receptive fields (RF) having the same RF center, preferred spatial frequency, and preferred orientation. The model integrates the equally weighted signals from both eyes and performs a threshold operation. Poggio and Fischer (1977) classified binocular disparity cells in the striate cortex into four groups: tuned excitatory (TE), tuned inhibitory (TI), near, and far cells. They also found that most of the TE cells are ocularly balanced and that the other three types are usually unbalanced. This model can imitate these four types of disparity sensitivities and their ocular dominance tendency. We perform model fittings to Poggio's data using the “simulated annealing” method and discuss parameter dependence of the model's response. The model can also respond with exceptional disparity sensitivity: i.e., flat type, alternating type, and intermediate type.     

A simple model for the arterial system

We present a simple model for the arterial part of the cardiovascular system, based on Poiseuille flow constrained by the power dissipated into the cells lining the vessels. This, together with the assumption of a volume-filling network, leads to correct predictions for the evolution of vessel radii, vessel lengths and blood pressure in the human arterial system. The model can also be used to find exponents for allometric scaling, and gives good agreement with data on mammals.     

Conformational propagation with prion-like characteristics in a simple model of protein folding

Protein refolding/misfolding to an alternative form plays an aetiologic role in many diseases in humans, including Alzheimer's disease, the systemic amyloidoses, and the prion diseases. Here we have discovered that such refolding can occur readily for a simple lattice model of proteins in a propagatable manner without designing for any particular alternative native state. The model uses a simple contact energy function for interactions between residues and does not consider the peculiarities of polypeptide geometry. In this model, under conditions where the normal (N) native state is marginally stable or unstable, two chains refold from the N native state to an alternative multimeric energetic minimum comprising a single refolded conformation that can then propagate itself to other protein chains. The only requirement for efficient propagation is that a two-faced mode of packing must be in the ground state as a dimer (a higher-energy state for this packing leads to less efficient propagation). For random sequences, these ground-state dimeric configurations tend to have more beta-sheet-like extended structure than almost any other sort of dimeric ground-state assembly. This implies that propagating states (such as for prions) are beta-sheet rich because the only likely propagating forms are beta-sheet rich. We examine the details of our simulations to see to what extent the observed properties of prion propagation can be predicted by a simple protein folding model. The formation of the alternative state in the present model shows several distinct features of amyloidogenesis and of prion propagation. For example, an analog of the phenomenon of conformationally distinct strains in prions is observed. We find a parallel between 'glassy' behavior in liquids and the formation of a propagatable state in proteins. This is the first report of simulation of conformational propagation using any heteropolymer model. The results imply that some (but not most) small protein sequences must maintain a sequence signal that resists refolding to propagatable alternative native states and that the ability to form such states is not limited to polypeptides (or reliant on regular hydrogen bonding per se) but can occur for other protein-like heteropolymers.     

A kinetic model of RNA folding

The RNA folding process is represented as a Markov process with states corresponding to RNA secondary structures and transition probabilities corresponding to transformations of a secondary structure caused by formation or disintegration of a helix. Transition probabilities (kinetic constants) are determined. A notion of a group of structures is introduced, and it allows to reduce the state space. Energetic and kinetic parameters of pseudoknots are estimated. Algorithms for computation of a kinetic ensemble for structures and groups of structures are presented, as well as their modifications that take into account pseudoknots. The described algorithms are implemented as a procedure for prediction of RNA secondary structure that is included in the package DNA-SUN.     

A decision tree model for the prediction of homodimer folding mechanism

The formation of protein homodimer complexes for molecular catalysis and regulation is fascinating. The homodimer formation through 2S (2 state), 3SMI (3 state with monomer intermediate) and 3SDI (3 state with dimer intermediate) folding mechanism is known for 47 homodimer structures. Our dataset of forty-seven homodimers consists of twenty-eight 2S, twelve 3SMI and seven 3SDI. The dataset is characterized using monomer length, interface area and interface/total (I/T) residue ratio. It is found that 2S are often small in size with large I/T ratio and 3SDI are frequently large in size with small I/T ratio. Nonetheless, 3SMI have a mixture of these features. Hence, we used these parameters to develop a decision tree model. The decision tree model produced positive predictive values (PPV) of 72% for 2S, 58% for 3SMI and 57% for 3SDI in cross validation. Thus, the method finds application in assigning homodimers with folding mechanism.     

A model for the origin and properties of flicker-induced geometric phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.     

A simple model for gene targeting

Sequence-specific binding to genomic-size DNA sequences by artificial agents is of major interest for the development of gene-targeting strategies, gene-diagnostic applications, and biotechnical tools. The binding of one such agent, peptide nucleic acid (PNA), to a randomized human genome has been modeled with statistical mass action calculations. With the length of the PNA probe, the average per-base binding constant k(0), and the binding affinity loss of a mismatched base pair as main parameters, the specificity was gauged as a "therapeutic ratio" G = maximum safe [PNA](tot)/minimal efficient [PNA](tot). This general, though simple, model suggests that, above a certain threshold length of the PNA, the microscopic binding constant k(0) is the primary determinant for optimal discrimination, and that only a narrow range of rather low k(0) values gives a high therapeutic ratio G. For diagnostic purposes, the value of k(0) could readily be modulated by changing the temperature, due to the substantial Delta H degrees associated with the binding equilibrium. Applied to gene therapy, our results stress the need for appropriate control of the binding constant and added amount of the gene-targeting agent, to meet the varying conditions (ionic strength, presence of competing DNA-binding molecules) found in the cell.     

A simple model for early morphogenesis

Despite the large amount of knowledge which continues to accumulate about early developmental events, very little is known about the processes which control them. Part of the problem may lie in that workers applying different approaches and techniques have different points of view and appear to be reluctant to read each others' literature. My aim in this paper is not to give a generative, formal model for early development, but rather to suggest several connecting strands between the physiological, biochemical, cell biological and experimental embryological approaches which may stimulate new research in fields between those already exploited.     

A simple model for plankton patchiness

Recent work on zooplankton spatial variability shows that thepower spectrum of the wave-number variance is flatter than thatfor chlorophyll, as a consequence of greater fine structurein the herbivores. The relative slopes of the power spectracan result from white noise forcing of simple coupled phytoplankton-herbivoremodels with diffusion.