Neuronal Fractal Dynamics.

Synapse formation is a unique biological phenomenon. The molecular biological perspective of this phenomenon is different from the fractal geometrical one. However, these perspectives are not mutually exclusive and supplement each other. The cornerstone of the first one is a chain of biochemical reactions with the Markov property, that is, a deterministic, conditional, memoryless process ordered in time and in space, in which the consecutive stages are determined by the expression of some regulatory proteins. The coordination of molecular and cellular events leading to synapse formation occurs in fractal time space, that is, the space that is not only the arena of events but also actively influences those events. This time space emerges owing to coupling of time and space through nonlinear dynamics. The process of synapse formation possesses fractal dynamics with non-Gaussian distribution of probability and a reduced number of molecular Markov chains ready for transfer of biologically relevant information.

Computer-Aided Image Analysis and Fractal Synthesis in the Quantitative Evaluation of Tumor Aggressiveness in Prostate Carcinomas.

The subjective evaluation of tumor aggressiveness is a cornerstone of the contemporary tumor pathology. A large intra- and interobserver variability is a known limiting factor of this approach. This fundamental weakness influences the statistical deterministic models of progression risk assessment. It is unlikely that the recent modification of tumor grading according to Gleason criteria for prostate carcinoma will cause a qualitative change and improve significantly the accuracy. The Gleason system does not allow the identification of low aggressive carcinomas by some precise criteria. The ontological dichotomy implies the application of an objective, quantitative approach for the evaluation of tumor aggressiveness as an alternative. That novel approach must be developed and validated in a manner that is independent of the results of any subjective evaluation. For example, computer-aided image analysis can provide information about geometry of the spatial distribution of cancer cell nuclei. A series of the interrelated complexity measures characterizes unequivocally the complex tumor images. Using those measures, carcinomas can be classified into the classes of equivalence and compared with each other. Furthermore, those measures define the quantitative criteria for the identification of low- and high-aggressive prostate carcinomas, the information that the subjective approach is not able to provide. The co-application of those complexity measures in cluster analysis leads to the conclusion that either the subjective or objective classification of tumor aggressiveness for prostate carcinomas should comprise maximal three grades (or classes). Finally, this set of the global fractal dimensions enables a look into dynamics of the underlying cellular system of interacting cells and the reconstruction of the temporal-spatial attractor based on the Taken's embedding theorem. Both computer-aided image analysis and the subsequent fractal synthesis could be performed effectively using the standardized software implemented on the world internet platform. This platform should help to verify the quantitative criteria for the identification of indolent prostate cancers or highly aggressive cancers as well as to test the improved statistical models for progression risk assessment within a single prospective study.

The Quantitative Criteria Based on the Fractal Dimensions, Entropy, and Lacunarity for the Spatial Distribution of Cancer Cell Nuclei Enable Identification of Low or High Aggressive Prostate Carcinomas.

BACKGROUND: Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell nuclei in a larger, independent set of prostate carcinomas. METHODS: The global fractal capacity D 0, information D 1 and correlation D 2 dimension, the local fractal dimension (LFD) and the local connected fractal dimension (LCFD), Shannon entropy H and lacunarity λ were measured using computer algorithms in digitalized images of both the reference set (n = 60) and the test set (n = 208) of prostate carcinomas. RESULTS: Prostate carcinomas were re-stratified into seven classes of equivalence. The cut-off D 0-values 1.5450, 1.5820, 1.6270, 1.6490, 1.6980, 1.7640 defined the classes from C1 to C7, respectively. The other measures but the D 1 failed to define the same classes of equivalence. The pairs (D 0, LFD), (D 0, H), (D 0, λ), (D 1, LFD), (D 1, H), (D 1, λ) characterized the spatial distribution of cancer cell nuclei in each class. The co-application of those measures enabled the subordination of prostate carcinomas to one out of three clusters associated with different tumor aggressiveness. For D 0 < 1.5820, LFD < 1.3, LCFD > 1.5, H < 0.7, and λ > 0.8, the class C1 or C2 contains low complexity low aggressive carcinomas exclusively. For D 0 > 1.6980, LFD > 1.7644, LCFD > 1.7051, H > 0.9, and λ < 0.7, the class C6 or C7 contains high complexity high aggressive carcinomas. CONCLUSIONS: The cut-off D 0-values defining the classes of equivalence were validated in this study. The cluster analysis suggested that the number of the subjective Gleason grades and the number of the objective classes of equivalence could be decreased from seven to three without a loss of clinically relevant information. Two novel quantitative criteria based on the complexity and the diversity measures enabled the identification of low or high aggressive prostate carcinomas and should be verified in the future multicenter, randomized studies.

On complexity and homogeneity measures in predicting biological aggressiveness of prostate cancer; Implication of the cellular automata model of tumor growth.

BACKGROUND AND OBJECTIVES: We propose a novel approach for the quantitative evaluation of aggressiveness in prostate carcinomas. METHODS: The spatial distribution of cancer cell nuclei was characterized by the global spatial fractal dimensions D0, D1, and D2. Two hundred eighteen prostate carcinomas were stratified into the classes of equivalence using results of ROC analysis. A simulation of the cellular automata mix defined a theoretical frame for a specific geometric representation of the cell nuclei distribution called a local structure correlation diagram (LSCD). The LSCD and dispersion Hd were computed for each carcinoma. Data mining generated some quantitative criteria describing tumor aggressiveness. RESULTS: Alterations in tumor architecture along progression were associated with some changes in both shape and the quantitative characteristics of the LSCD consistent with those in the automata mix model. Low-grade prostate carcinomas with low complexity and very low biological aggressiveness are defined by the condition D0 < 1.545 and Hd < 38. High-grade carcinomas with high complexity and very high biological aggressiveness are defined by the condition D0 > 1.764 and Hd < 38. CONCLUSIONS: The novel homogeneity measure Hd identifies carcinomas with very low aggressiveness within the class of complexity C1 or carcinomas with very high aggressiveness in the class C7.

Methylation analysis of histone H4K12ac-associated promoters in sperm of healthy donors and subfertile patients.

BACKGROUND: Histone to protamine exchange and the hyperacetylation of the remaining histones are hallmarks of spermiogenesis. Acetylation of histone H4 at lysine 12 (H4K12ac) was observed prior to full decondensation of sperm chromatin after fertilization suggesting an important role for the regulation of gene expression in early embryogenesis. Similarly, DNA methylation may contribute to gene silencing of several developmentally important genes. Following the identification of H4K12ac-binding promoters in sperm of fertile and subfertile patients, we aimed to investigate whether the depletion of histone-binding is associated with aberrant DNA methylation in sperm of subfertile men. Furthermore, we monitored the transmission of H4K12ac, 5-methylcytosine (5mC) and 5-hydroxymethylcytosine (5hmC) from the paternal chromatin to the embryo applying mouse in vitro fertilization and immunofluorescence. RESULTS: Chromatin immunoprecipitation (ChIP) with anti-H4K12ac antibody was performed with chromatin isolated from spermatozoa of subfertile patients with impaired sperm chromatin condensation assessed by aniline blue staining. Fertile donors were used as control. DNA methylation analysis of selected H4K12ac-interacting promoters in spermatozoa was performed by pyrosequencing. Depletion of binding sites for H4K12ac was observed within the following developmentally important promoters: AFF4, EP300, LRP5, RUVBL1, USP9X, NCOA6, NSD1, and POU2F1. We found 5% to 10% hypomethylation within CpG islands of selected promoters in the sperm of fertile donors, and it was not significantly altered in the subfertile group. Our results demonstrate that the H4K12ac depletion in selected developmentally important promoters of subfertile patients was not accompanied by a change of DNA methylation. Using a murine model, immunofluorescence revealed that H4K12ac co-localize with 5mC in the sperm nucleus. During fertilization, when the pronuclei are formed, the paternal pronucleus exhibits a strong acetylation signal on H4K12, while in the maternal pronucleus, there is a permanent increase of H4K12ac until pronuclei fusion. Simultaneously, there is an increase of the 5hmC signal and a decrease of the 5mC signal. CONCLUSIONS: We suggest that aberrant histone acetylation within developmentally important gene promoters in subfertile men, but not DNA methylation, may reflect insufficient sperm chromatin compaction affecting the transfer of epigenetic marks to the oocyte.

On the relationship between tumor structure and complexity of the spatial distribution of cancer cell nuclei: a fractal geometrical model of prostate carcinoma.

BACKGROUND: A risk of the prostate cancer patient is defined by both the objective and subjective criteria, that is, PSA concentration, Gleason score, and pTNM-stage. The subjectivity of tumor grading influences the risk assessment owing to a large inter- and intra-observer variability. Pathologists propose a central prostate pathology review as a remedy for this problem; yet, the review cannot eliminate the subjectivity from the diagnostic algorithm. The spatial distribution of cancer cell nuclei changes during tumor progression. It implies changes in complexity measured by the capacity dimension D0, the information dimension D1, and the correlation dimension D2. METHODS: The cornerstone of the approach is a model of prostate carcinomas composed of the circular fractals CF(4), CF(6 + 0), and CF(6 + 1). This model is both geometrical and analytical, that is, its structure is well-defined, the capacity fractal dimension D0 can be calculated for the infinite circular fractals, and the dimensions D0, D1, D2 can be computed for their finite counterparts representing distribution of cell nuclei. The model enabled both the calibration of the software and the validation of the measurements in 124 prostate carcinomas. The ROC analysis defined the cut-off D0 values for seven classes of complexity. RESULTS: The Gleason classification matched in part with the classification based on the D0 values. The mean ROC sensitivity was 81.3% and the mean ROC specificity 75.2%. Prostate carcinomas were re-stratified into seven classes of complexity according to their D0 values. This increased both the mean ROC sensitivity and the mean ROC specificity to 100%. All homogeneous Gleason patterns were subordinated to the class C1, C4, or C7. D0 = 1.5820 was the cut-off D0 value between the complexity class C2 and C3 representing low-risk cancers and intermediate-risk cancers, respectively. CONCLUSIONS: The global fractal dimensions eliminate the subjectivity in the diagnostic algorithm of prostate cancer. Those complexity measures enable the objective subordination of carcinomas to the well-defined complexity classes, and define subgroups of carcinomas with very low malignant potential (complexity class C1) or at a large risk of progression (complexity ass C7).

Expression of the Bcl-2 family genes and complexes involved in the mitochondrial transport in prostate cancer cells.

Alteration of molecular pathways triggering apoptosis gives raise to various pathological tissue processes, such as tumorigenesis. The mitochondrial pathway is regulated by both the genes of the Bcl-2 family and the genes encoding mitochondrial transport molecules. Those proteins allow a release of cyctochrome c through the outer mitochondrial membrane. This release activates the caspase cascade resulting in death of cells. There are at least two main transport systems associated with the family of Bcl-2 proteins that are involved in transport of molecules through the outer mitochondrial membrane, i.e., the voltage dependent anion channels (VDACs) and translocases of the outer mitochondrial membrane proteins (TOMs). We investigated the expression of genes of the Bcl-2 family, i.e., pro-apoptotic Bak and Bid, and anti-apoptotic Bcl-2; VDAC gene, i.e., VDAC1, VDAC2 and VDAC3; and TOMM genes, i.e., TOMM20, TOMM22 and TOMM40. This study was performed at the mRNA and the protein level. Fourteen paraffin embedded prostate cancer tissues and five normal prostate tissues were analyzed by the quantitative PCR array and immunohistochemistry. We found a significant increase in both mRNA expression of the anti-apoptotic Bcl-2 gene and VDAC1 gene in prostate cancer tissue in comparison with their normal counterparts. Translation of the anti-apoptotic Bcl-2 and VDAC1 genes in prostate cancer tissue was slightly increased. We observed no significant differences in the mRNA expression of the pro-apoptotic Bak and Bid genes, VDAC2 or VDAC3 genes or the three TOMM genes in these tissues. The pro-apoptotic Bax protein was downtranslated significantly in secretory cells of prostate cancer as compared to normal prostate. We suggest that this protein is a good candidate as biomarker for prostate cancer.

Reducing infection rates after prostate biopsy.

Over the years, prostate biopsy has become the gold-standard technique for diagnosing prostate carcinoma. Worldwide, several million prostate biopsies are performed every year, most commonly using the transrectal approach. Preoperative antibiotic prophylaxis with fluoroquinolones has been shown to be effective for reducing infection rates. However, in recent years, an increase in febrile infection rates after transrectal prostate biopsy (from 1% to 4%) has been reported in retrospective and prospective studies. The predominant risk factor for infection seems to be the presence of fluoroquinolone-resistant bacteria in faeces. Patients at risk of fluoroquinolone resistance should receive carefully selected antibiotics at sufficient concentrations to be effective. Targeted prophylaxis after rectal flora swabbing has been shown to be efficacious compared with empirical antibiotic prophylaxis. Several forms of bowel preparations are under investigation, although none have yet been shown to significantly reduce infection rates. Perineal prostate biopsy is currently being evaluated as a strategy for preventing the inoculation of rectal flora, but limited data support this approach at present.

Prospective evaluation of interobserver variability of the hydronephrosis index and the renal resistive index as sonographic examination methods for the evaluation of acute hydronephrosis.

OBJECTIVE: To confirm the reliability of assessements of the renal resistive index (RRI) and the hydronephrosis index (HI) comprising two sonographic techniques providing additional information in patients with acute renal colic. PATIENTS AND METHODS: Sonographic measurement of hydronephrosis and assessment of common clinical criteria was performed in 22 consecutive patients presenting with unilateral stone-related renal colic. RRI and HI were separately recorded by two investigators within a prospective study. Interobserver agreement and comparison of sonographic with computed tomography (CT) findings were assessed with the Cohen's kappa statistic (κ) for attributive ordinal characteristics and Spearman's rank correlation/rho (ρ) for attributive metric characteristics. RESULTS: There was a significant correlation between HI and the sonographically-evaluated grade of hydronephrosis, although not between RRI and the grade of hydronephrosis. For all procedures (RRI, HI, sonography and CT), significant differences between the symptomatic and the asymptomatic kidney were assessed. Interobserver agreement was excellent for the grade assessment of hydronephrosis by conventional sonography (κ = 0.82; P < 0.001), good to very good for HI (ρ = 0.60; P = 0.003) and acceptable to good for RRI (ρ = 0.49; P = 0.021). CONCLUSIONS: The RRI and HI methods are both easily practicable as stageless examination methods in patients presenting with stone-related renal colic, and both also reliably distinguish between obstruction and non-obstruction. Exact thresholds for both methods must still be defined based on further successive studies. Additionally, changes of values under medical expulsive therapy and correlation with the functional status of the obstructed kidney remain to be examined.

A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization.

The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.

On time-space of nonlinear phenomena with Gompertzian dynamics.

This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

Neuronal differentiation and synapse formation occur in space and time with fractal dimension.

The analysis of a set of experimental data obtained by an independent team of researchers confirms that neuronal differentiation or synapse formation do occur in time and space with fractal dimension. The interacting cells create first a dynamic system with its own attractor, (i.e., a fragment of time and space where the dynamic processes occur and where no further evolution of the system is possible at all owing to the action of the intrasystemic forces unless some extrasystemic forces act upon it). This attractor is then modified in the active manner by the differentiating cells until the system attains a degenerated stationary state and differentiation ends. The fractal structure of the system is also lost in the course of tumor progression. Our data indicate that the cellular system can attain the degenerated stationary state, leaving the attractor with a fractal dimension directly or undergoing diversification into many attractors and going through the areas of deterministic chaos. Since evolution of the cellular system is driven by the cooperative dynamic processes, as reflected by the changes of the mean fractal dimension between the intervals of the Gompertzian curve, it is likely that cells differentiate into neurons and create synapses with a conjugated probability and non-Gaussian distribution rather than with the classical probability and the Gaussian distribution. These findings can help to optimize features of artificial neural networks. They also define a simple in vitro biological model for biophysical and biochemical studies on natural neural networks.