Simple neural networks for the amplification and utilization of small changes in neuron firing rates.

I describe physiologically plausible "voter-coincidence" neural networks such that secondary "coincidence" neurons fire on the simultaneous receipt of sufficiently large sets of input pulses from primary sets of neurons. The networks operate such that the firing rate of the secondary, output neurons increases (or decreases) sharply when the mean firing rate of primary neurons increases (or decreases) to a much smaller degree. In certain sensory systems, signals that are generally smaller than the noise levels of individual primary detectors, are manifest in very small increases in the firing rates of sets of afferent neurons. For such systems, this kind of network can act to generate relatively large changes in the firing rate of secondary "coincidence" neurons. These differential amplification systems can be cascaded to generate sharp, "yes-no" spike signals that can direct behavioral responses.

A model of the detection of warmth and cold by cutaneous sensors through effects on voltage-gated membrane channels.

Warmth and cold sensations are known to derive from separate warm and cold cutaneous thermoreceptors in the form of differentiated afferent nerves. The firing rate of warm-sensing nerves increases as the temperature increases; the firing rate of cold-sensing nerves increases if the temperature is reduced. I postulate that the primary sensitivity of the warm sensors derives from voltage-gated Ca(2+) membrane channels configured such that an increase in temperature opens channels and increases the ion influx while a reduction in temperature increases the ion influx through voltage-gated Na(+) channels in the cold sensory nerve ends. In either case, the initial cation influx causes a small cellular depolarization that further opens Ca(2+) channels, admitting more cations in a positive feedback process that leads to the depolarization of the membrane, thus initiating an action potential pulse. Monte Carlo calculations based on a well defined model of such processes, which include effects of noise, demonstrate quantitative agreement of the model with an extensive body of data.

Effects of very weak magnetic fields on radical pair reformation.

We can expect that biological responses to very weak ELF electromagnetic fields will be masked by thermal noise. However, the spin of electrons bound to biologically important molecules is not strongly coupled to the thermal bath, and the effects of the precession of those spins by external magnetic fields is not bounded by thermal noise. Hence, the known role of spin orientation in the recombination of radical pairs (RP) may constitute a mechanism for the biological effects of very weak fields. That recombination will generally take place only if the valence electrons in the two radicals are in a singlet state and the effect of the magnetic field is manifest through differential spin precessions that affect the occupation of that state. Because the spin relaxation times are of the order of microseconds, any effects must be largely independent of frequency up to values of a few megahertz. Using exact calculations on an appropriately general model system, we show that one can expect small, but significant, modifications of the recombination rate by a 50 microT field only under a narrow range of circumstances: the cage time during which the two elements are together must be exceptionally long--of the order of 50 ns or longer; the hyperfine field of either radical must not be so great as to generate a precession period greater than the cage containment time; and the characteristic recombination time of the radical pair in the singlet state must be about equal to the containment time. Thus, even under such singularly favorable conditions, fields as small as 5 microT (50 milligauss) cannot change the recombination rate by as much as 1%. Hence, we conclude that environmental magnetic fields much weaker than the earth's field cannot be expected to affect biology significantly by modifying radical pair recombination probabilities.

Theoretical limits on the threshold for the response of long cells to weak extremely low frequency electric fields due to ionic and molecular flux rectification.

Understanding exposure thresholds for the response of biological systems to extremely low frequency (ELF) electric and magnetic fields is a fundamental problem of long-standing interest. We consider a two-state model for voltage-gated channels in the membrane of an isolated elongated cell (Lcell = 1 mm; rcell = 25 micron) and use a previously described process of ionic and molecular flux rectification to set lower bounds for a threshold exposure. A key assumption is that it is the ability of weak physical fields to alter biochemistry that is limiting, not the ability of a small number of molecules to alter biological systems. Moreover, molecular shot noise, not thermal voltage noise, is the basis of threshold estimates. Models with and without stochastic resonance are used, with a long exposure time, texp = 10(4) s. We also determined the dependence of the threshold on the basal transport rate. By considering both spherical and elongated cells, we find that the lowest bound for the threshold is Emin approximately 9 x 10(-3) V m-1 (9 x 10(-5) V cm-1). Using a conservative value for the loop radius rloop = 0.3 m for induced current, the corresponding lower bound in the human body for a magnetic field exposure is Bmin approximately 6 x 10(-4) T (6 G). Unless large, organized, and electrically amplifying multicellular systems such as the ampullae of Lorenzini of elasmobranch fish are involved, these results strongly suggest that the biophysical mechanism of voltage-gated macromolecules in the membranes of cells can be ruled out as a basis of possible effects of weak ELF electric and magnetic fields in humans.

A physical analysis of the ion parametric resonance model.

We show, in elementary terms, using for the most part only elementary mathematics, the physical bases for the ion parametric resonance model so as to clarify the assumptions and consequences of the model. The analysis shows why, contrary to earlier conclusions, no combination of weak DC and AC magnetic fields can modify the transition rate to the ground state of excited ions. Although reinterpretations of the biological consequences of the motion of the excited ions circumvent that particular objection to the model, those changes introduce other difficulties. Also, other objections to the mechanism still stand; hence the model cannot account for any purported biological effects of weak extremely low frequency magnetic fields.

Extremely low frequency electromagnetic fields do not interact directly with DNA.

Blank and Goodman [(1997): Bioelectromagnetics 18:111-115] suggest that weak extremely low frequency (ELF) electric and magnetic fields affect intracellular DNA directly. We show that such a conclusion is not in accord with physical principles.

Didactic discussion of stochastic resonance effects and weak signals.

A simple, paradigmatic, model is used to illustrate some general properties of effects subsumed under the label "stochastic resonance." In particular, analyses of the transparent model show that 1) a small amount of noise added to a much larger signal can greatly increase the response to the signal, but 2) a weak signal added to much larger noise will not generate a substantial added response. The conclusions drawn from the model illustrate the general result that stochastic resonance effects do not provide an avenue for signals that are much smaller than noise to affect biology. A further analysis demonstrates the effects of small signals in the shifting of biologically important chemical equilibria under conditions where stochastic resonance effects are significant.

Measurements described in a paper by Blackman, Blanchard, Benane, and House are statistically invalid.

Blackman et al. [1994] describe an experiment that purports to show that weak 45 Hz magnetic fields inhibit the growth of neurites from PC-12 cells treated with a growth stimulation factor. I present a statistical analysis of the data in that paper that shows that the data were corrupted in some way; hence, the results are invalid.

Ultrashort microwave signals: a didactic discussion.

As a consequence of the variation with frequency of the attenuation and phase velocity of electromagnetic waves in tissue, the shape (variation of the electric field with time) of short electromagnetic pulses incident on tissue changes with depth of penetration. We show that a conjecture that such well-known and long understood changes in pulse shape may generate harmful biological effects is not credible. We also consider the suggestion that such pulses may be useful in medical imaging and the mapping of the electrical properties of complex tissues and show that such use is impracticably difficult for fundamental reasons.

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.

Biological responses to weak 60-Hz electric and magnetic fields must vary as the square of the field strength.

Under quite general conditions, the biological response j(G) to a very weak continuous 60-Hz electric or magnetic field G is shown to be proportional to the square of the field strength. This conclusion follows from the continuity of the function j(G) and the first three derivatives of j(G) with respect to G over the amplitude of G. That continuity is ensured in nominally discontinuous systems by the presence of thermal noise. I argue the validity of the conjecture that all plausible biological responses to weak 60-Hz fields vary with the square of the field strength. A specific model is used to illustrate characteristic dependencies of biological responses to exposure times.

Constraints of thermal noise on the effects of weak 60-Hz magnetic fields acting on biological magnetite.

Previous calculations of limits imposed by thermal noise on the effects of weak 60-Hz magnetic fields on biological magnetite are generalized and extended to consider multiple signals, the possibility of anomalously large magnetosome structures, and the possibility of anomalously small cytoplasm viscosities. The results indicate that the energies transmitted to the magnetite elements by fields less than 5 microT, characteristic of the electric power distribution system, will be much less than thermal noise energies. Hence, the effects of such weak fields will be masked by that noise and cannot be expected to affect biology or, therefore, the health of populations.

Marital status and psychiatric disorders among blacks and whites.

This paper examines the association between marital status and psychiatric disorder for Blacks and explores the extent to which these patterns differ from those for Whites. Widowed and separated/divorced Black males and females have higher rates of disorder than the married; never-married Blacks do not have an elevated risk of psychiatric illness. The association between marital status and disorder for White males is similar and stronger than that observed for Blacks. For White women, the separated/divorced have a higher risk of disorder than the married, and unmarried White females have higher rates of the substance abuse disorders, but lower rates of the anxiety disorder than the married. Across all marital status groups, Black males and White males have higher rates of disorder (except for depression), than females. A complex pattern emerges when gender differences in the relative rates of disorder for unmarried Blacks compared to married Blacks are considered. Separated/divorced Black men, widowed Black women, and never-married Black men are worse off than their respective peers. Except for the separated/divorced, opposite patterns are evident for Whites. Directions for further research are outlined.

Criticism of Lednev's mechanism for the influence of weak magnetic fields on biological systems.

V. V. Lednev has proposed a mechanism that he suggests would allow very weak magnetic fields, at the cyclotron resonance frequency for Ca2+ ions in the earth's field, to induce biological effects. I show that for four independent reasons no such mechanism can operate.

The protective efficacy of polyvalent pneumococcal polysaccharide vaccine.

BACKGROUND: Although the protective efficacy of pneumococcal polysaccharide vaccine has been demonstrated in randomized trials in young African gold miners, there has been controversy about its efficacy in older Americans at risk for serious pneumococcal infections. To assess the vaccine's protective efficacy against invasive pneumococcal infections, we conducted a hospital-based case-control study of the efficacy of pneumococcal vaccine in adults with a condition recognized to be an indication for receiving the vaccine. METHODS: From 1984 to 1990, adults in whom Streptococcus pneumoniae was isolated from any normally sterile site were identified by prospective surveillance in the microbiology laboratories of 11 large hospitals; those with an indication for pneumococcal vaccine were enrolled as case patients. For each case patient, one control was matched according to age, underlying illness, and site of hospitalization. We contacted all providers of medical care to ascertain each subject's history of immunization with pneumococcal vaccine. Isolates of S. pneumoniae were serotyped by an investigator unaware of the subject's vaccination history. RESULTS: Thirteen percent of the 1,054 case patients and 20 percent of the 1,054 matched controls had received pneumococcal vaccine (P less than 0.001). When vaccine was given in either its 14-valent or its 23-valent form, its aggregate protective efficacy (calculated as a percentage: 1 minus the odds ratio of having been vaccinated times 100) against infections caused by the serotypes represented in the vaccine was 56 percent (95 percent confidence interval, 42 percent to 67 percent; P less than 0.00001) for all 983 patients infected with a serotype represented in the vaccine, 61 percent for a subgroup of 808 immunocompetent patients (95 percent confidence interval, 47 percent to 72 percent; P less than 0.00001), and 21 percent for a subgroup of 175 immunocompromised patients (95 percent confidence interval, -55 percent to 60 percent; P = 0.48). The vaccine was not efficacious against infections caused by serotypes not represented in the vaccine (protective efficacy, -73 percent; 95 percent confidence interval, -263 percent to 18 percent; P = 0.15). CONCLUSIONS: Polyvalent pneumococcal vaccine is efficacious in preventing invasive pneumococcal infections in immunocompetent patients with indications for its administration. This vaccine should be used more widely.

Biological effects on the cellular level of electric field pulses.

Analysis of electric and magnetic fields in the human body generated upon exposure to external pulsed electric fields are used to consider possible biological effects at the cellular level. For peak external field strengths as high as 100 kV m-1, the effects of the consequent internal electric fields on sensitive cell elements, such as the membranes, organelles, and the macromolecules that carry genetic information, are shown to be small compared with the normal thermal agitation of the elements. Hence, based on the description of the cell and the analysis presented here, such pulses cannot be expected to produce any biological effects at the cellular level.