Biological Coordination

How receptor state, tissue timing and biological memory connect a physical input to functional gates and population outcomes.

Calcium · redox · hormone production

Calcium and the local clock converge on steroidogenesis

CaMKI–NUR77 regulates StAR transcription. A separate connection runs through RORα–BMAL1 and steroidogenic gene regulation. These branches join the same production system, allowing calcium and clock state to influence local hormone capacity.

CaMKI and CaMKII are different kinases. A single clock-gene expression measurement describes expression; a rhythm requires measurements across time.

Martin et al. (2008)iAkashi et al. (2005)i

Explore the shared mechanism and its studies

A biological signal has to meet a receptive structure at the right time. BERM develops this principle into one continuous route: physical structure → receptor response → chemical and tissue memory → endocrine coordination → functional success → encounters and population distributions.

The geometric starting point and the biological bridge

Start from Lindgren’s 2025 i ansatz, gμν = ημν + κAμAν. Splitting A into a background Ab and an external component a gives the tensor identity below. BERM then names a state-dependent receiving operator K: it connects the geometric perturbation to receptor activity z, with receptor state S carrying orientation, cofactors, redox, biological phase and recovery history. This biological coupling is an explicit model assumption; the studies below anchor its candidate implementations and downstream transitions in their own experimental systems. FieldState contributes observations for estimating the upstream physical state.

\delta g_{\mu\nu}=\kappa\left(A_{b,\mu}a_\nu+a_\mu A_{b,\nu}+a_\mu a_\nu\right)

z_r(t)=\int_0^\infty K_r^{\mu\nu}(\tau;S_r(t))\,\delta g_{\mu\nu}(t-\tau)\,d\tau

Follow the tensor derivation →

1. A receiving state that changes with physiology

Receptor orientation, internal chemistry, endocrine state and timing are separately describable inputs to the response.

In a chemical compass experiment, rotating an optically selected molecular ensemble rotated its magnetic response pattern; isotope substitution changed the response through internal chemistry. The CPF model-molecule experiment was performed at 120 K. In mouse fibroblasts, a defined tNMR protocol produced different clock responses depending on application time and glucocorticoid pretreatment. These interventions identify variables that a receiving operator can represent. Kerpal 2019 i; Thoeni 2024 i.

The response sign depends on the starting state. In the hypomagnetic mouse experiment, a ROS-raising intervention improved neurogenesis under hypomagnetic conditions and impaired it under the geomagnetic control (Zhang 2021 i). RF preconditioning also protected cells from a later chemical challenge, with autophagy interventions removing that protection (Sannino 2024 i; Sannino 2022 i). BERM therefore separates receiving state s, repair A, damage D and functional capacity C and compares their time courses.

2. CRY connects clock state directly to hormone response

Cryptochromes participate directly in glucocorticoid-receptor transcriptional regulation and hepatic glucagon–cAMP signalling.

CRY1 and CRY2 interact with the glucocorticoid receptor, while hepatic cryptochromes suppress glucagon-linked G-protein/cAMP signalling. These links extend the existing nutritional CRY pathway: cofactors, AMPK-mediated turnover and membrane state can feed into hormone responsiveness and metabolism. The BERM synthesis closes a feedback loop in which endocrine state changes reception and clock activity changes subsequent endocrine response. Lamia 2011 i; Zhang 2010 i.

Reproductive regulation · behaviour · feedback

Prolactin reveals why one signal can have different outputs

Prolactin–kisspeptin experiments locate a reproductive-axis brake; a distinct prolactin-sensitive MPOA–VTA pathway supports offspring contact. In women with hyperprolactinaemia, kisspeptin increased LH pulses without a significant overall fall in prolactin. BERM connects the studies through the shared hormone and the receiving circuit, retaining each experiment’s own endpoint and time course.

Sonigo et al. (2012)iHoskova et al. (2022)iClarkson et al. (2026)i

Follow the three branches and their evidence

3. Fast selection can leave a slow molecular trace

Successive stages can carry biological memory on different timescales: reaction selection, chemical populations, protein conformation and tissue state.

RF control of photo-generated radical-pair chemistry in algal CraCry and engineered iLOV proteins linked fast spin processes to slower chemical-state accumulation under laboratory protocols. Earlier work showed chemical amplification of magnetic effects. A 2026 Cry4a preprint connects redox state to an allosteric protein conformation. These studies supply different parts of the sequence rather than one combined experiment. Meng 2026 i; Kattnig 2016 i; Kish 2026, preprint i.

At a longer timescale, transient bioelectric intervention in planarians altered subsequent regeneration, illustrating tissue-state memory. In humans, millisecond light flashes delivered at particular intervals shifted the circadian clock efficiently. BERM represents accumulation and recovery explicitly while retaining the receptor, field protocol and timescale of each component experiment. Durant 2017 i; Najjar & Zeitzer 2016 i.

4. Hormonal function depends on signal–tissue timing

Redox and electrical clock activity form a biological connection through ion-channel regulation.

Redox state modulates suprachiasmatic neuronal excitability through potassium channels. This provides a route from chemical state into clock timing and, through rhythmic endocrine outputs and metabolism, back into chemical state. Wang 2012 i.

Hormone concentration, tissue responsiveness and their temporal overlap jointly determine a functional response.

Sleep misalignment altered human blood-transcript rhythms and the temporal organisation of glucocorticoid-signalling genes while the circulating cortisol rhythm persisted. Archer 2014 and the 2022 reanalysis share a dataset family. Pulsatile glucocorticoid experiments give a complementary anchor for temporal decoding at the receptor and gene-response level. Archer 2014 i; Archer 2022 i; Stavreva 2009 i.

\langle H S\rangle=H_0S_0+\frac{hs}{2}\cos\Delta\phi

For illustrative sinusoidal hormone H and receptivity S, their mean product depends on phase even when both individual means remain fixed. H₀ and S₀ are means; h and s are oscillation amplitudes.

Different environmental inputs can shift different tissue rhythms by different amounts.

Delayed meals shifted glucose and adipose PER2 rhythms differently while melatonin and cortisol timing remained similar. A simulated night-work experiment showed that maintaining daytime eating preserved glucose tolerance. BERM consequently describes appropriate phase relations across organs and treats nutrition as both a chemical input and a timing input. Wehrens 2017 i; Chellappa 2021 i.

Loading intervention profiles…

Explore timing, recovery and individual differences

These examples show the mathematical consequences of declared inputs. Values are normalised illustrations, with no fitted environmental field effect or clinical prediction. Changing a selection compares the model’s precomputed scenarios.

Signal and receiving window

Hold the average hormone signal and average receptivity fixed. Shift only their relative phase and inspect the resulting mean functional response.

Hormone–receptor phase relation

Normalised value

Hours in the illustrative cycle

Hormone signalReceptivityFunctional response

Mean functional response: 1.125
Relative to aligned response: 100.0%

Fixed means: hormone 1; receptivity 1. Each amplitude is 0.5. The example period is 24 hours.

Repeated pulses and recovery

The same increment is delivered repeatedly. The interval between events determines how much of the earlier trace remains when the next pulse arrives. Both charts show the same number of pulses; their elapsed times differ.

Pulse interval relative to recovery time

Stored trace

Elapsed time / recovery time τ

Stored trace

Long-run level just after a pulse: 10.508
Increment per pulse: 1

τ denotes the declared recovery time. This illustration isolates retention and decay; a separate receptor-readiness process is needed to represent an optimal interval or adaptation.

The same mean, different waiting-time tails

Compare a uniform population with a mixed population whose initial mean per-cycle conception probability is the same. Probabilities remain fixed for each group, and all couples are assumed to keep trying.

Distribution of per-cycle probabilities

Cumulative conception probability

Trying cycle

Everyone: 20% per cycleHalf: 10%; half: 30%

Conceived by cycle 12: 93.1%
Still waiting after cycle 12: 6.9%
Next-cycle chance among those still waiting: 20.0%

The endpoint is first conception. Pregnancy continuation and live birth require subsequent gates. The declining conditional chance in the mixed group comes from the changing composition of couples still waiting.

Show the values

Everyone: 20% per cycle
Trying cycle	Cumulative conception probability	Next-cycle chance among those still waiting
0	0.0%	20.0%
1	20.0%	20.0%
2	36.0%	20.0%
3	48.8%	20.0%
4	59.0%	20.0%
5	67.2%	20.0%
6	73.8%	20.0%
7	79.0%	20.0%
8	83.2%	20.0%
9	86.6%	20.0%
10	89.3%	20.0%
11	91.4%	20.0%
12	93.1%	20.0%

Download the example inputs and results (JSON) →

From mechanism to population arithmetic

Compare how timing, receptivity, repair and differences between couples pass through the same computational chain. Select one change at a time.

Illustrative model: inputs and transfer coefficients are chosen examples. The numbers are not measured field effects or country forecasts.

Choose a comparison

The same driver integral is applied early or late. Calcium and recovery retain the event order.

Changed input	Reference state	Changed state
Pulse timingseconds	0–2 s	2–4 s

Cell time course

Relative model state units

━ Reference state┄ Changed state

The chart shows the example protocol for the first age group. All seven groups use the same cell inputs here. Hormone phase and waiting distributions act at later stages, so cell traces may remain unchanged.

Cytosolic Ca²⁺	Reference state	Changed state
4 s	0.204	0.374

Functional gate

Cell state is mapped to function through a separately chosen response window. Its coefficient requires its own observational calibration.

Cell functional factor: 0.877 → 0.533

Couple biological capacity: 0.877 → 0.533

Population biological ratio: 0.608

This ratio includes the optional waiting distribution. A distributional change can affect the result even when the individual example couple's capacity is unchanged.

Example TFR · Reference state

3.5

Example TFR · Changed state

2.128

Conditional change

-39.2 %

Reference ASFR is 100 births per thousand women per year in every age group. TFR 3.5 is the resulting synthetic comparison baseline.

Age-specific calculation

Age group	Reference state	Changed state
15-19	100	60.8
20-24	100	60.8
25-29	100	60.8
30-34	100	60.8
35-39	100	60.8
40-44	100	60.8
45-49	100	60.8

ASFR: births per thousand women per year. TFR uses five-year age groups. The waiting-distribution ratio is a conditional scenario assumption; it does not by itself describe calendar-year birth probability.

Assumptions and scope

Every coefficient is a named illustrative input, not an effect size estimated from observations.
Reference ASFR is 100 per 1000 in all seven age groups. TFR 3.5 is an arithmetic example baseline.
The driver is a local biological scenario input. Conversion from a measured electromagnetic field and the L2 bridge remain open.
Cell and hormone time scales are separate; they are not assumed to have the same duration.
Waiting replaces the capacity ratio. It is not itself a calendar-year birth probability.

Download all inputs and results (JSON)

5. Local reproductive gates become a waiting-time distribution

Successful reproduction depends on functional transitions with distinct local requirements.

Human CatSper deficiency can impair sperm hyperactivation and fertilisation despite normal routine semen parameters. In a mouse steroidogenic-cell clock-gene deletion, ovulation persisted while implantation was strongly impaired; progesterone and ovarian transplantation located the affected functional gate. BERM composes such stages through conditional probabilities so a shared mechanism is counted once. Young 2024 i; Liu 2014 i.

Individual differences in per-cycle success affect the long waiting-time tail and the opportunity to progress to a subsequent birth.

Among couples still waiting, the distribution progressively concentrates on lower success probabilities under a stable heterogeneous-probability model. European analyses link waiting at least a year to smaller realised family size; this anchors the next transition from prolonged waiting to parity progression. BERM can therefore carry a biological state distribution through waiting time and age to realised births. The explorer illustrates the distributional mathematics with explicitly chosen inputs. Gnoth 2003 i; Joffe 2009 i.

6. Successful encounters connect biology to networks

Encounter frequency, functional success and temporal overlap jointly determine the flow of successful interactions; feedback changes the subsequent network.

A pollinator-removal experiment changed the behaviour of the remaining pollinators and reduced seed production. Human sleep-loss experiments changed social approach and willingness to help, while cooperation experiments show that one participant’s behaviour can influence subsequent partners. These are separate empirical anchors for encounter quality and network propagation. Brosi & Briggs 2013 i; Ben Simon & Walker 2018 i; Ben Simon 2022 i; Fowler & Christakis 2010 i.

The computational continuation keeps direct biological change and network propagation separate: δb(t+1)=u(t)+βWδb(t), with node order, time step and measured outcome declared. Institution renewal uses I_next=rI+αΣw_i actions_i−withdrawal. Signed behavioral deviations need an explicit baseline-to-action mapping before entering that stock. Ecological encounters use Δt·k_ij·m_ij(state)·n_i·n_j, followed by signed consequences for both species and their own birth/death rates. All species and social coefficients remain supplied assumptions until endpoint calibration; stored capacity and feedback give the aggregate its own time constants.

7. Multiple sources meet a spatially selective receiver

Lindgren’s cross terms preserve relationships between sources; a biological response requires their explicit contraction through a receiving operator.

Oscillating components produce sum- and difference-frequency terms in the tensor expansion. An independent implementation example comes from temporal-interference stimulation: two electrode fields at 2,000 and 2,005 Hz produced a 5 Hz envelope, and changing their current ratio changed hippocampal targeting. This anchors spatial targeting in that stimulation setting. Its relationship to BERM geometry is carried by the named biological bridge. Violante 2023 i.

Existing data for the next measurements

These resources provide measured component behaviour. Their variables can constrain the corresponding biological or spatial operators in the model.