## TITLE('Biochemistry: Cross-Communication in a Merging Pathway')
## DESCRIPTION
## Five-part progressive problem about feed-forward cross-activation in a
## merging metabolic pathway. The diagram shows two input branches that
## converge into a shared trunk. Students must identify feed-forward
## activators, cross-activation targets, and predict coordination effects.
## Parts A and B use checkboxes (select all that apply). Part C randomly
## selects between overproduction, lost cross-activation, or imbalance
## scenarios. Part D examines blocked branch effects. Part E tests
## understanding of why cross-activation exists.
## ENDDESCRIPTION
## KEYWORDS('feed-forward','cross-activation','metabolic pathway','committed step','anabolic pathway','merging pathway','convergent pathway','coordination')
## DBsubject('Biochemistry')
## DBchapter('Enzymes')
## DBsection('Regulation')
## Level(4)
## Date('2026-03-30')
## Author('Dr. Neil R. Voss')
## Institution('Roosevelt University')
## Language(en)
# https://github.com/vosslab
# https://bsky.app/profile/neilvosslab.bsky.social
# This work is licensed under CC BY 4.0 (Creative Commons Attribution 4.0
# International License).
# https://creativecommons.org/licenses/by/4.0/
# Source code portions are licensed under LGPLv3.
DOCUMENT();
# ----------------------------
# 1) Preamble
# ----------------------------
loadMacros(
'PGstandard.pl',
'MathObjects.pl',
'PGML.pl',
'niceTables.pl',
'parserCheckboxList.pl',
'parserRadioButtons.pl',
'PGcourse.pl',
);
$showPartialCorrectAnswers = 0;
# ============================================
# 2) Setup
# ============================================
# ----------------------------
# 2a) Deterministic local RNG
# ----------------------------
my $local_random = PGrandom->new();
$local_random->srand($problemSeed);
# ----------------------------
# 2b) Pathway data
# ----------------------------
my $b1_len = $local_random->random(3, 4, 1);
my $b2_len = $local_random->random(3, 4, 1);
my $trunk_len = $local_random->random(3, 4, 1);
my $total_mols = $b1_len + $b2_len + $trunk_len;
# color palette (14 high-contrast colors)
my @palette = (
'#d40000', '#b74300', '#935d00', '#6c6c00', '#3b7600',
'#007a00', '#00775f', '#007576', '#076dad', '#003fff',
'#0067cc', '#a719db', '#c80085', '#cc0066',
);
my $c_shift = $local_random->random(0, $#palette, 1);
my @dbl_pal = (@palette, @palette);
my @colors = @dbl_pal[$c_shift .. $c_shift + $total_mols - 1];
# letter assignment
my @alpha = ('A'..'Z');
my $l_shift = $local_random->random(0, 26 - $total_mols - 1, 1);
my @letters = @alpha[$l_shift .. $l_shift + $total_mols - 1];
# assign metabolites: b1 first, then b2, then trunk
my @b1 = ();
for my $i (0 .. $b1_len - 1) {
push @b1, { L => $letters[$i], C => $colors[$i] };
}
my @b2 = ();
for my $i (0 .. $b2_len - 1) {
my $idx = $b1_len + $i;
push @b2, { L => $letters[$idx], C => $colors[$idx] };
}
my @trunk = ();
for my $i (0 .. $trunk_len - 1) {
my $idx = $b1_len + $b2_len + $i;
push @trunk, { L => $letters[$idx], C => $colors[$idx] };
}
# ----------------------------
# 2c) Enzyme numbering and feedback biology
# ----------------------------
# In a merging pathway:
# - First enzymes of each input branch are committed steps
# - Trunk end product inhibits the committed steps of both input branches
# - Enzyme numbering: b1 internal, merge, trunk internal, b2 internal
# - E1..E(b1_len-1) = b1 arrows, E(b1_len) = merge, E(b1_len+1).. = trunk, then b2
my $e_b1_first = 1;
my $e_merge = $b1_len;
my $e_trunk_first = $b1_len + 1;
my $e_b2_first = $b1_len + $trunk_len;
my $total_enzymes = $b1_len + $b2_len + $trunk_len - 1;
my $b1_start = $b1[0];
my $b2_start = $b2[0];
my $mp_mol = $trunk[0]; # first trunk metabolite (merge point)
my $trunk_end = $trunk[$#trunk];
# pick one branch randomly for parts C-D
my $focus_branch = $local_random->random(1, 2, 1);
my $focus_name = ($focus_branch == 1) ? 'first' : 'second';
my $other_name = ($focus_branch == 1) ? 'second' : 'first';
my $focus_enzyme = ($focus_branch == 1) ? $e_b1_first : $e_b2_first;
my $focus_branch_start = ($focus_branch == 1) ? $b1_start : $b2_start;
my $other_branch_start = ($focus_branch == 1) ? $b2_start : $b1_start;
my $focus_branch_obj = ($focus_branch == 1) ? \@b1 : \@b2;
my $other_branch_obj = ($focus_branch == 1) ? \@b2 : \@b1;
my $other_enzyme = ($focus_branch == 1) ? $e_b2_first : $e_b1_first;
my $focus_branch_end = ($focus_branch == 1) ? $b1[$#b1] : $b2[$#b2];
my $other_branch_end = ($focus_branch == 1) ? $b2[$#b2] : $b1[$#b1];
# ============================================
# 2d) HTML helpers
# ============================================
my $css_met = 'border:0; text-align:center; padding:2px 4px;';
my $css_arr = 'border:0; text-align:center; padding:2px 2px; font-size:150%;';
my $css_lbl = 'border:0; text-align:center; padding:0 2px; '
. 'font-size:75%; vertical-align:bottom;';
my $css_empty = 'border:0; padding:2px 4px;';
my $css_dots = 'border:0; text-align:center; padding:2px 2px; '
. 'font-size:120%; color:#888; letter-spacing:2px;';
sub met_node {
my ($letter, $color) = @_;
return "${letter}";
}
sub met_txt {
my ($letter, $color) = @_;
return "${letter}";
}
# ============================================
# 2e) Grid geometry
# ============================================
# Grid layout for merging pathway:
# Branches on LEFT, trunk on RIGHT
# Two branches (top and bottom) converge into a single trunk
my $max_branch_len = ($b1_len > $b2_len) ? $b1_len : $b2_len;
my $branch_cols = 2 * $max_branch_len - 1; # met + arrow + met + ... pairs
my $merge_col = $branch_cols;
my $trunk_arrow_col = $merge_col + 1;
my $trunk_met_start = $trunk_arrow_col + 1;
my $total_cols = $trunk_met_start + 2 * $trunk_len;
# ============================================
# 2f) Build diagram rows (no feedback arrows)
# ============================================
# 6-row layout using LayoutTable:
# Row 0: Branch 1 enzyme labels (left-padded if shorter than max)
# Row 1: Branch 1 metabolites + NE arrow at merge point
# Row 2: Trunk enzyme labels (right side)
# Row 3: Trunk metabolites + arrows
# Row 4: Branch 2 metabolites + SE arrow at merge point
# Row 5: Branch 2 enzyme labels (left-padded if shorter than max)
# --- Branch 1 enzyme label row ---
my @b1_enzyme_row = ();
for (1 .. $total_cols) { push @b1_enzyme_row, ['', cellcss => $css_empty]; }
# Add padding if b1 is shorter than max_branch_len
my $b1_padding = $max_branch_len - $b1_len;
# enzyme labels go above arrows (odd columns between metabolites)
for my $i (0 .. $b1_len - 2) {
my $en = $e_b1_first + $i;
# arrow column is at offset 1 from the metabolite column
my $col = 2 * ($b1_padding + $i) + 1;
$b1_enzyme_row[$col] = ["E${en}", cellcss => $css_lbl];
}
# --- Branch 1 structure row ---
my @b1_struct_row = ();
for (1 .. $total_cols) { push @b1_struct_row, ['', cellcss => $css_empty]; }
# Merge point arrow (SE, upper branch goes down to merge)
$b1_struct_row[$merge_col] = ['↘', cellcss => $css_arr];
# Metabolites and arrows
for my $i (0 .. $b1_len - 1) {
my $col = 2 * ($b1_padding + $i);
$b1_struct_row[$col] = [met_node($b1[$i]->{L}, $b1[$i]->{C}),
cellcss => $css_met];
if ($i < $b1_len - 1) {
$b1_struct_row[$col + 1] = ['→', cellcss => $css_arr];
}
}
# --- Trunk enzyme label row ---
my @trunk_enzyme_row = ();
for (1 .. $total_cols) { push @trunk_enzyme_row, ['', cellcss => $css_empty]; }
# merge enzyme label at the merge column
$trunk_enzyme_row[$merge_col] = ["E${e_merge}", cellcss => $css_lbl];
# trunk internal enzyme labels
for my $i (0 .. $trunk_len - 2) {
my $en = $e_trunk_first + $i;
my $col = $trunk_met_start + 1 + 2 * $i;
$trunk_enzyme_row[$col] = ["E${en}", cellcss => $css_lbl];
}
# --- Trunk structure row ---
my @trunk_struct_row = ();
for (1 .. $total_cols) { push @trunk_struct_row, ['', cellcss => $css_empty]; }
# merge arrow-tail + regular arrow before first trunk metabolite
$trunk_struct_row[$merge_col] = ['⤚', cellcss => $css_arr];
$trunk_struct_row[$trunk_arrow_col] = ['→', cellcss => $css_arr];
# Metabolites and arrows
for my $i (0 .. $trunk_len - 1) {
my $col = $trunk_met_start + 2 * $i;
$trunk_struct_row[$col] = [met_node($trunk[$i]->{L}, $trunk[$i]->{C}),
cellcss => $css_met];
if ($i < $trunk_len - 1) {
$trunk_struct_row[$col + 1] = ['→', cellcss => $css_arr];
}
}
# Add ellipsis at far right
$trunk_struct_row[$total_cols - 1] = ['···',
cellcss => $css_dots];
# --- Branch 2 enzyme label row ---
my @b2_enzyme_row = ();
for (1 .. $total_cols) { push @b2_enzyme_row, ['', cellcss => $css_empty]; }
# Add padding if b2 is shorter than max_branch_len
my $b2_padding = $max_branch_len - $b2_len;
# enzyme labels go above arrows (odd columns between metabolites)
for my $i (0 .. $b2_len - 2) {
my $en = $e_b2_first + $i;
my $col = 2 * ($b2_padding + $i) + 1;
$b2_enzyme_row[$col] = ["E${en}", cellcss => $css_lbl];
}
# --- Branch 2 structure row ---
my @b2_struct_row = ();
for (1 .. $total_cols) { push @b2_struct_row, ['', cellcss => $css_empty]; }
# Merge point arrow (NE, lower branch goes up to merge)
$b2_struct_row[$merge_col] = ['↗', cellcss => $css_arr];
# Metabolites and arrows
for my $i (0 .. $b2_len - 1) {
my $col = 2 * ($b2_padding + $i);
$b2_struct_row[$col] = [met_node($b2[$i]->{L}, $b2[$i]->{C}),
cellcss => $css_met];
if ($i < $b2_len - 1) {
$b2_struct_row[$col + 1] = ['→', cellcss => $css_arr];
}
}
# --- Assemble: b1 above trunk above b2 ---
my @all_rows = ();
push @all_rows, [@b1_enzyme_row];
push @all_rows, [@b1_struct_row];
push @all_rows, [@trunk_enzyme_row];
push @all_rows, [@trunk_struct_row];
push @all_rows, [@b2_struct_row];
push @all_rows, [@b2_enzyme_row];
$diagram = LayoutTable(
[@all_rows],
center => 0,
tablecss => 'border-collapse:collapse; border:0;',
allcellcss => 'border:0; padding:2px;',
);
# ============================================
# 2g) Text references
# ============================================
my $b1_start_txt = met_txt($b1_start->{L}, $b1_start->{C});
my $b2_start_txt = met_txt($b2_start->{L}, $b2_start->{C});
my $mp_txt = met_txt($mp_mol->{L}, $mp_mol->{C});
my $trunk_end_txt = met_txt($trunk_end->{L}, $trunk_end->{C});
my $focus_start_txt = met_txt($focus_branch_start->{L}, $focus_branch_start->{C});
my $other_start_txt = met_txt($other_branch_start->{L}, $other_branch_start->{C});
my $focus_end_txt = met_txt($focus_branch_end->{L}, $focus_branch_end->{C});
my $other_end_txt = met_txt($other_branch_end->{L}, $other_branch_end->{C});
# color lookup
my %met_color = ();
for my $m (@b1) { $met_color{$m->{L}} = $m->{C}; }
for my $m (@b2) { $met_color{$m->{L}} = $m->{C}; }
for my $m (@trunk) { $met_color{$m->{L}} = $m->{C}; }
# ============================================
# 2h) Part A: Identify feed-forward activators (CheckboxList)
# ============================================
# In a merging pathway, each branch's end product activates the committed
# step of the OTHER branch (cross-activation for coordinated supply).
# Correct: both branch end products. Distractors: starting mols, intermediates.
# collect all candidate metabolites for Part A, then order by letter
my @pA_pool = (
$b1_start,
$b2_start,
$focus_branch_end,
$other_branch_end,
$mp_mol,
);
if ($b1_len >= 3) {
push @pA_pool, $b1[1];
}
# insertion sort by letter (avoids blocked 'sort' in safe compartment)
my @pA_selected = ($pA_pool[0]);
for my $k (1 .. $#pA_pool) {
my $inserted = 0;
for my $j (0 .. $#pA_selected) {
if ($pA_pool[$k]->{L} lt $pA_selected[$j]->{L}) {
splice(@pA_selected, $j, 0, $pA_pool[$k]);
$inserted = 1;
last;
}
}
if (!$inserted) { push @pA_selected, $pA_pool[$k]; }
}
my @pA_choices = ();
my @pA_correct_indices = ();
for my $i (0 .. $#pA_selected) {
my $m = $pA_selected[$i];
push @pA_choices, "metabolite " . met_txt($m->{L}, $m->{C});
# correct: both branch end products
if ($m->{L} eq $focus_branch_end->{L}
|| $m->{L} eq $other_branch_end->{L}) {
push @pA_correct_indices, $i;
}
}
$cbA = CheckboxList(
[@pA_choices],
[@pA_correct_indices],
separator => '
',
);
$qA = "Which metabolites provide positive regulatory signals "
. "to enzymes in the other branch? "
. "(Select all that apply.)";
$solA = "The two feed-forward activators are: ${focus_end_txt} "
. "(end product of the ${focus_name} branch, activates "
. "E${other_enzyme}) and ${other_end_txt} "
. "(end product of the ${other_name} branch, activates "
. "E${focus_enzyme}). Each branch's end product "
. "cross-activates the other branch's committed step, coordinating "
. "supply of both substrates for the merge reaction.";
# ============================================
# 2i) Part B: Identify cross-activation targets (CheckboxList)
# ============================================
# Correct: E(e_b1_first) and E(e_b2_first) -- the committed steps
# These are targets of feed-forward cross-activation from the other branch
# Distractors: merge enzyme, trunk enzymes, downstream branch enzymes
my @pB_selected_nums = ();
# committed steps of both branches (correct -- targets of cross-activation)
push @pB_selected_nums, $e_b1_first;
push @pB_selected_nums, $e_b2_first;
# merge enzyme as distractor
push @pB_selected_nums, $e_merge;
# downstream branch enzymes as distractors
if ($b1_len >= 2) {
push @pB_selected_nums, $e_b1_first + 1;
}
if ($b2_len >= 2) {
push @pB_selected_nums, $e_b2_first + 1;
}
# deduplicate and keep order
my %pB_seen;
my @pB_unique = ();
for my $e (@pB_selected_nums) {
next if $pB_seen{$e}++;
push @pB_unique, $e;
}
my @pB_choices = ();
my @pB_correct_indices = ();
for my $i (0 .. $#pB_unique) {
my $e = $pB_unique[$i];
push @pB_choices, "enzyme E${e}";
# correct: committed steps (targets of cross-activation)
if ($e == $e_b1_first || $e == $e_b2_first) {
push @pB_correct_indices, $i;
}
}
$cbB = CheckboxList(
[@pB_choices],
[@pB_correct_indices],
separator => '
',
);
$qB = "Which enzymes receive positive regulatory signals "
. "from a metabolite in the other branch? "
. "(Select all that apply.)";
$solB = "The two cross-activation targets are: "
. "E${e_b1_first} (committed step of the ${focus_name} branch, "
. "activated by ${other_end_txt}) and "
. "E${e_b2_first} (committed step of the ${other_name} branch, "
. "activated by ${focus_end_txt}). The committed step is the first enzyme "
. "unique to each branch. Cross-activation ensures coordinated "
. "substrate supply for the merge reaction.";
# ============================================
# 2j) Part C: Coordination reasoning (3 sub-scenarios)
# ============================================
# Randomly select: 1=overproduction, 2=lost cross-activation, 3=branch imbalance
my $pC_subscenario = $local_random->random(1, 3, 1);
if ($pC_subscenario == 1) {
# Sub-scenario 1: One branch overproduces (cross-activation consequence)
$qC = "If the ${focus_name} branch overproduces ${focus_end_txt}, "
. "what is the most likely effect on the ${other_name} branch?";
my $pC_correct = "the ${other_name} branch is stimulated because "
. "${focus_end_txt} activates E${other_enzyme}, "
. "tending to increase ${other_end_txt} production";
my @pC_choices = (
$pC_correct,
"the ${other_name} branch slows because "
. "${focus_end_txt} inhibits E${other_enzyme}",
"the ${other_name} branch is unaffected because "
. "the two branches are independent",
"the excess ${focus_end_txt} is rerouted into "
. "the ${other_name} branch",
"the ${other_name} branch shuts down because "
. "only one branch is needed",
);
for my $i (reverse 1 .. $#pC_choices) {
my $j = $local_random->random(0, $i, 1);
@pC_choices[$i, $j] = @pC_choices[$j, $i];
}
$rbC = RadioButtons(
[[@pC_choices]], $pC_correct,
labels => 'ABC', displayLabels => 1,
separator => '',
);
$solC = "When the ${focus_name} branch overproduces ${focus_end_txt}, "
. "the excess ${focus_end_txt} cross-activates "
. "E${other_enzyme} (the committed step of the "
. "${other_name} branch). This stimulates the ${other_name} branch "
. "to increase ${other_end_txt} production, coordinating substrate "
. "supply for the merge reaction.";
}
elsif ($pC_subscenario == 2) {
# Sub-scenario 2: Lost cross-activation (mutation)
$qC = "If a mutation eliminates the activation of "
. "E${other_enzyme} by ${focus_end_txt}, "
. "but all enzymes remain functional, "
. "what is the most likely effect on the pathway?";
my $pC_correct = "the ${other_name} branch loses feed-forward "
. "stimulation; substrate supply becomes imbalanced; the merge "
. "step tends to be limited by ${other_end_txt} availability";
my @pC_choices = (
$pC_correct,
"the ${other_name} branch shuts down completely because "
. "E${other_enzyme} requires activation to function",
"the ${focus_name} branch compensates by increasing its "
. "own production of ${focus_end_txt}",
"the pathway is unaffected because feed-forward activation "
. "is not essential for enzyme function",
"${mp_txt} production increases because the "
. "${other_name} branch runs unchecked",
);
my $pC_lost_correct = $pC_correct;
for my $i (reverse 1 .. $#pC_choices) {
my $j = $local_random->random(0, $i, 1);
@pC_choices[$i, $j] = @pC_choices[$j, $i];
}
$rbC = RadioButtons(
[[@pC_choices]], $pC_lost_correct,
labels => 'ABC', displayLabels => 1,
separator => '',
);
$solC = "Without feed-forward activation from ${focus_end_txt}, "
. "E${other_enzyme} still functions but at its basal "
. "rate. The ${other_name} branch is no longer stimulated when the "
. "${focus_name} branch speeds up, breaking the coordination "
. "mechanism. The merge step tends to become limited by "
. "${other_end_txt} availability because the two branches "
. "are no longer balanced.";
}
else {
# Sub-scenario 3: Branch imbalance (core constraint question)
$qC = "If the ${focus_name} branch produces an excess of "
. "${focus_end_txt} but the ${other_name} branch produces "
. "less ${other_end_txt} than normal, what is the most "
. "likely effect on ${mp_txt} production?";
my $pC_correct = "${mp_txt} production is limited by the "
. "${other_name} branch; excess ${focus_end_txt} cannot "
. "compensate for insufficient ${other_end_txt}";
my @pC_choices = (
$pC_correct,
"${mp_txt} increases because more ${focus_end_txt} "
. "is available for the merge reaction",
"excess ${focus_end_txt} drives the merge reaction forward "
. "despite low ${other_end_txt}",
"the excess ${focus_end_txt} is rerouted to increase "
. "${other_end_txt} production",
"${mp_txt} is unchanged because the branches "
. "are independent of each other",
);
my $pC_imb_correct = $pC_correct;
for my $i (reverse 1 .. $#pC_choices) {
my $j = $local_random->random(0, $i, 1);
@pC_choices[$i, $j] = @pC_choices[$j, $i];
}
$rbC = RadioButtons(
[[@pC_choices]], $pC_imb_correct,
labels => 'ABC', displayLabels => 1,
separator => '',
);
$solC = "The merge reaction requires both ${focus_end_txt} and "
. "${other_end_txt} as substrates. When the ${other_name} branch "
. "produces less ${other_end_txt} than normal, the merge step "
. "becomes limited by ${other_end_txt} availability. Excess "
. "${focus_end_txt} from the ${focus_name} branch cannot "
. "compensate, because the merge reaction requires both inputs. "
. "This is the key constraint in converging pathways: flux is "
. "limited by whichever input branch is slower.";
}
# ============================================
# 2k) Part D: Blocked input branch (MC)
# ============================================
$qD = "If enzyme E${focus_enzyme} is completely "
. "inactivated, what happens to the production of ${mp_txt}?";
my @pD_choices = (
"metabolite ${mp_txt} "
. "decreases "
. "because the ${focus_name} input branch is blocked; "
. "the ${other_name} branch alone cannot supply enough substrate",
"metabolite ${mp_txt} "
. "increases "
. "because the ${other_name} branch compensates fully",
"metabolite ${mp_txt} production is "
. "unchanged because "
. "both branches contribute equally",
"metabolite ${mp_txt} production "
. "stops completely "
. "because the merge reaction requires input from both branches",
);
my $pD_correct = $pD_choices[0];
for my $i (reverse 1 .. $#pD_choices) {
my $j = $local_random->random(0, $i, 1);
@pD_choices[$i, $j] = @pD_choices[$j, $i];
}
$rbD = RadioButtons(
[[@pD_choices]], $pD_correct,
labels => 'ABC', displayLabels => 1,
separator => '',
);
$solD = "When E${focus_enzyme} is inactivated, the "
. "${focus_name} input branch can no longer supply substrate for "
. "the merge. The ${other_name} branch alone must supply all the "
. "input to produce ${mp_txt}. Because the merge reaction requires "
. "both substrates (no rerouting is possible), ${mp_txt} production "
. "decreases but does not stop entirely, since the ${other_name} "
. "branch still provides some input.";
# ============================================
# 2l) Part E: Feed-forward coordination (advanced, MC)
# ============================================
$qE = "In many converging pathways, each branch's end product activates "
. "the committed step of the other branch (feed-forward "
. "cross-activation). If ${focus_end_txt} activates "
. "E${other_enzyme}, what problem does this "
. "regulatory mechanism solve?";
my @pE_choices = (
"it matches production of both substrates required for the "
. "merge reaction; when one branch increases output, it stimulates "
. "the other branch to keep pace",
"it provides a backup pathway if one branch fails, ensuring "
. "${trunk_end_txt} is still produced",
"it inhibits the ${other_name} branch to prevent overproduction "
. "of ${other_end_txt}",
"it has no functional advantage; it is an evolutionary artifact "
. "with no effect on pathway flux",
);
my $pE_correct = $pE_choices[0];
for my $i (reverse 1 .. $#pE_choices) {
my $j = $local_random->random(0, $i, 1);
@pE_choices[$i, $j] = @pE_choices[$j, $i];
}
$rbE = RadioButtons(
[[@pE_choices]], $pE_correct,
labels => 'ABC', displayLabels => 1,
separator => '',
);
$solE = "Feed-forward cross-activation solves the stoichiometric "
. "coordination problem in converging pathways. The merge reaction "
. "requires both ${focus_end_txt} and ${other_end_txt} as substrates. "
. "When the ${focus_name} branch produces more ${focus_end_txt}, "
. "that excess activates E${other_enzyme}, stimulating "
. "the ${other_name} branch to increase ${other_end_txt} production "
. "to match. This ensures balanced supply of both substrates for "
. "the merge step (Tymoczko et al., Biochemistry: A Short Course).";
# ============================================
# 3) Statement (PGML)
# ============================================
BEGIN_PGML
*Negative Feedback in a Converging Metabolic Pathway*
A series of enzymes catalyze reactions involving the metabolites in the merging metabolic pathway shown below. Two independent input branches converge into a shared trunk pathway. The ellipsis (...) indicates that additional downstream steps are not shown.
[$diagram]*
---
*Part A: Identify the Feed-Forward Activators*
[$qA]*
[_]{$cbA}
---
*Part B: Identify the Cross-Activation Targets*
[$qB]*
[_]{$cbB}
---
*Part C: Perturbation Reasoning*
[$qC]*
[_]{$rbC}
---
*Part D: Blocked Input Branch*
[$qD]*
[_]{$rbD}
---
*Part E: Feed-Forward Coordination (Advanced)*
[$qE]*
[_]{$rbE}
END_PGML
# ----------------------------
# 4) Hint
# ----------------------------
BEGIN_PGML_HINT
*Part A:* Look at the regulatory signals in the diagram. Which metabolites send positive signals across branches?
*Part B:* Follow the positive regulatory arrows. Where do they point?
*Part C:* If one metabolite increases, trace its regulatory arrows to predict what changes downstream.
*Part D:* The merge reaction requires both substrates. What happens if one source is removed?
*Part E:* Consider what would happen without this coordination. What problem would arise at the merge step?
END_PGML_HINT
# ----------------------------
# 5) Solution
# ----------------------------
BEGIN_PGML_SOLUTION
*Part A:* [$solA]*
*Part B:* [$solB]*
*Part C:* [$solC]*
*Part D:* [$solD]*
*Part E:* [$solE]*
END_PGML_SOLUTION
ENDDOCUMENT();